{"1": {"fulltext": "", "height": "4527", "width": "2787", "jp2-path": "introductiont00olms_0001.jp2"}, "2": {"fulltext": "", "height": "4448", "width": "2736", "jp2-path": "introductiont00olms_0002.jp2"}, "3": {"fulltext": "", "height": "4448", "width": "2736", "jp2-path": "introductiont00olms_0003.jp2"}, "4": {"fulltext": "", "height": "4331", "width": "2387", "jp2-path": "introductiont00olms_0004.jp2"}, "5": {"fulltext": "", "height": "4331", "width": "2387", "jp2-path": "introductiont00olms_0005.jp2"}, "6": {"fulltext": "", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0006.jp2"}, "7": {"fulltext": "", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0007.jp2"}, "8": {"fulltext": "Tif/.l\\nJ?iQ_ 2 .tins A. S.J iintiersm\\nX. Telescopic -7zew- o\u00c2\u00a3 -fke itijl Mx on.. S.TeLescoprc vi.-w of Saturn ..is xiug*.\\ncLo of a^gmt of the Moon mesa? cp^iaili-atiLL p 4. do of Jiwttpr NTooois.", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0008.jp2"}, "9": {"fulltext": "AN\\nINTRODUCTION\\nTO\\nASTRONOMY\\nDESIGNED AS A\\nTEXT-BOOK\\nFOR THE USE OF\\nSTUDENTS IS COLLEGE.\\nBY\\nDEOTSON OLMSTED, LL.D.,\\nPROFESSOR OP ASTRONOMY IN TALE COLLEGE,\\nAND\\nE. S. SNELL, LL.D.,\\nPROFESSOR OP MATHEMATICS IN AMHERST COLLEGE.\\nTHIRD STEREOTYPE EDITION\\nCarefully revised, with additions.\\nNEW YORK:\\nCOLLINS BROTHER,\\n414 BROADWAY.\\nV", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0011.jp2"}, "10": {"fulltext": "Q3*\\n3\\nJLatared according to Act of Congress, in th^, yet- la-Mt\\nBy DENISON OLMSTED,\\nin tne Clerk s Office of the District Court of Cot lectiofflt\\nRevised Edition.\\nEntered according to Act of Congress, in the year 18 I,\\nBy JULIA M. OLMSTED,\\nFor the Children of Demson Olmsted, deceased,\\nLs 3he Clerk s Office of the District Court of the District of Ckmasettaftg\\nThibd Stereotype Edition.\\nEnteied according to Act of Congress, in the year 1866,\\nBy JULIA M. OLMSTED,\\nFor the Children of Demson Olmsted, deceased,\\nLi iko Clark s Office of the District Court jf the Dfcfcr? at Coa eetlMk\\nThird Stereotype Edition.\\nCarefully revised, with, additions;\\nCopyright, 1883,\\nBy JULIA M. OLMSTED.", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0012.jp2"}, "11": {"fulltext": "PREFACE TO THE EDITION OF 1883.\\nThe late discoveries made in Astronomy, principally by\\nthe aid of the spectroscope, require that something be added to\\nthe descriptive parte of this work. In the present edition,,\\ntherefore, information of this nature, accompanied with illus-\\ntrations, is given in an Appendix, with references to and from\\nthe corresponding articles in the text.\\nThe mean equatorial Horizontal Parallax of the Sun, adopted\\nfrom Professor Newcomb s Investigation of the Distance of\\nthe Sun and the Elements which depend on it, is 8 848. This\\nnumber is founded upon a discussion and combination (with\\ntheir relative weights) of the results given by all the different\\nmethods of obtaining the parallax, and therefore is as near an\\napproximation to the truth as can be made at present. The\\ndistances and magnitudes throughout the work are reduced to\\nconform to this value.\\nThis edition contains the latest emendations of Professor\\nSnell and also various numerical corrections, in accordance\\nwith the best authorities, for which the Publishers are indebted\\nto Professor Selden J. Coffin, Lafayette College.\\nProfessor Coffin has also added to Art.. 264, Appendix M,\\nand has enlarged and thoroughly revised Tables II, IV,\\nand V.\\nAugust, 1883.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0013.jp2"}, "12": {"fulltext": "CONTENTS\\nCHAPTER I.\\nPA\u00c2\u00ab\u00c2\u00bb\\nAstronomy.\u00e2\u0080\u0094 Its subject. Globular form of the earth proved.\u00e2\u0080\u0094 Modes of\\nmeasuring the earth. The terrestrial equator. The horizon and seconda-\\nries. The celestial equator. The ecliptic. The diurnal motion. Its phe-\\nnomena. Problems on the globes 1-14\\nCHAPTER II.\\nParallax. Diurnal parallax.\u00e2\u0080\u0094 Its variation.\u00e2\u0080\u0094 To find the parallax of the moon.\\nAtmospheric refraction. Illumination of the sky. Twilight 15-28\\nCHAPTER III.\\nThe observatory. The transit-instrument. The astronomical clock. Measur-\\ning right ascension. The mural circle. Measuring declination. Altitude\\nand azimuth instruments.\u00e2\u0080\u0094 The sextant. Spherical problems 24-3$\\nCHAPTER IV.\\nObservations of the sun s place. The ecliptic and zodiac. The annual mo-\\ntion. The change of seasons. Arrangement of heat and cold. Form of the\\nearth s orbit. Mode of determining it 88-47\\nCHAPTER V.\\nThe sidereal and solar day. Mean and apparent solar time. Reasons why\\nsolar days are unequal. The equation of time. The calendar 47-54\\nCHAPTER VI.\\nProjectile, centripetal, and centrifugal forces. Laws of centrifugal force. Its\\neffects on the earth. Loss of weight. Spheroidal form. Proofs of diurnal\\nmotion 54-63\\nCHAPTER VII.\\nThe sun. Its form. Its distance. Its dimansions. Its rotation. Solar spots\\n\u00e2\u0080\u0094Theory of spots. Condition of the sun s surface. The zodiacal light 62 -68", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0014.jp2"}, "13": {"fulltext": "CONTENTS.\\nCHAPTER VIII.\\nPAGB\\nKepler s laws, Law of areas proved. Law of gravity proved. Its prevalence\\nthroughout the system. The paths of projectiles. Effect of an impulse on\\none body of a system 69-8Q\\nCHAPTER IX.\\nPrecession of equinoxes. Consequent motion of the poles. Cause. Compo-\\nsition of rotations. The tropical and sidereal years. Nutation. Aber-\\nration of light. Velocity of light discovered. Advance of apsides. Its\\ncause. How to find the sun s true place 80-88\\nCHAPTER X.\\nThe moon. Its distance and size. Its motion round the earth. Its orbit.\\nLibrations. Its path about the sun. Its phases. The harvest moon.\\nThe moon s surface. Measurement of its mountains. Appearance of the\\nearth from the moon 88-102\\nCHAPTER XL\\nThe moon s motion disturbed by the sun. Gravity to the earth diminished.\\nEquations for finding the moon s place. Equation of the center. Evec-\\ntion. Variation. Annual equation. Advance of apsides. Eetrogradation\\nof nodes. Periodical and secular equations 102-109\\nCHAPTER XII.\\nEclipses. Their cause. Eclipse months. The earth s shadow. Its dimen-\\nsions computed. To find beginning, middle, and end of a lunar eclipse.\\nEclipse of the sun. Dimensions of the moon s shadow. Its velocity over\\nthe earth. The Saros. Phenomena of a solar eclipse 109-124\\nCHAPTER XIII.\\n(ftethods of determining longitude. By the chronometer. By eclipses. By\\nthe lunar method. By the telegraph. Change of days in going round the\\nearth 125-1 29\\nCHAPTER XIV.\\nTides. Form of equilibrium under the action of the moon. Joint action of\\nsun and moon. Diurnal inequalities. Effect of coasts. Tides in seas and\\nlakes 180-185\\nCHAPTER XV.\\nPlanets grouped. Distances from the sun. Revolutions. Dimensions.\\nMasses and densities. Mercury. Its motions. Its phases. Its transits.\\nVenus. Its transits. Parallax of the sun found. Mars. Its motions 135-151", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0015.jp2"}, "14": {"fulltext": "CONTENTS.\\nCHAPTER XVI.\\nPA6S\\nThe planetoids. Jupiter. Its belts. Its satellites. Their eclipses and oo-\\ncultations. The velocity of light found by them. Saturn. Its rings.\\nTheir disappearances. The satellites of Saturn. Uranus. Its satellites.\\nNeptune. Its discovery 152\u00e2\u0080\u0094 Kit\\nCHAPTER XVII.\\nMoments of a planetary orbit. Method of finding the first. The second.\\nThe third. The fourth. The fifth and sixth. The masses of the planets\\nfound. Perturbations. In the positions of orbits. In their forms.\u00e2\u0080\u0094 Sta-\\nbility of the system. Relations of the planets 165-180\\nCHAPTER XVIII.\\nComets. Their number. Effects of eccentricity of orbit, Dimensions of\\ncomets. Their masses. How to find their orbits. Halley s comet.\\nComets of short period. A resisting medium. Remarkable comets.\\nShooting stars. Meteoric showers. Aerolites 180-194\\nCHAPTER XIX.\\nThe stellar universe. Classifications of stars. Constellations. Annual par-\\nallax. Stars whose distance is known. Nature of fixed stars. Proper\\nmotions. Double stars. Binary stars. Their orbits. Their masses.\u00e2\u0080\u0094\\nPeriodic stars. Clusters. Nebulae. The galaxy. The Nebular hypothe\\nsis 194-218\\nAppendix A to M 214-224\\nTables I.\u00e2\u0080\u0094 The Calendar 226-227\\nII.\u00e2\u0080\u0094 Elements of the Planets 228\\nIII.\u00e2\u0080\u0094 Elements of the Satellites 229\\nIV.\u00e2\u0080\u0094 Mean Places of Principal Stars 230\\nY.\u00e2\u0080\u0094 Planetoids i 231-233\\nPlates.\u00e2\u0080\u0094 Spectroscope 225\\nChronograph 234\\nComet of 1843.\\nComet of 1858.\u00e2\u0080\u0094 Nebulae.\\nPart of Galaxy.\u00e2\u0080\u0094 Double Stars.\\nClusters.\u00e2\u0080\u0094 Nebulae.", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0016.jp2"}, "15": {"fulltext": "ASTRONOMY.\\nCHAPTEE I.\\nGENERAL FORM AND DIMENSIONS OF THE EARTH. THE\\nDIURNAL MOTION. ARTIFICIAL GLOBES.\\n1. General definitions. Astronomy is the science which\\ntreats of the heavenly bodies that is, of the sun, the planets\\nand their satellites, the comets, and the fixed stars.\\nThe sun, planets, satellites, and comets constitute the solar\\nsystem, which is so called because the sun is the principal body\\nbelonging to it, and controls the movements of all the others.\\nThe fixed stars are the bodies situated at vast distances out\\nside of the solar system, and which, on account of that distance,\\nexhibit little or no change of position with respect to each\\nother.\\n2. The Copernican system. This name is given, in honor of\\nCopernicus, to the science of astronomy as now established by\\ndemonstration, in distinction from the erroneous systems of the\\nancients. It explains the diurnal and annual motions of the\\nheavens, by supposing the earth to rotate each day on its axis,\\nand to revolve once a year around the sun.\\n3. The globular form of the earth. That the earth is nearly\\nif not exactly a sphere, is indicated in several ways.\\n1. It is one of the planets. And, as we see the other planets\\nto be nearly spherical, we reason from analogy that the earth is\\n6pherical also.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0017.jp2"}, "16": {"fulltext": "2 DIP OF THE HORIZON.\\n2. Iii a lunar eclipse, whichever side is turned toward the\\nmoon, the outline of its shadow, projected on that lody, is\\nalways circular.\\n3. Its convexity, by which it wholly or partially conceals\\ndistant objects, as a lighthouse or a ship at sea, appears to be\\nequally great on all parts of the ocean.\\n4. An arc of a given number of miles, measured on any part\\nof the earth, is found always to subtend an angle of nearly\\nequal size at the center showing that the curvature is every-\\nwhere nearly the same.\\n5. The depression, or dip of the horizon, is equally great at\\nevery place, and on every side of the observer, provided his\\nelevation above the ocean level is the same. This will be un-\\nderstood by the next article.\\nFig.l.\\n4. Dip of the horizon. If the eye were at A (Fig. 1) on\\nthe surface of the earth, the vault of the heavens would be lim-\\nited by a plane touching the earth at\\nA, and would therefore be just a hemi-\\nsphere. But if the eye is elevated, as\\nto O, and tangent lines are drawn from\\nthat point to the earth on every side,\\nthen more than a hemisphere of the\\nsky is visible. Let ZC be the direc-\\ntion of a plumb-line, and let HOR\\nrepresent a plane perpendicular to it\\nthen there would be a celestial hemi-\\nsphere in view above this plane, and\\nthe remotest visible points on the earth\\nwould be depressed below the plane by\\nthe angle HOD or ROE. This angle\\nis called the dip of the horizon. If AO is a given height,\\nit is found that the angle HOD is sensibly equal on whatever\\nside of the station, or on whatever part of the earth, the\\nmeasurement is made. It follows from this that the earth is\\nvery nearly a sphere.\\nAt the height of 100 feet, the depression is about 10 and\\nvaries nearly as the square root of the height.\\nThe word down expresses the direction in which a plumb-", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0018.jp2"}, "17": {"fulltext": "DIMENSIONS OF THE EARTH. 3\\nline hangs, or a body falls that is, toward the center of the\\nearth. Hence, on different parts of the earth, down denotes\\nall possible directions. So up, or from the center, is in every\\ndirection and the direction which is down at one place, is up\\nat a place on the opposite side of the earth.\\nFig. 2.\\n5. Dimensions of the earth. The semi-diameter of the\\nearth may be approximately fonnd by measuring the height oi\\nthe station AO (Fig. 1), and the\\nlength of the tangent line OD. If O\\nwere the summit of a mountain, then\\nD would be the most distant point\\nfrom which it could be discerned. In\\nFig. 2, suppose that the height of the\\nmountain BD, and the distance to the\\npoint where it is just seen in the hori-\\nzon AD, have been measured. Let\\nBD A, and AD d, and the radius,\\nAC or BO x. Then a? 2 d 2 ={x hy\\n\u00e2\u0096\u00a0x* 2 hx h\\\\ Hence, 2 hx d 2 h% and x\\n2A\\nThus, the semi-diameter of the earth is found in terms of k\\nand d.\\nThe magnitude of the earth may be more accurately found,\\nby measuring the arc of a meridian. Let a line be carefully\\nmeasured due north on the earth s surface, and the correspond-\\ning difference of latitude be observed, as indicated by the\\nchange in the elevation of the stars. Then, the surveyed line\\nis the same part of the earth s circumference, which the differ-\\nence of latitude is of 360\u00c2\u00b0. Thus, if the arc is 1\u00c2\u00b0 30 r its length\\nis found to be about 103.5 miles. Hence,\\n1\u00c2\u00b0 30 360\u00c2\u00b0 103.5 24,840;\\nwhich is nearly the number of miles in the circumference oi\\nthe earth. By a comparison of the most accurate measure\\nments, it is ascertained that\\nThe circumference of the earth 24,857 miles.\\nThe diameter (24,857 -f- 3.14159+) 7,912.4 miles.\\nOne degree of the circumference 365,000 feet.\\nOne second about 100 feet.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0019.jp2"}, "18": {"fulltext": "4 SECONDARIES OF THE EQUATOR.\\n6. Inequalities of surface. Although the surface of the\\nearth is uneven, and there are high mountains and deep valleys\\nin many parts of it, yet these are very minute compared with\\nthe magnitude of the entire earth so that the spherical form\\nis not disturbed by their existence. Mountains, four or five\\nmiles high on the earth, are relatively no more than are the\\nparticles of dust which adhere to a globe one foot in diameter.\\nThin writing-paper, pasted upon such a globe in the form ot\\nthe continents, would be sufficiently thick to represent their\\ngeneral elevation above the oceans.\\n7. The diurnal rotation. The earth revolves continually\\nfrom west to east, on an imaginary line drawn through its cen-\\nter, called the earth? s axis. The time occupied in completing a\\nrevolution is called a day, which is divided into twenty-four\\nhours. A great circle of the earth, perpendicular to the axis,\\nis called the equator. In the diurnal rotation, every particle of\\nthe earth describes a circle, whose plane is either parallel to\\nthe equator or coincident with it. The extremities of the axis\\nare called respectively the north and south poles.\\n8. Secondaries of the equator. All great circles passing\\nthrough the poles, and therefore perpendicular to the equator,\\nare called meridians. Such a circle may be supposed to pass\\nthrough any place whatever on the earth, and is called the me-\\nridian of that place. As all great circles of a sphere which are\\nperpendicular to a given great circle, are called its secondaries^\\nthe meridians are secondaries of the equator.\\nThe latitude of a place is its distance north or south from the\\nequator, measured on the meridian of that place, in degrees,\\nminutes, and seconds. Parallels of latitude are small circles\\nof the earth, parallel to the equator.\\nThe longitude of a place is the distance of its meridian in\\ndegrees, minutes, and seconds, east or west from ^ome standard\\nmeridian, as that of the observatory of Greenwich. The people\\nof different nations usually reckon longitude from s^Oie import-\\nant observatory of their own country. Thus, the X lench reckon\\nfrom Paris, and the Americans from Washington. Any place\\non the earth is determined by giving its latitude and longitude", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0020.jp2"}, "19": {"fulltext": "THE HORIZON AND ITS SECONDARIES. 5\\n9. The celestial sphere. The earth is called the terrestrial\\nsphere. The celestial sphere is that apparent vault, called the\\nsky, which surrounds the earth on every side, and to which all\\nthe heavenly bodies seem to be attached. The center of the\\nearth is regarded as the center of the celestial sphere also. Bat\\nthe distance of nearly all the heavenly bodies is so immense,\\nthat it is immaterial from what point of the earth they are\\nviewed. Hence, for most purposes of astronomy, the eye of\\nthe observer may be considered as the center of the celestial\\nsphere.\\n10. The horizon and its secondaries. If the plumb-line\\n(usually called the vertical), at any place on the earth, is sup-\\nposed to be extended till it intersects the celestial sphere, it\\nmarks the zenith above the place, and the nadir below it.\\nAnd a plane passed through the center of the earth, perpendic-\\nular to the vertical, is called the rational horizon of that place.\\nThis is a great circle of the celestial sphere, and divides it into\\n-upper and lower hemispheres. The sensible horizon is parallel\\nto the rational horizon, and passes through the place on the\\nearth s surface. The planes of these two horizons are therefore\\nnear 4,000 miles apart but so great is the distance of the\\nheavenly bodies, that the two planes seem to unite in the same\\ngreat circle of the heavens.\\nIf the observer is at all elevated above the earth s surface,\\nthe boundary line between sky and water is a little lower than\\nthe horizon, so that somewhat more than half of the celestial\\nsphere is in view (Art. 4). The secondaries of the horizon\\nintersect each other in the vertical line, and are called vertical\\ncircles. One of them is the meridian of the place. The inter-\\nsections of the meridian and horizon are the north and south\\npoints of compass. The vertical circle at right angles to the\\nmeridian is called the prime vertical. This intersects the hori-\\nzon in the points called east and west.\\nThe altitude of a heavenly body is its elevation above the\\nhorizon, measured on the vertical circle passing through the\\nbody. The zenith distance of a body is the distance between\\nit and the zenith, and is therefore the complement of its\\nAltitude.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0021.jp2"}, "20": {"fulltext": "6 CELESTIAL EQUATOR.\\nThe azimuth of a heavenly body is an arc of the horizon\\nmeasured from the meridian to the vertical circle, which passes\\nthrough the body. The amplitude is measured from the verti\\ncal circle passing through the body to the prime vertical, and\\nis therefore the complement of the azimuth. The altitude, or\\nzenith distance of a heavenly body, along with its azimuth or\\namplitude, determines its place in the visible heavens.\\n1 1 The celestial equator and its secondaries. If the axis on\\nwhich the earth revolves is produced to the heavens, it becomes\\nthe axis of the celestial sphere, and marks the north and south\\npoles of that sphere. The north pole is at present in the con-\\nstellation of Ursa Minor. If the plane of the equator be ex-\\ntended in like manner, it becomes the celestial equator. The\\nsecondaries to this circle are called meridians, as on the earth*\\nThey are also called hour-circles, because the arcs of the\\nequator intercepted between them are used as measures of\\ntime.\\nFig. 3.\\nZD\\nLet n (Fig. 3) represent the north pole of the earth, s its\\nbo nth pole, eqthe equator (projected in a straight line), o a given", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0022.jp2"}, "21": {"fulltext": "THE ECLIPTIC. 7\\nplace whose north latitude is eo. Then N, S, are the poles of\\nthe celestial sphere, EQ is the celestial equator, Z is the zenith\\nof the place o, R is its nadir, and HO its rational horizon.\\noesqn is the terrestrial meridian of the same place, and\\nZESQK is its celestial meridian, or hour-circle.\\n1 2. The ecliptic. Besides the equator, there is an import-\\nant circle of the celestial sphere, called the ecliptic. It is that\\nin which the sun appears to make its annual circuit around the\\nheavens. It is inclined to the equator at an angle of nearly\\n23J\u00c2\u00b0, crossing it in two opposite points, called the equinoctial\\npoints, or equinoxes. The word equinoxes is used also to\\nexpress the times at which the sun crosses the equator, because\\nat those times the nights are equal to the days. The vernal\\nequinox is the time when the sun passes the equator from south\\nto north, as it occurs in the spring, about March 20th. The\\nautumnal equinox occurs on or near September 22d, when the\\nsun returns to the south of the equator.\\nThe solstitial points, or solstices, are those points of the\\necliptic, which are furthest north or south from the equator,\\nsituated therefore midway between the equinoxes. They are\\nso named, because there the sun stops in his advance north-\\nward or southward, and begins to return. The summer solstice\\nis the point where, and also the time when the sun is furthest\\nnorth, about the 21st of June. He passes the winter solstice on\\nor near the 21st of December.\\nThe equinoctial colure is that secondary to the equator\\nwhich passes through the equinoxes. The solstitial colure is\\nthat which passes through the solstices. They are therefore at\\nright angles to each other, and the latter is a secondary to the\\necliptic, as well as to the equator.\\n13. Signs of the ecliptic\u00e2\u0080\u0094 The ecliptic is divided into\\n12 equal parts of 30\u00c2\u00b0 each, called signs, which, beginning at\\nthe vernal equinox, succeed each other eastward, in the follow\\ning order", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0023.jp2"}, "22": {"fulltext": "DIUKNAL MOTION OF THE HEAVENS.\\nNorthern.\\nSouthern.\\n1. Aries\\nf\\n7. Libra\\n=Cb\\n2. Taurus\\n8\\n8. Scorpio\\nm\\n3. Gemini\\nn\\n9. Sagittarius\\n4. Cancer\\n10. Capricornus\\nV3\\n5. Leo\\n$1\\n11. Aquarius\\nAW\\n6. Yirgo\\nT02.\\n12. Pisces\\nX\\nThe vernal equinox being at the first point of Aries, the sum\\nmer solstice is at the first of Cancer, the autumnal equinox at\\nthe first of Libra, and the winter solstice at the first of Capricorn.\\n14. R ght ascension and declination. The right ascen-\\nsion of a heavenly body is the angular distance of its meridian\\nfrom the vernal equinox, measured eastward on the equator.\\nThe declination of a body is its angular distance north or south\\nfrom the equator, measured on the meridian of the body.\\nThe equator is the plane of reference for right ascension and\\ndeclination on the celestial sphere, as it is for latitude and\\nlongitude on the terrestrial. But terrestrial longitude is reck-\\noned both east and west, while right ascension is reckoned only\\nto the east.\\n15. Celestial longitude and latitude. On the celestial\\nsphere, longitude and latitude are referred to the ecliptic, not\\nto the equator. Suppose a secondary to the ecliptic to pass\\nthrough a heavenly body the distance of the body from the\\necliptic, measured on the secondary, is its latitude and the dis-\\ntance of this secondary from the vernal equinox, measured\\neastward on the ecliptic, is its longitude.\\nEight ascension and longitude are reckoned only eastward,\\nfrom 0\u00c2\u00b0 to 360\u00c2\u00b0, the first on the equator, the other on the\\necliptic.\\n1 6. Apparent diurnal motion of the heavens. As the earth\\nrevolves from west to east on the axis ns, an observer, not\\nbeing conscious of this motion, sees the heavenly bodies appa-\\nrently revolving in the opposite direction that is, from east to\\nwest, about the axis NS. The sun, moon, and every planet,", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0024.jp2"}, "23": {"fulltext": "comet, and star, is observed to pass over from the eastern part\\nof the sky toward the western, with a regular motion, reap-\\npearing again in the east, after the lapse of about one day, in\\nthe same, or nearly the same place. The fixed stars describe\\ncircles, which are exactly parallel to the equator, and in pre-\\ncisely the same length of time. But the other bodies vary\\nsomewhat in their paths, and the periods of describing them,\\nthus indicating that they are affected by other motions besides\\nthe diurnal rotation.\\n17. Rising, setting, and culmination. In Fig. 3, AB,\\nDO, FG, etc., drawn parallel to EQ, represent the diurnal\\ncircles of stars, projected in straight lines. Some of these\\ncircles intersect the horizon HO. These intersections are the\\npoints of rising or setting. Thus, a star describing the circle\\nGF, rises in the northeast quartei, and sets in the northwest,\\nat points which are both represented by r. The star, whose\\ndiurnal circle is IK, rises in the southeast, and sets in the south-\\nwest, at t. A star on the equator rises exactly in the east, and\\nsets in the west, at the point G.\\nThe points, in which these circles cut the meridian, are\\ncalled the points of culmination. Thus, the star on FG makes\\nits upper culmination at F, arid its lower one at G. On AB,\\nboth the upper and lower culminations are above the horizon\\non MP, they are both below. If both culminations of a star are\\nabove the horizon, it is always in view; if both below, it never\\ncomes in sight. The number of stars which do not rise and set,\\ndepends on the position of the celestial poles in relation to the\\nhorizon that is, on the latitude of the place.\\nBy the culmination of a body, in the ordinary use of the\\nword, is meant its upper culmination.\\n18. Relations of the horizon to the diurnal circles.\\nEvery change of position on the earth changes the horizon. If\\nan observer moves eastward, all the heavenly bodies which rise\\nand set, rise earlier, and also culminate and set earlier. If he\\nmoves westward, they rise, culminate, and set later. If he\\nmoves toward the nearer pole of the earth, the corresponding\\npole of the celestial sphere becomes more elevated, and the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0025.jp2"}, "24": {"fulltext": "10 THE PARALLEL SPHERE.\\nother more depressed and the contrary, if he moves from the\\nnearer pole that is, toward the equator. In all north latitudes,\\nthe north pole is elevated, and the south pole depressed and\\nthe reverse in south latitudes. And the elevation of one pole,\\nand the depression of the other, equals the latitude. For\\n(Fig. 3) NO, the elevation of one pole (=HS, the depression 01\\nthe other), equals EZ, since each is the complement of ZN\\nBut EZ= 9, the latitude, because they subtend the same angl\\natC.\\nThe elevation of the celestial equator equals the complement\\nof latitude. For EH is the complement of EZ, which equals\\neo, the latitude. Hence, the angle by which all the circles of\\ndiurnal motion are inclined to the plane of the horizon, equals\\nthe complement of latitude, since they are parallel to the\\nequator.\\nOn account of this change of inclination between the horizon\\nand the diurnal circles, the aspect of the diurnal rotation is\\nvery different in different parts of the earth.\\n19. Tht right sphere. This name is given to those posi-\\ntions, in which the diurnal circles cut the horizon at right\\nangles. All points of the equator are so situated. As the\\nlatitude is zero, the poles, having no elevation or depression\\n(Art. 18), are both in the horizon the celestial equator passes\\nthrough the zenith, thus coinciding with the prime vertical;\\nand all the paths of daily motion, being parallel to the equator,\\nare perpendicular to the horizon. Every heavenly body, unless\\nsituated exactly at one of the poles, rises and sets during each\\nrevolution, and continues above the horizon just as long as it\\nremains below it. If a star rises in the east, it sets in the west,\\nand culminates in the zenith and nadir.\\n20. The parallel sphere. This term expresses the appear-\\nance of the heavens at those points of the earth where the\\ncircles of daily rotation are parallel to the horizon. This aspect\\ncan be presented only at the poles. For, at those points, the\\nlatitude being 90\u00c2\u00b0. one pole must be elevated 90\u00c2\u00b0 that is, to the\\nzenith and the other depressed 90\u00c2\u00b0, or to the nadir. Hence.\\nU?e diurnal circles, being perpendicular to the axis, must Iks", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0026.jp2"}, "25": {"fulltext": "ARTIFICIAL GLOBES. 11\\nhorizontal, and the equator must coincide with the horizon.\\nEvery star in view passes around the sky, maintaining the\\nsame elevation at every point of its path. JSTo one of the iixed\\nstars ever rises or sets, and every point of a diurnal circle may\\nbe regarded as a point of culmination, since it is on a meridian\\npassing through the observer s place.\\nAt the north pole, that half the year in which the sun is\\nnorth of the equator, is uninterrupted day during the other\\nhalf, the sun being south of the equator, it is constant night.\\nIn the right sphere, the whole sky is seen, and every part of\\nit just half the time in the parallel sphere, only one-half the\\nsky is ever seen, but it is seen the whole time.\\n2 I The oblique sphere. At all latitudes, except 0\u00c2\u00b0 and\\n90\u00c2\u00b0, the circles of daily motion are oblique to the horizon, since\\nthey incline at an angle equal to the complement of the lati-\\ntude. Thus, at latitude 42\u00c2\u00b0 N., the celestial equator is elevated\\n48\u00c2\u00b0 above the southern horizon, and all the diurnal circles have\\nthe same inclination, as shown in Fig. 3. The circle OD,\\nwhose distance from the elevated pole equals its elevation, just\\ntouches the horizon at the lower culmination, and is the limit\\nof that part of the sky which is always in view. This is called\\nthe circle of perpetual apparition. The circle HL, at the same\\ndistance from the depressed pole, also touches the horizon, and\\nis called the circle oft. perpetual occultatio?i, since it limits that\\npart of the sky which is always concealed.\\nThe horizon HO, bisects the equator EQ. Hence, a body\\non the equator is as long above the horizon as below it, in every\\npart of the earth. But all bodies between the equator and the\\nelevated pole are longer above the horizon than below, while\\non the opposite side they are longer below than above.\\n22. Artificial globes. They are of two kinds, terrestrial\\nand celestial. The terrestrial globe is a miniature representa-\\ntion of the earth, having also the equator and several meridians\\nand parallels of latitude traced upon it. The celestial globe\\nexhibits the principal fixed stars in their relations to each\\nother, and to the equator and ecliptic.\\nThe artificial globe is suspended in a strong brass ring by an", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0027.jp2"}, "26": {"fulltext": "Cl PROBLEMS ON THE GLOBES.\\naxis passing through the north and south poles, Dn which it is\\nfree to revolve. This ring represents the meridian of any place,\\nand is supported vertically within a horizontal wooden ring\\nwhich stands upon a tripod. The wooden ring represents the\\nhorizon. The brass ring may be slid around in its own plane,\\nso as to elevate or depress either pole to any angle with the\\nhorizon. It is graduated from the equator each way to the\\npoles, for measuring latitude and declination while the horizon\\nring has near its inner edge two graduated circles, one for\\nazimuth, and the other for amplitude. On this ring also, for\\nconvenient reference, are delineated the signs of the ecliptic,\\nand the sun s place in it for every day of the year.\\nAround the north pole is a small circle, marked with the\\nhours of the day and at the same pole, a brass index is attached\\nto the meridian, which can be set at any hour of the circle.\\nThe quadrant of altitude is a flexible strip of brass, graduated\\ninto 90 parts, each equal to a degree of the globe. This can\\nbe used for measuring angular distances in any direction on the\\nsphere and when applied to a vertical circle of the celestial\\nglobe, it determines the altitude, or zenith distance of a heav-\\nenly body.\\nTo adjust either globe for any place on the earth, elevate the\\ncorresponding pole to a height equal to the latitude. The axis\\nwill then form the proper angle with the horizon. And if the\\nglobe is turned (the celestial westward, or the terrestrial east-\\nward), the diurnal motion will be truly represented.\\n23. Problems on the terrestrial v\\n1. To And the latitude and longitude of a place.\\nTurn the globe so as to bring the place to the brass\\nmeridian then the degree and minute on the meridian\\nover the place shows its latitude, and the point of the\\nequator, under the meridian, shows its longitude.\\nExample. What are the latitude and longitude of\\nNew York?\\n2. To find a place by its given latitude and longitude.\\nFind the given longitude on the equator, and bring\\nit to the meridian; then under the meridian, at the\\ngiven latitude, will be found the required place.", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0028.jp2"}, "27": {"fulltext": "PROBLEMS ON THE GLOBES. 13\\nEx. What place is in latitude 39\u00c2\u00b0 2SL, and longitude\\n77\u00c2\u00b0 W.\\n3. To find the beaiing and distance of one place from\\nanother.\\nAdjust the globe for one of the places, and bring it\\nto the meridian screw the quadrant of altitude directly\\nover the place, aud bring its edge to the other place.\\nThen the azimuth will be the bearing of the second\\nplace from the first, and the number of degrees between\\nthem, multiplied by 69J, will give their distance apart\\nin miles.\\nEx. Find the bearing of New Orleans from New\\nYork, and the distance between them.\\n4. To find the difference of time at different places.\\nBring to the meridian the place which lies west of the\\nother, and set the hour-index at XII. Turn the globe\\nwestward, until the other place comes to the meridian,\\nand the index will show the hour at the second place\\nwhen it is noon at the first. The hour thus found ie\\nthe difference required.\\nEx. When it is noon at New York, what time is it\\nat London\\n5. The hour being given at any place, to find what hour\\nit is at any other place.\\nFind the difference of time between the two places,\\nas in (4) then, if the place, whose time is required, is\\neast of the other, add this difference to the given time\\nbut if west, subtract it.\\nEx. What time is it in Boston, when it is 2 p. m. in\\nParis\\n6. To find the antiscii, the perioeci, and the antipodes of a\\ngiven place.\\nBring the given place to the meridian then, under\\nthe meridian, in the opposite hemisphere, in the same\\ndegree of latitude, are found the antiscii. Set the\\nindex to XII., and turn the globe until the other XII.\\nis under the index then, the perioeci will be at the\\nsame point of the meridian as the given place was, and\\nthe antipodes will bo where the antiscr. wpra", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0029.jp2"}, "28": {"fulltext": "14 PROBLEMS ON THE GLOBES.\\nEx. Find the antiscii, the perioeci, and the antipodes\\nof Lake Superior.\\nTo the antiscii, the hour of the day is the same as at\\nthe given place, but the season is reversed. To the\\nperioeci, the season is the same, but the hour opposite.\\nTo the antipodes, both hour and season are opposite\\n24. Problems on the celestial globe.\\n1. To find the right ascension and declination of a heav\\nenly body.\\nBring the place of the body to the meridian then\\nthe point directly over it shows its declination and the\\npoint of the equator under the meridian, its right\\nascension.\\nEx. Find the right ascension and declination of a\\nLyras. Also, of the sun on the 3d of May.\\n2. To represent the appearance of the heavens at any time.\\nAdjust the globe for the place. (Art. 22.) On the\\nwooden horizon find the day of the month, and against\\nit is given the sun s place in the ecliptic. On the\\necliptic find the same sign and degree, and bring the\\npoint to the meridian. The globe then presents the\\npositions of the stars at noon. Set the hour-index at\\nXII., and turn the globe till the index points to the\\nrequired hour. The aspect of the heavens at that hour\\nis then represented.\\nEx. Required the aspect of the stars at Lat. 51\u00c2\u00b0, Dec.\\n5th, at 10 p. m.\\n3. To find the time of the rising and setting of any heav-\\nenly body, at a given place.\\nHaving adjusted for the latitude, bring the sun s\\nplace in the ecliptic to the meridian, and set the index\\nat XII. Turn the globe eastward, and then westward,\\ntill the given body meets the horizon, and the index\\nwill show the times of rising and setting.\\nThe times of the surfs rising and setting may be\\nfound in the same manner, on the terrestrial globe,\\nsince the ecliptic is usually represented on it.", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0030.jp2"}, "29": {"fulltext": "PARALLAX DEFINED. 15\\nMb. At what time does the sun rise and set on the\\n4th of July?\\nFind the time of the rising and setting of Arcturua\\non the 10th of November.\\ni. To find the altitude and azimuth of a star for a given\\nlatitude and time.\\nAdjust the globe for the aspect of the heavens (2)\\nscrew the quadrant of altitude to the zenith, and direct\\nit through the place of the star. Then, the arc between\\nthe star and the horizon is the altitude and the arc of\\nthe horizon between the quadrant of altitude and the\\nmeridian, is the azimuth.\\nEx. Find the altitude and azimuth of Sirius, Dec.\\n25th, at 9 p. m. Lat. 43\u00c2\u00b0.\\nft To find the angular distance between two stars.\\nLay the quadrant of altitude across the two stars, so\\nthat the zero shall fall on one of them then, the degree\\nat the other will show their distance from each other.\\nEx. Find the distance between Arcturus and a Lyrse.\\n6. To find the sun s meridian altitude for a given latitude\\nand day.\\nFind the sun s place, and bring it to the meridian.\\nThe degree over it will show its declination. If the\\ndeclination and latitude are both north or south, add\\nthe declination to the co-latitude if not, subtract it.\\nEx. Find the sun s meridian altitude at noon, Aug.\\n1st. Lat. 38\u00c2\u00b0 30 K\\nCHAPTER II.\\nPARALLAX. ATMOSPHERIC REFRACTION. TWILIGHT.\\n25. Parallax defined. When a person changes his place,\\nobjects about him in general appear in different directions from\\nhim. This change of direction is called parallax. If, for ex-\\nample, he moves north, an object, which was directly west or", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0031.jp2"}, "30": {"fulltext": "16\\nDIURNAL PARALLAX.\\nhim, is moved by parallax towards the southwest and an\\nobject which was east, now appears in the southeast quarter.\\nThe direction of every thing is more or less altered, except\\nthose objects which are in the line of his motion.\\n26. Diurnal parallax. While a person therefore travels\\nover the earth, or is carried about it by the diurnal rotation,\\nthe heavenly bodies mnst in the same way suffer some paral-\\nlactic change.\\nBy the true place of a heavenly body, is meant that which it\\nwould seem to occupy if viewed from the center of the earth.\\nAt the surface, therefore, it appears generally displaced from\\nits true position and this displacement is called the diurnal\\nparallax. Thus, the true place of the body M (Fig. 4.), is in\\nthe direction CK but at A it appears in the line AH and the\\nparallax is the angle AMC.\\nSo, the true place of M is Q,\\nits apparent place is P, and\\nthe parallax is AM C. But\\nthe body W appears at Z,\\nwhether viewed from A or C,\\nand the parallax in this case is\\nzero. Since the earth s radius,\\nin each instance, subtends the\\nangle of parallax, we have the\\nfollowing definition\\nThe diurnal parallax of a\\nbody is the angle at that body\\nsubtended by the semi-diameter of the earth.\\nFig. 4.\\n27. On what diurnal parallax depends. In the triangle\\nACM let AC=r, CM and the parallax, AM C=p. Let\\nthe zenith distance of the body, ZAM z then, the angle\\nCAM is the supplement of z. Hence,\\nsin^ sins r d:\\nr sin z\\nsmi ___\\nSince p is always very small, sinj? varies nearly as^? itsell", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0032.jp2"}, "31": {"fulltext": "PARALLAX OF THE MOON. 17\\nTherefore, regarding r as constant, p x \u00e2\u0080\u0094-7\u00e2\u0080\u0094. That is, The\\nparallax of a tody varies directly as the sine of its zenith\\ndistance, and inversely as its distance from the earth? s center,\\n28. Horizontal parallax. The largest diurnal parallax,\\nwhich a body can have, occurs when the body is seen in the\\nhorizon, as at M. It is then called horizontal parallax. From\\nthe horizon to the zenith, the parallax diminishes through all\\nvalues to zero.\\nIn the case of a given body, d is usually constant and if its\\nparallax, at a certain elevation, has been obtained, its horizontal\\nparallax is found by the variation, p oo sin z. At the horizon,\\ns 90\u00c2\u00b0, and sin z rad. If, when the zenith distance is 53\u00c2\u00b0,\\nthe moon s parallax is found by observation to be 45 then\\nsin 53\u00c2\u00b0 rad 45 56 21 which is its horizontal parallax.\\n29. To correct for parallax. The effect of parallax is to\\ncause a body to appear lower than its true place. Hence, the\\ntrue altitude of a body is obtained by adding the parallax to\\nits apparent altitude.\\nAs parallax is a depression on a vertical circle, then, if a\\nbody is on the meridian, the parallax affects its declination just\\nas much as its altitude, since the meridian is also a vertical bu\\nin other cases, the vertical circle being oblique to the equator\\nthe parallax can be resolved into two components, one of which,\\nparallel to the equator, is parallax in right ascension the other\\nperpendicular to the equator, is parallax in declination.\\n30. To find the parallax of the moon. Let A and B\\n(Fig. 5) be two stations on the same meridian, taken as far\\napart as possible. The latitude of each place being known, the\\narc AB that is, the angle ACB is known. When the moon\\ncrosses the meridian, let its zenith distance be observed at each\\nstation. The observer A sees the moon projected in the sky at\\nY, and the zenith distance is the angle ZAY, while that at B\\nis Z BY The supplements of these angles, MAC, MBC, are\\ntherefore known. In the isosceles triangle ABC, obtain the\\nangles A and B, and the side AB subtract the angles from", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0033.jp2"}, "32": {"fulltext": "18\\nATMOSPHEEIC REFRACTION.\\nFig. 5.\\nMAC and MBC respectively, then MBA, MAB are known,\\nwhich, with the side AB, will give AM and BM. Finally, in\\nthe triangle AMC, the angle A and sides including it will fur-\\nnish the angle AMC, which is the parallax sought for the\\nstation A, at the zenith\\ndistance ZAY. From\\nthis the horizontal paral-\\nlax can be obtained, as in\\nArt. 28.\\nThe horizontal paral-\\nlax of the moon is much\\ngreater than that of any\\nother heavenly body. Its\\nmean value is about 57\\nand is correctly repre-\\nsented by the angle\\nEMC, in Fig. 6.\\nThe above method has\\nalso been employed for\\ntwo or three of the\\nplanets, when they come near to the earth. But, with these\\nexceptions, all the heavenly bodies are so far from us, that their\\nhorizontal parallax is too small to be obtained in this way with\\nsufficient accuracy. The parallax of the sun is less than 9\\nthat of nearly all the planets is much smaller than this and as\\nto bodies outside of the solar system, they afford not the\\nslightest indication of any diurnal parallax.\\nE\\nFig. 6.\\nM\\n31. Atmospheric refraction. Before the true place of a\\nbody can be found by observation, a correction must also be\\napplied for the refraction of its light by the atmosphere. While\\nparallax depresses bodies below their true places, more or less\\naccording to their distance, refraction elevates them, the near\\nand the distant alike.\\nThe earth s atmosphere may be conceived to consist of an", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0034.jp2"}, "33": {"fulltext": "ATMOSPHERIC REFRACTION.\\n19\\nindefinite n amber of strata, bounded by spherical surfaces, as\\nAA, BB, etc. (Fig. 7), these strata being more dense according\\nas the j are nearer the earth. Light from a star S, entering the\\nair at a, is bent toward the perpendicular to its surface (which\\nFig. 7.\\nis the earth s radius produced to that point), and describes ab f\\ninstead of ax. For the same reason, it is again bent into ho,\\nand then into cO and therefore the star appears in the direc-\\ntion of cO produced, at S higher than its true place. The\\npath of the ray from a to O is in reality not a broken line, as\\nin the figure, but a curve, because the changes of density occur\\nat every point. A body at the zenith is not moved out of\\nplace, because its light strikes the surfaces perpendicularly.\\nThe refraction at the horizon is about 35 This is the greatest\\nof all, since the angle of incidence there is the greatest possible.\\nFrom the zenith to the horizon the refraction constantly in\\ncreases, slowly at great elevations, but very rapidly near the\\nhorizon, as shown in the following table.\\nElevation.\\nEefraction.\\nElevation.\\nEefraction.\\n90\u00c2\u00b0\\n0 0\\n20\u00c2\u00b0\\n2 37\\n80\\n10\\n10\\n5 16\\n60\\n33\\n5\\n9 47\\n45\\n58\\n2\\n18 09\\n40\\n1 09\\n1\\n24 25\\n30\\n1 40\\nU 54\\nThe true size of the largest angle of refraction is seen in", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0035.jp2"}, "34": {"fulltext": "20 METHODS OF MEASURING REFRACTION.\\nFig. 8. AB is a portion of the surface of the earth, ah the\\nsurface of the atmosphere, AC, BC portions of the radii of the\\nearth S is the true place of a star, S the place as elevated by\\nhorizontal refraction.\\nFig. 8.\\n32. Measurement of refraction, At latitudes greater\\nthan 45\u00c2\u00b0, stars which culminate in the zenith make their\\nlower culminations above the horizon. Such a star is observed\\nat both culminations, and its distance from the pole is measured\\nat each. These polar distances are really equal, but appa-\\nrently unequal, because below the pole the star is elevated by\\nrefraction, while at the zenith it is not displaced. The differ-\\nence of the apparent polar distances, therefore, gives the\\namount of refraction at the place of lower culmination.\\nThe refraction within several degrees of the zenith is so\\nslight, and its change so uniform, that observations may be\\nmade in the same way on stars which culminate several degrees\\nnorth or south of the zenith and thus, by applying a small\\ncorrection, the refraction may be measured at many different\\naltitudes.\\n33. General method of measuring refraction. A star,\\nvrhose declination is known, may be used for determining re-\\nfraction at any altitude, in the following manner.\\nLet m n (Fig. 9) be the path of diurnal rotation of a star,\\nwhose declination xr is known. When the star is at x, let its\\napparent altitude be measured, and let the exact time also be\\nobserved. When it culminates at m, observe the time again.\\nThe difference of these times, allowing 15\u00c2\u00b0 for an hour, will\\ngive the angle at the pole ZPx. The co-latitude of the place,\\nZP, and the co-declination of the star, P#, being known in the", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0036.jp2"}, "35": {"fulltext": "TABLES OF REFRACTION.\\n21\\nspherical triangle ZP#, the side Za? can be computed. Its\\ncomplement xy is the true altitude. This, subtracted from the\\napparent altitude before observed, gives the refraction at that\\nelevation.\\nFig. 9.\\n34. Tables of refraction. It is demonstrated, that except\\nnear the horizon, the mean refraction varies as the tangent ol\\nthe zenith distance. Tables of atmospheric refraction are cal-\\nculated in accordance with this law, for all zenith distances\\nless than 80\u00c2\u00b0. They are, however, extended beyond that limit\\ndown to the horizon, being calculated for the last 10\u00c2\u00b0 by a\\ndifferent and more complex law, and the results of calculation\\nbeing more uncertain. On this account, all astronomical\\nmeasurements are made, so far as is possible, within 75\u00c2\u00b0 of the\\nzenith. In order to obtain the place of a body with the utmost\\naccuracy, tables of refraction are accompanied with means of\\ncorrecting for the state of the barometer and the thermometer\\nat the time of observation.\\n35. Time of rising and setting affected by refraction.\\nSince any heavenly body at the horizon is considerably elevated\\nby refraction, it therefore appears to rise earlier and set later", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0037.jp2"}, "36": {"fulltext": "22 TWILIGHT.\\nthan it would do if there were no atmosphere. The angular\\nbreadth of the sun is about 32 while horizontal refraction is a\\nlittle more than this\u00e2\u0080\u0094 35 Therefore, the sun appears just\\nabove the horizon, when, in truth, it is wholly below. This\\nadds at least four minutes to the day, two in the morning and\\ntwo at evening.\\n36. Distortion of the sun s and moon s disk by refrac-\\ntion. The change in the amount of refraction is so rapid near\\nthe horizon, that when the sun has just risen, or is just about to\\nset, the lower limb is elevated more than the upper, by a very\\nperceptible quantity. Its form, therefore, does not appear cir-\\ncular, but nearly elliptical, the vertical diameter being shortened\\nabout 5 7 or 6 The lower half, however, appears more flat-\\ntened than the upper half, because the difference of refraction\\nbetween the lower limb and the center is greater than that,\\nbetween the center and the upper limb.\\n37. Illumination of the shy. During the day, the atmos-\\nphere is illuminated by the light of the sun, which penetrates\\nevery part of it, and is reflected in all directions. If there were\\nno air, the sky, instead of appearing luminous by day, would\\nexhibit the same blackness as by night, and the stars would be\\nvisible alike at all times. We should, in that case, lose a great\\npart of that generally diffused light which illuminates the\\ninterior of buildings, and other places screened from the direct\\nrays of the sun. The earth s surface, and all terrestrial objects,\\non which the sunlight falls directly, would indeed, by radiant\\nreflection, cause a degree of illumination, but it would be far\\nless than we now enjoy. It has been observed, in ascending to\\ngreat heights, either on mountains or in balloons, where, of\\ncourse, the air which is most dense and reflects most abun-\\ndantly is left below, that the sky assumes a very dark hue, and\\nthe general illumination is greatly diminished.\\n38. Twilight. The illumination of the sky begins before\\nthe sun rises, and continues after it sets it is then called twi-\\nlight. More or less of it is visible, as long as the sun is not\\nmore than 18\u00c2\u00b0 vertically below the horizon. Those parts of the", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0038.jp2"}, "37": {"fulltext": "DtrBATION OF TWILIGHT.\\n23\\natmosphere are most luminous, which lie nearest to the direc\u00c2\u00ab\\ntion of the sun. Thus, in Fig. 10, let A be a place on the\\nearth, where the sun is just setting. The whole sky, IEFH, is\\nilluminated. But, to a place further east, as B, the twilight\\nextends from E to H, the part of the sky, IIK, remote from\\nthe sun, being in the shadow of the earth. At C, only FH is\\nilluminated, and HL is dark. At D, the twilight is entirely\\ngone.\\nFig. 10.\\nThough the twilight terminates at H, there is no abrupt\\ntransition from light to shade at that point, since the reflection\\nfrom those high and rare parts of the air is exceedingly feeble\\nand also, because the thickness of the illuminated segment,\\nthrough which we look, diminishes gradually to that limit, as\\nis obvious from an inspection of the figure.\\n39. Duration of twilight. To an observer at the equator,\\nat those times of the year when the sun is on the celestial\\nequator, the twilight continues lh. 12m. For, in the diurnal\\nmotion, 15\u00c2\u00b0 are described in an hour, and therefore 18\u00c2\u00b0 in\\nl T 3 jh. lh. 12m. This is the shortest duration possible. For,\\nif the sun were on a parallel of declination, the degrees of diurnal\\nmotion would be shorter than those on a great circle. And,\\nif the observer were on some parallel of latitude, the circles of\\ndaily motion would be oblique to his horizon, and the sun must\\ntherefore pass over more than 18\u00c2\u00b0, in order to move 18\u00c2\u00b0 verti\\neally. An extreme case occurs at the poles, where twilight\\nlasts several months.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0039.jp2"}, "38": {"fulltext": "24\\nTHE TRANSIT INSTRUMENT.\\nCHAPTEE III.\\nTHE OBSERVATORY AND ITS INSTRUMENTS.-\\nPROBLEMS.\\n-SPHERICAL\\n40. The observatory. Accurate knowledge of the motions\\nof the heavenly bodies is mostly obtained by observing their\\nrelations to the diurnal rotation. The observatory is furnished\\nwith several instruments by which such observations are made.\\n41. The transit instrument. This is a telescope so mount-\\ned as to observe a heavenly body, at the instant when it cul-\\nminates^ that is, makes a transit of the meridian. AD\\n(Fig. 11) represents the telescope supported by a horizontal\\naxis, which consists of two hollow cones, placed base to base,\\nso as to combine lightness and strength. The ends of the axis\\nrest in sockets, Attached to two stone piers, E and W. That", "height": "4416", "width": "2633", "jp2-path": "introductiont00olms_0040.jp2"}, "39": {"fulltext": "ADJUSTMENT OF TRANSIT INSTRUMENT.\\n25\\nthe instrument may receive no tremors from the building, the\\npiers stand on a firm foundation in the ground, passing through\\nthe floor without contact. The axis being placed east and\\nwest horizontally, the telescope, which is perpendicular to it,\\nwill, when turned, revolve in the plane of the meridian. A\\ngraduated circle, n, is attached to one end of the axis, for\\nmarking altitudes or zenith distances. The whole instrument\\ncan be raised from the sockets, and the axis inverted, so that\\nthe east end shall rest on the pier W, and the west end on the\\npier E.\\n42. Adjustments of the transit instrument. The visual\\naxis of the telescope, AD, is called the line of collimation^ and\\nis marked by the intersection of two exceedingly fine wires in\\nthe focus of the eye-glass. One of these wires is horizontal, fh\\n(Fig. 12), the other vertical, d e the latter visibly marks the\\ndirection of the meridian, when the instrument has been prop-\\nerly adjusted. The sockets, in which the ends of the axis\\nrest, are so connected with the stone piers, that one of them can\\nbe raised or lowered by a\\nscrew, and the other can, in\\na similar manner, be moved\\nnorth or south. By the\\nspirit-level, L, which hangs\\non the axis, it can be seen\\nwhether the axis is horizon-\\ntal. If not, raise or lower\\nthe end which admits of\\nvertical motion. To find\\nwhether the line of collima-\\ntion is perpendicular to the\\naxis of revolution, observe\\nwhether a distant terrestrial\\nobject, which is on the vertical wire, remains on it after the\\nends of the axis have been inverted in their sockets. If not,\\nmove the plate which carries the wires laterally, till the vertical\\nwire bisects the distance between the two positions of the\\nobject. And finally, to determine whether the axis is east and\\nwest, observe if a circumpolar star occupies the same length oi", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0041.jp2"}, "40": {"fulltext": "26 TO OBSERVE RIGHT ASCENSION.\\ntime in passing from the upper to the lower culmination, as\\nfrom the lower to the upper and if not, move the end of the\\naxis horizontally, till the intervals are equal.\\nFor fuller instructions on adjustment, see Loomis s Practical\\nAstronomy.\\n43. The astronomical clock. The transit instrument marks\\nthe event of crossing the meridian the clock must be used in\\nconnection with it, to fix the time of the transit. The clock of\\nthe observatory is made to keep sidereal time, that is, it marks\\noff 24 hours in the interval between two successive transits of a\\nstar, instead of the sun. This interval is called a sidereal day,\\nand is about 4 minutes less than a solar day. The sidereal day\\nbegins when the vernal equinox transits the meridian. At that\\ninstant, the clock is at Oh. Om. Os. and any hour of the clock\\nshows how long a time has elapsed since the equinox culmi-\\nnated.\\n44. Error and rate of clock, The uniform movement of\\nthe clock is its most important excellence. This may be tested\\nby the transit instrument, and a list of right ascensions of stars.\\nIf it does not indicate Oh. Om. Os. when the vernal equinox cul-\\nminates, the difference is called its error. If it marks any more\\nor less than 24 hours between two successive transits of a star,\\nthis gain or loss is called its rate. If both error and rate are\\nknown, then the true time is known and generally it is not\\nbest to alter the clock, but only to keep a record of error and\\nrate.\\n45. To observe the right ascension of a heavenly body.\\nHaving elevated the telescope to the altitude of the body at the\\ntime of culmination, notice the exact instant when it appears\\non the vertical wire de (Fig. 12). This is its right ascension,\\nwhich may be given either in time or in arc. Thus, if the\\nclock is at 13h. 46m. 32s. when a star passes the wire, its right\\nascension is 13h. 46m. 32s. or, at the rate of 15\u00c2\u00b0 for each\\nhour, 206\u00c2\u00b0 38 0\\nTo secure greater accuracy, several equidistant wires are\\nplaced parallel to de, an equal number on each side, as in Fig", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0042.jp2"}, "41": {"fulltext": "THE CHKO.N0GKAPH. 27\\n12. The time of passing each wire is noted, and the average of\\nall obtained for the time of crossing the central one.\\nTo observe the right ascension of the snn or a planet, the\\ntransit of each limb must be noticed, and the mean of all the\\ntimes will be the right ascension of the center of the disk.\\nIn order to render the wires visible by night, the field of\\nview is faintly illuminated by a lamp, placed at one end of the\\nhollow axis, the light of which, after entering the telescope, is\\nreflected toward the eye-piece.\\n46. Transits recorded by the chro?iograph. To observe the\\ntime of a star-transit, the eye must discern the instant of its\\nbisection by the wire, and the ear must hear the beat of the\\nclock, the seconds being counted from the last completed\\nminute before the observation began. If the bisection occurs\\nbetween two beats, as it commonly does, the observer needs\\nmuch practice to be able to divide the second accurately into\\ntenths, and decide at which of them the transit takes place.\\nTransits are now generally observed and recorded with much\\ngreater ease and accuracy by the use of the galvanic circuit.\\nFig. 13.\\nThe pendulum of the observatory clock is arranged to close\\nthe circuit of a battery and break it again, at the beginning of\\nevery beat. The closing of the circuit gives a small lateral\\nmotion to the registering pen, under which the paper is ad-\\nvancing on a revolving cylinder, about an inch per second.\\nThus the seconds are all permanently recorded by notches one\\ninch asunder in a straight line, as a, b, c, d (Fig. 13). The\\nmark at the beginning of each minute has some peculiarity by\\nwhich it may be distinguished from the rest. The observer has\\nunder his hand a key, which, by a quick touch, will also close\\nand break the circuit. Whenever a star is on one of the wires\\nof the transit instrument, he touches the key, the pen is moved\\naside, and indents the line as at A, and the observation is thus\\nrecorded and the place where this motion commenced between\\nthe second-marks can afterward be carefully examined. Thus,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0043.jp2"}, "42": {"fulltext": "28\\nTHE MUEAL CIECLE.\\nwithout the distraction of attending to the clock, he can record\\nthe transits of all the wires and if he only notices within what\\nminute the work begins, he can read the entire record with\\naccuracy to the T or even the too of a second. Since the\\ngeneral adoption of this method, the number of wires has been\\nincreased, sometimes to 30 or 40, so as to obtain the mean of\\nmore numerous observations on the same star. The instru\\nment, as above described, is known as the chronograph.\\n47. The mural circle. The circle of the transit instrument\\nis used principally for finding a body whose altitude is known,\\nand is too small for accurate measurement of arcs on the meri*\\nFig. 14.\\nuian. For measuring meridian arcs, the mural circle is em-\\nployed so called, because it revolves by the side of a vertical\\nwall. It consists of a circle usually six or eight feet in diame-\\nter, and a telescope attached to its face. It is made so large, in", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0044.jp2"}, "43": {"fulltext": "THE VERNIER.\\n29\\norder that very small angles may be measured by the divisions\\non its limb. Fig. 14 represents the instrument attached to the\\nmeridian wall. Its radii are hollow and of conical form. The\\naxis, which is on one side only, is firmly set in the wall and\\nthe circle and telescope revolve upon it. The graduations are\\nmade on the rim, and not on the face of the circle, and are read\\nby means of microscopes attached to the wall.\\n48. Subdivisions of the graduated limb. The reading of a.\\ngraduated arc can always be carried much lower than the\\ndivisions actually marked on it. This is sometimes accom-\\nplished by the vernier, and sometimes by the reading micro-\\nscope.\\n49. TJie vernier. This contrivance, so named from the in-\\nventor, is a short graduated arc, which slides along the limb of\\nthe circle that is to be subdivided. For example, AB (Fig. 15)^\\nis a vernier for dividing the 12 spaces of the arc on its right\\ninto portions of 1 each. For this purpose, the vernier consists\\nof 12 parts, which together are equal to 11 of the divisions of\\nthe limb. Since 12 parts of the vernier are\\nless than 12 divisions of the arc by a whole\\ndivision, one part of the vernier is less than one\\ndivision of the arc by yV of a division two are\\nless than two by \u00c2\u00b0f a division, and so on.\\nNow, in the figure, the zero of the vernier has\\npassed 10\u00c2\u00b0 24/ and in order to find how many\\ntwelfths of the next space it has passed, it is\\nonly necessary to look along the vernier, and\\nobserve the number of the division line, which\\ncoincides with a line of the arc. In this case\\nwe find it to be the 8th. Hence, the 8 parts\\nof the vernier from to 8 are less than the cor-\\nresponding S divisions of the arc by T 8 2 that\\nis, zero is T 8 2 of 12 beyond 10\u00c2\u00b0 24\\\\ Therefore\\nthe reading is 10\u00c2\u00b0 32\\nThe vernier is sometimes made, so that a\\ngiven number of parts equals one more, instead\\nof one less, than the same number on the limb.\\nRut the principle of making subdivisions is the same.\\nFig. 15.\\n13\u00c2\u00b0\\n-12\u00c2\u00b0\\n\u00e2\u0096\u00a0ir\\n\u00e2\u0096\u00a0io c", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0045.jp2"}, "44": {"fulltext": "30 TO FIND DECLINATION.\\n50. The reading microscope. This is a compound micro-\\nscope, having in the focus of its eye-piece a pair of spider-linea\\nintersecting each other, and in the same field of view are the\\nmagnified divisions of the arc. The intersection of the spider-\\niines is moved laterally from one division line of the arc to\\nanother by a screw. If the divisions, for example, are equal to\\n5 each, then the screw is so made as to move the intersection\\nfrom one line to another by five revolutions, and therefore each\\nrevolution indicates a motion of V. A circle is attached to the\\naxis of the screw, having its circumference divided into 60\\nequal parts. As each revolution of the screw can thus be\\ndivided into 60 equal parts, so each minute of the arc can be\\ndivided into seconds.\\nOne of these reading microscopes is represented at A (Fig.\\n14) and the places of others are marked at B, C, D, E, F, 60\u00c2\u00b0\\nfrom each other. Six are used, instead of one, for the purpose\\nof obtaining a more accurate result, by taking a mean of the\\nseconds in the several readings.\\n51. To find the declination of a heavenly body. This may\\nbe done by measuring its meridian altitude. Let the mural\\ncircle be adjusted in altitude, so that, at the instant when the\\nbody crosses the vertical wire of the telescope, it is on the\\nhorizontal wire also. The graduation of the limb shows its\\naltitude. The latitude of the observatory being known, the\\nelevation of the equator is known and the difference between\\nthe altitude of the body and the elevation of the equator, is the\\ndecimation sought. In northern latitudes, if the altitude of the\\nheavenly body exceeds the elevation of the equator, the differ\\nence is a northern declination if it is less, the decimation is\\nsouth.\\nBefore altitudes can be measured, the horizontal position ol\\nthe telescope must be determined. This may be done by\\nbisecting the angle between the direction of a fixed star, as seen\\nat culmination, and its apparent direction, when seen at\\nanother culmination in a mirror of liquid mercury, called the\\nartificial horizon. By a law of optics, the apparent depression\\nbelow the horizon equals the elevation above it, sc chat the\\nwhole angle equals twice the altitude.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0046.jp2"}, "45": {"fulltext": "ALTITUDE AND AZIMUTH INSTEUMENT.\\n31\\n5 2. The transit circle. Sometimes the circle of the transit\\nir. .trument is made of much larger size than is represented in\\nFig. 11, in order that declinations as well as right ascensions\\nmay be observed by it. This combination of the transit instru-\\nment and mural circle is called the transit circle, and is con-\\nsidered by some practical astronomers to possess an advantage\\nover the mural circle in the steadiness of its axis.\\n53. The altitude and azimuth instrument. The essential\\nparts of this instrument are, a telescope and two graduated\\ncircles, one vertical, the other horizontal. Fig. 16 presents one\\nof its more simple forms. The telescope AB is movable on a\\nFig. 16.\\nhorizontal axis at the center of the vertical circle dbc, and also\\non a vertical axis, passing through the center of the horizontal\\ncircle EFGL The levels g and A, placed at right angles to each\\nother, show when the circle EFG- is brought to a horizontal\\nposition by the tripod screws. The tangent screws, d and\\ngive slow motions, one in a vertical, the other in a horizontal\\nplane. If the reading of the vertical circle is taken when the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0047.jp2"}, "46": {"fulltext": "32 THE SEXTANT.\\ntelescope is horizontal and again when it is directed U a star\\nthe difference of the readings is equal to the altitude of the star\\nIn a similar manner, if the horizontal circle is read, when the\\ntelescope is directed to the north, and read again when it ia\\ndirected to a star, the difference is its azimuth.\\n54. The sextant. This is an instrument for measuring the\\nangular distance between two points situated in any plane\\nwhatever. It is represented in Fig. IT. I and H are two\\nsmall mirrors, and T a small telescope. ID is a movable radius\\nor index, carrying the index mirror at the center of motion, I,\\nFig. 17.\\n*8\u00e2\u0080\u0094\\nand a vernier at the extremity, D. The horizon glass, H, is\\nsilvered only on one-half of its surface. When the zero oi\\nthe vernier coincides with that of the arc at F, the mirrors\\nare precisely parallel. If now we direct the telescope to a\\nstar, it may be seen in the transparent part of the horizon\\nglass, and its image in close contact with it, in the silvered part.\\nThis is owing to the fact, that a heavenly body is so far dis-\\ntant, that the rays from it to the two mirrors are sensibly par-\\nallel to each other.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0048.jp2"}, "47": {"fulltext": "SPHERICAL PROBLEMS. 33\\n55. To measure an angle by the sextant. Let it he required\\nto measure the angular distance between the star S and the\\nmoon M. The telescope being directed to S, and the sextant\\nbeing held so that the plane of reflection shall pass through the\\ntwo objects, turn the index from F toward E, until the image\\nof the moon is brought to the star, its nearer limb just touch-\\ning S. Now, according to an optical principle, the angular\\ndistance between the moon and its image is just twice that be-\\ntween the mirrors. Therefore, by reading the vernier at D, we\\nobtain the angular distance between the star and the moon s\\nnearer limb. Again, bring the further limb to the star, and\\nfind its distance. Half their sum is the angular distance be-\\ntween the moon s center and the star.\\nIn like manner, the altitude of a body may be found, by\\nbringing its image to coincide w r ith the image of the same body\\nseen in the artificial horizon. One-half the angle read from\\nthe vernier is the altitude of the body.\\nThe graduation on the limb of the sextant, for convenience,\\ncorresponds, not to the actual length of the arc passed over by\\nthe vernier, but to the angular motion of the body, which is\\ntwice as rapid. Hence, on the arc of 60\u00c2\u00b0, the graduation\\nreaches 120\u00c2\u00b0 and all angles not greater than this can be\\nmeasured by the instrument.\\nThe two instruments just described are sometimes conven-\\nient at the observatory, but their chief use is elsewhere. The\\naltitude and azimuth instrument is of great value in trigono-\\nmetrical surveying. The sextant is important for the naviga-\\ntor, since a stationary instrument\\ncannot be employed at sea. Fi S- 18\\n56. Spherical problems.\\nI. To compute the sun s right\\nascension, declination, or longi-\\ntude, or the obliquity of the eclip-\\ntic to the equator, when any two\\nof the others are given.\\nLet PEP (Fig. 18) represent\\nthe solstitial colure, PP the axis,\\nEQ the equator, E C the ecliptic,\\n3", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0049.jp2"}, "48": {"fulltext": "34 SPHERICAL PROBLEMS.\\nand PSP a secondary of the equator passing through the sun\\nS. Then SAR is the obliquity of the ecliptic, and RS the dec-\\nlination of the sun. And if its longitude is less than 90\u00c2\u00b0, AS\\nis its longitude, and AR its right ascension. If its longitude\\nis more than 90\u00c2\u00b0, AS and AR are the supplements of longitude\\nand right ascension. In both cases the declination is north.\\nWhen the sun s place is represented by S and its longitude is\\nbetween 180\u00c2\u00b0 and 270\u00c2\u00b0, then the longitude 180\u00c2\u00b0 AS and\\nthe right ascension 180\u00c2\u00b0 -f- AR But if its longitude is\\nmore than 270\u00c2\u00b0, longitude 360\u00c2\u00b0 AS and right ascen-\\nsion 360\u00c2\u00b0 AR In each case the declination is south.\\nThe triangle ARS is right-angled at R and by Napier s\\nrule, any one of the parts may be found, whea two others are\\ngiven.\\nEx. 1. When the sun s right ascension is 53\u00c2\u00b0 38 and its dec-\\nlination, 19\u00c2\u00b0 15 57 required its longitude, and the obliquity\\nof the ecliptic.\\n1. Rad cos AS =cos AR cos RS.\\n2. Rad sin AR tan RS cot A.\\nAns. Long. 55\u00c2\u00b0 57 43 Obi. 23\u00c2\u00b0 27 501\\nEx. 2. On March 31st, the sun s declination was observed to\\nbe 4\u00c2\u00b0 13 31| and the obliquity was 23\u00c2\u00b0 27 51 required\\nthe sun s right ascension. Ans. 9\u00c2\u00b0 47 59\\nEx. 3. What is the sun s longitude in November, when its\\ndeclination is 21\u00c2\u00b0 16 4 and its right ascension is 16h. 14m.\\n58.4s. Ans. 245\u00c2\u00b0 39 10\\nThe above data show that the sun s longitude is more than\\n180\u00c2\u00b0 and less than 270\u00c2\u00b0, and the declination south. The tri-\\nangle for computation is AR S\\nEx. 4. The sun s longitude being 8 s 7\u00c2\u00b0 40 56 and the\\nobliquity 23\u00c2\u00b0 27 42\u00c2\u00a3 required right ascension in time.\\nAns. lt)h. 23m. 34s.\\nII. Given the latitude of a place, and the declination of the\\nsun, to find the time of its rising and setting.\\nLet PEP (Fig. 19) be the meridian of the place, Z its zenith,\\nand HO its horizon. Let LL be the diurnal circle of the sun\\nRS is its declination, S the place of its rising and setting, and\\nLS the arc described between either and midnight. But LS,\\nin degrees, equals QR, the complement of AR. The angle", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0050.jp2"}, "49": {"fulltext": "SPHEEICAL PROBLEMS.\\n35\\nFig 19.\\nS AE E AH, which is measured by\\nEH, the co-latitude, and E is a right\\nangle. Therefore, rad sin AE\\ncot A tan ES.\\nEx. 1. Eequired the time of sun-\\nrise at latitude 52\u00c2\u00b0 13 1ST., when the\\nsun s declination is 23\u00c2\u00b0 28 K\\nWe find AE=34\u00c2\u00b0 3 21*\\nQE 55\u00c2\u00b0 56 38f (in time) 3h.\\n43m. 46\u00c2\u00b1s. This is the time of sun-\\nrise. The same subtracted from\\n12h., gives 8h. 16m. 13Js. for the time of sunset.\\nEx. 2. Eequired the time of sunrise at latitude 57\u00c2\u00b0\\nK, when the sun s declination is 23\u00c2\u00b0 28 K\\nArts. 3h. 11m,\\nEx. 3. How long is the sun above the horizon in latitude 58\u00c2\u00b0\\n12 K, when its declination is 18\u00c2\u00b0 40 S.\\nAna. 7h. 35m. 52s.\\nIn a similar manner, if the declination of any heavenly body\\nbe given, the interval of time between its culmination, and its\\nrising or setting, can be computed.\\nIII. Given the latitude of a place, and the declination of a\\nheavenly body, to compute its altitude and azimuth, when on\\nthe six o clock hour-circle.\\nLet PEP 7 (Fig. 20) be the meridian of the place, and P the\\nelevated pole. Then PP r rep-\\n2 54\\n49s.\\nresents the six o clock hour-\\ncircle, which is at right angles\\nto the meridian, and therefore\\nprojected in a straight line.\\nLet the body cross it at S, and\\nlet ZSB be the vertical circle\\npassing through it. In the tri-\\nangle ASB, AS is the declina-\\ntion, SB the altitude, AB the\\namplitude or complement to\\nthe azimuth OB, and B is a\\nright angle.\\nEx. 1. What were the altitude\\nFig. 20.\\nand azimuth of Arcturus,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0051.jp2"}, "50": {"fulltext": "36\\nSPHERICAL PROBLEMS.\\nwhen on the six o clock hour-circle, latitude 51\u00c2\u00b0 28 40 N. its\\ndeclination being 20\u00c2\u00b0 6 50 N. I\\n^n*. Altitude 15\u00c2\u00b0 36 27 Azimuth 77\u00c2\u00b0 9 4\\nEx. 2. In latitude 62\u00c2\u00b0 12 1ST. the altitude of the sun at sis\\no clock, a. m., was observed to be 18\u00c2\u00b0 20 23 Eequired its\\ndeclination and azimuth.\\nAm. Declination 20\u00c2\u00b0 50 12 1ST. Azimuth 79\u00c2\u00b0 56 4\\nLV. Given the latitude of a place and the sun s declination.\\nto find the time a. m. when it will cease shining on the north\\nside of a building, or the time p. m. when it will begin to shine\\nupon it.\\nLet PEP 7 (Fig. 21) be the meridian of the place, ZAK the\\nprime vertical, and S the place where\\nthe sun crosses it, and thus ceases to\\nshine on the north side of a vertical\\nwall. Let PSB be the hour-circle\\nthrough the sun at S. BS is the sun s\\ndeclination, BAS (=EZ) is the lati-\\ntude, and AB, changed into time, will\\nshow how long after six o clock a. m.,\\nor before six p. m., the sun transits\\nthe prime vertical.\\nEx. 1. In latitude 42\u00c2\u00b0 22 17 K,\\nwhen the sun s declination is 23\u00c2\u00b0 27 36 K., at what times does\\nthe sunshine begin and end on the north and south sides of a\\nbuilding? Ans. 7h. 53m. 3Ss. a. m., and 4h. 6m. 22s. p. m.\\nEx. 2. How long does the sun shine on the south side of a\\nvertical wall, in latitude 20\u00c2\u00b0 30 N., when the sun s declination\\nis 20\u00c2\u00b0 N? Ans. lh. 45m. 48s.\\nY. The latitude and the sun s declination being given, to\\nfind the time of day by the sun s altitude.\\nLet Z (Fig. 22) be the zenith of the place, P the pole, and 8\\nthe place of the sun. Measure ZS, the\\nzenith distance of the sun, and correct\\nit for refraction and parallax. PZ is\\nthe co-latitude of the place, and PS the\\nco-declination of the sun. Therefore,\\nthe sides of the spherical triangle PZS\\nare all known, and the angle ZPS can", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0052.jp2"}, "51": {"fulltext": "SPHERICAL PROBLEMS.\\n37\\nFiar. 23.\\nbe computed which, changed to time, shows how long before\\nor after noon the observation was made.\\nVI. Given the latitude and the sun s declination, to find the\\ntime when twilight begins and ends.\\nThe twilight begins or ends when the sun is about 18\u00c2\u00b0\\nbelow the horizon (Art. 38). Let Z (Fig. 23) be the zenith, P\\nthe pole, and S the place of the sun at the beginning or ei.d of\\ntwilight. ZS 108\u00c2\u00b0, ZP co-lat,\\nPS co-decl. The three sides of\\nZPS are given, to find the hour-angle\\nZPS. This may be done by dropping\\nthe perpendicular arc P/ and using\\nthe proportion (Sph. Trig.) tan J ZS\\ntan (PS +ZP) tan (PS ZP)\\ntan (Bp Zp). Having obtained\\nZp and Sp, compute the angles at P,\\nand add them together.\\nEx. In lat. 42\u00c2\u00b0 22 when does twi-\\nlight begin and end, at midsummer,\\nthe sun s declination being 23\u00c2\u00b0 2S\\nAns. 2h. 6m. 20s. a. m.\\nVII. Given the right ascension and declination of a body, to\\nfind its longitude and latitude.\\nLet EQ (Fig. 24) be the equator, and P its north pole, E O\\nthe ecliptic, and B. its pole, and\\nS the place of the body. Join\\nPS and ES, and draw the arc\\nSB perpendicular to PC. PS,\\nthe complement of declination,\\nis known likewise RP, which\\nequals EE the obliquity. As\\nA is the vernal equinox, SPQ\\nis the complement of right as-\\ncension, and therefore known.\\nSRC is the complement of lon-\\ngitude, and PS is the comple-\\nment of latitude.\\nIn the right-angled triangle PSB, PS and P being known,\\nfind PB. Then KB(=RP+PB) is known. Then (Sph.\\n9h. 53m. 40s. p. m.\\nFig. 24.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0053.jp2"}, "52": {"fulltext": "38 THE sun s eight ascension.\\nTrig.) sin KB sin PB tan P tan E. Thus R, the com\\nplement of longitude, is found. Then, in the right-angled\\ntriangle BSB, BB and the angle K enable us to find BS, the\\ncomplement of latitude.\\nEx. 1. The right ascension of a planet was observed to be\\n82\u00c2\u00b0 7 and its declination 24\u00c2\u00b0 26 K Calling the obliquity\\n23\u00c2\u00b0 27 20 what were the longitude and latitude of the\\nplanet Ans. Long. 82\u00c2\u00b0 49 30 Lat. 1\u00c2\u00b0 10 27 K\\nEx. 2. What are the longitude and latitude of the star,\\nwhose right ascension is 4h. 40m. 49s., and its declination 66*\\n6 37 K Ans. Long. 79\u00c2\u00b0 V 8 Lat. 43\u00c2\u00b0 24 5 K\\nCHAPTEB IV.\\nTHE EARTH S ANNUAL MOTION ABOUT THE SUN. THE\\nSEASONS. FIGURE OF THE EARTH S ORBIT.\\n57. Ohservatums of the suns place. If we employ the in-\\nstruments of the observatory in measuring from day to day the\\nright ascension and declination of the sun, at the moment of its\\ncrossing the meridian, it will be discovered that these quantities\\nare constantly changing or, in other words, that the sun is\\nconstantly shifting its place in relation to the stars.\\n58. Its right ascension. By the transit instrument and\\nclock, it is found that the sun s right ascension is always in-\\ncreasing by a quantity which is not quite uniform, but which\\namounts to nearly one degree every day. So that, in about\\n36 5 days, it describes the whole 360\u00c2\u00b0 of right ascension, and\\nappears again in the same place among the stars. This is the\\napparent annual motion of the sun, by which it seems to pass\\nround the heavens from west to east once in a year.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0054.jp2"}, "53": {"fulltext": "THE TROPICS AND POLAR CIRCLES. 39\\n59. Its declination. But while thus passing round, it also\\nmoves alternately north and south. For, by measuring the\\ndeclination each day by the mural circle, it is found that after\\npassing the vernal equinox, March 20th, its declination is\\nnorth, and increases to the summer solstice, June 21st, when it\\nreaches nearly 23^\u00c2\u00b0 from that point it diminishes to zero at\\nthe autumnal equinox, September 22d. The declination then\\nbecomes south, increasing to the winter solstice, December 21st,\\nwhen it is 23J\u00c2\u00b0, and thence diminishing to nothing at the\\nvernal equinox, on March 20th of the following year.\\n60. The ecliptic. The apparent annual path of the sun is\\nfound by the foregoing observations to lie in a plane, cutting\\nthe celestial sphere in a circle called the ecliptic (Art. 12), and\\ninclined to the plane of the equator at an angle of about 23\u00c2\u00b0 27\\nThis plane maintains almost a constant position among the\\nstars, and is used far more than any other circle of the sphere\\nas a plane of reference.\\nThe obliquity of the equator to the ecliptic in 1850 was\\n23\u00c2\u00b0 27 31 and diminishes at the rate of 46 in a century.\\n6 1 The zodiac. This name is given to a zone of the heav-\\nens, 16\u00c2\u00b0 wide, extending along the circle of the ecliptic, 8\u00c2\u00b0 on\\neach side of it. The paths of the principal planets lie within\\nthis zone. Its length is divided into 12 signs of 30\u00c2\u00b0 each,\\nhaving the same names and arranged in the same order as\\nthose of the ecliptic (Art. 13), though not coincident with them.\\nThe signs of the zodiac are distinguished from each other by\\nthe stars which occupy them.\\n62. The tropics and polar circles. Through the two points\\nof the ecliptic most distant from the equator, called the sol-\\nstices (Art. 12), we imagine circles to be drawn parallel to\\nthe equator, called the tropics. The northern circle, passing\\nthrough the first of Cancer on the ecliptic, is called the tropic\\nof Cancer the southern one, for a like reason, is called the\\ntropic of Capricorn. Two other parallels to the equator, passing\\nthrough the poles of the ecliptic, and therefore 23 d 27 from the\\n.poles of the equator, are called the polar circles.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0055.jp2"}, "54": {"fulltext": "40\\nANNUAL MOTION.\\n63. Terrestrial zones. On the terrestrial sphere, a similar\\nsystem of circles divides the earth s surface into the well-known\\nzones of geography, called the torrid, temperate, and frigid\\nzones. The tropics are the limits of vertical sunshine in mid-\\nsummer. The polar circles are the limits within which the\\nsun makes a diurnal revolution in midsummer and mid-winter,\\nwithout rising or setting\\n64. The annual motion observed without instruments. If\\nthe stars were visible in the daytime, we should perceive the\\nsun making progress among them toward the east, by a dis-\\ntance equal to nearly twice its own breadth every day, since\\nthe apparent diameter of the sun is a little more than half a\\ndegree. But, as they are invisible by day, we detect the same\\nfact, when we notice that at a given hour of the night, all the\\nstars are further west than on a previous night. For example, at\\n9 o clock p. m. that is, 9 hours after noon it is easily observed\\nthat there is, from one evening to another, a regular progress\\nof all the stars westward, as long as we choose to watch them.\\nIn other words, the sun is at the same rate advancing eastward\\nrelatively to the stars.\\nFig. 25.\\n65. The annual motion is a motion of the earth, not of the\\nmn. \u00e2\u0080\u0094There is abundant evidence that the motion of the sun", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0056.jp2"}, "55": {"fulltext": "CHANGE OF SEASONS.\\n41\\naround the earth, above des3ribed, is only apparent, and\\nresults from a real motion of the earth about the sun. Thus,\\nsuppose the earth to pass around the sun S (Fig. 25) in the\\norbit ABPC, in the order of the signs if we were unconscious\\nof this motion, the sun would appear to us to move about the\\nearth in the same order of the signs, though, at any given\\nmoment, in a contrary direction. When the earth is at B (in\\nthe sign T, as seen from the sun), we should see the sun in the\\nsign =a= when we reach tf the sun is seen in ^l and so on.\\n66. Cause of the change of seasons. The changes of the\\nseasons are due to the fact, that the two revolutions of the\\nearth, one on its axis, and the other around the sun, are in dif-\\nferent planes in other words, that the equator and the ecliptic\\nmake an angle with each other. In Fig. 26, let ABCD repre-\\nsent the ecliptic (seen obliquely), and suppose the earth to\\npass around in the order of the letters, occupying the position\\nA on the 20th of March, B on June 21st, C on Sept. 22d, and\\nD on Dec. 21st. In every position of the earth, the equator eq,\\nis inclined the same way, and always at the angle of 23^\u00c2\u00b0 with\\nthe ecliptic. The axis ns, being perpendicular to the equator,\\nis everywhere parallel to itself.\\nWhen the earth is at A the vernal equinox, the line of inter-\\nsection of the ecliptic and equator, passes through the sun S,\\nand the light just reaches the poles n and s so that, as the\\nearth rotates on ns, every place is one-half of the time in the\\nlight, and the other half in darkness. The days and nights are\\ntherefore equal.\\nAs the earth passes on toward B, the light readies beyond", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0057.jp2"}, "56": {"fulltext": "42\\nHEAT IN SUMMER AND COLD IN WINTER.\\nthe north pole more and more, till at B, the summer solstice,\\nit extends 23-J- beyond n, and falls as much short of s, the sun\\nbeing now north of the equator eq. As the earth now rotates\\non ns, all places north of eq are in the light longer than in the\\nshade, and the reverse is true of all places south of eq. It is\\nsummer in the northern hemisphere, and winter in the southern.\\nOn the 22d of September, the earth arrives at C, the autum-\\nnal equinox the intersection of the two planes again passes\\nthrough the sun, the light once more reaches the poles, and the\\ndays and nights are equal.\\nAt D, the winter solstice, the north pole n is turned as far\\nas possible into the shade, and s into the light. Every place\\nnorth of eq is in the light a shorter time than in the darkness,\\nand the reverse south of eq. It is now winter in the northern\\nhemisphere, and summer in the southern.\\nIf the equator were in the same plane with the ecliptic, the\\ncase would be represented by Fig. 26a. The axis ns would\\nthen be perpendicular to the ecliptic as well as to the equa-\\ntor, the circle of illumination would always reach just to the\\npoles n and s, and in the daily rotation, every place would be\\nhalf the time in the sunlight, and half in the darkness. There\\nwould, therefore, be no inequality of day and night, and no\\nchange of seasons.\\n67. Causes of heat in summer and cold in winter. These\\nare two.\\n1st. The length of the aay compared with the night. The\\nheat of the earth is passing off by radiation during the whole\\ntime, whether the sun shines or not But the earth receives", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0058.jp2"}, "57": {"fulltext": "GREATEST HEAT AND GREATEST COLD. 43\\nbeat from tlie sun, only while the sun is above tho horizon.\\nHence, the longer the period of sunshine, compared with the\\ntime of a diurnal revolution, the greater the heat. For this\\nreason, therefore, the summer is warmer than the winter.\\n2d. The different inclination of the rays to the general sur\\nface of the earth. The number of rays falling on a given sur-\\nface, varies as the sine of inclination. Let AB (Fig. 27) be\\nthe breadth of the surface. If the rays fall on it at the\\nangle ABC, the perpendicular\\nbreadth of the beam is AC if\\nat the angle ABD, the breadth\\nof the beam is AD while, if\\nthey fall perpendicularly, the\\nbreadth of the beam is AB\\nitself. Now, the number of\\nrays in the beam obviously\\nvaries as its perpendicular\\nbreadth. But these breadths,\\nAC, AD, and AB, are as the sines of the several inclinations.\\nIn summer, the sun rises to a greater elevation each day than at\\nother seasons, and therefore sheds a greater quantity of heat on\\nthat part of the earth.\\nEx. 1. What is the relative quantity of direct heat from the\\nBun at noon, on two equal horizontal areas, one in latitude 75\u00c2\u00b0\\nN., the other 30\u00c2\u00b0 K, when the sun s declination is 19\u00c2\u00b0 1ST.\\nAns. As 100 175J.\\nEx. 2. Find the ratio, as in Ex. 1, in latitude 50\u00c2\u00b0 !N and\\nlatitude 45\u00c2\u00b0 S., when the sun s declination is 15\u00c2\u00b0 45 S.\\nAns. As 100 212.4.\\n68. Why the greatest heat is later than the summer solstice,\\nand the greatest cold later than the winter solstice. If the sun\\nsheds on a given surface more heat each day than the surface\\nloses by radiation, then the heat accumulates from day to day.\\nThis is the case during the long days of summer and more\\nheat is gained than lost, till a month or more after the summer\\nsolstice. For a like reason, during the middle hours of the day,\\nheat is received from the sun more rapidly than it is lost by\\nradiation, so that the hottest hour is 2 or 3 o clock p. m.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0059.jp2"}, "58": {"fulltext": "44 GREATEST CHANGES OF SEASON.\\nIn the winter, on the contrary, the loss by radiation exceeds\\nthe quantity received from the sun, during all the shortest days,\\nso that the temperature descends till many weeks after the\\nwinter solstice.\\nIf loss by radiation were at a uniform rate at all tempera-\\ntures, and the temperature of successive years should remain\\nconstant, as it now is, then the greatest heat would be near the\\nautumnal equinox, and the greatest cold near the vernal equi-\\nnox, the times when the surface receives heat at the mean rate.\\nOn the contrary, if the existing amount of loss by radiation\\nwere distributed so as to be exactly proportional to the acces-\\nsions received from the sun, there would be no change of tem-\\nperature at the different seasons of the year or the different\\nhours of the day.\\nBut the radiation of heat follows neither of these laws the\\nquantity radiated is greater, when the quantity received is\\ngreater, but it does not vary at so rapid a rate.\\n69. No change of seasons, if there were no obliquity. The\\nangle between the planes of the two motions of the earth being\\nthe cause of the change of seasons, it follows that there would\\nbe no such change if those motions were in the same plane. If,\\nwhile the earth advances in its orbit about the sun, it should\\nrotate in the same direction on its axis, then the sun would\\nalways be in the plane of the equator, and would, every day,\\ndescribe the equator as its diurnal circle, rising exactly in the\\neast, culminating at a zenith distance equal to the latitude of the\\nplace, and setting exactly in the west. At the equator, the sun\\nw r ould always follow the prime vertical, and at either pole it\\nwould always be passing round in the horizon. See Fig. 26a.\\n7 0. The greatest changes of season, if the obliquity were\\n90\u00c2\u00b0. If, while the earth revolves on its axis from west to east,\\nit should pass around the sun in a plane lying north and south,\\nthen the ecliptic would pass through the north and south poles,\\nand the solstices would be at the poles. Hence, at a station on\\nthe equator, the sunw T ould, during the year, describe the prime\\nvertical and various small circles parallel to it, down to the\\noorth and south points of the horizon, where it would be", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0060.jp2"}, "59": {"fulltext": "FORM OF THE EARTH S ORBIT.\\n45\\nstationary alternately at the times of the solstices. At the\\nequator, therefore, there would be an alternation from summer\\nto winter, or the reverse, every three months.\\nAt either pole there would be but one summer and one\\nwinter in a year; but the extremes would be far more intense.\\nFor the sim, in describing diurnal circles parallel to the\\nhorizon, would occupy six months in ascending to the zenith\\nand returning to the horizon, and the remaining six months in\\nperforming corresponding revolutions below the horizon.\\nAt intermediate places, the extremes of the seasons would\\nalso be intermediate.\\n7 1 Mode of determining the form of the earth? s orbit.\\nThe earth s orbit is an ellipse described about the sun, which is\\nsituated in one of its foci. This is ascertained by observing the\\nchanges in the sun s apparent diameter throughout the year^\\nWhen the sun appears smallest, it is most distant and when\\nlargest, it is nearest. And its distance, in all cases, varies in-\\nversely as its apparent diameter. Therefore, if the sun s angu-\\nlar diameter be accurately measured as frequently as possible,\\nthe reciprocals of those angles express the relative distances\\nand these distances determine the form of the orbit.\\nThus, suppose the earth to be at E (Fig. 28), and that the\\nsun s apparent diameter is\\nmeasured when in the di-\\nrection E#. After it has\\nadvanced eastward some\\ndays, so as to be seen in the\\ndirection E let another\\nmeasurement be made and\\nso on, at every opportunity\\nthrough the year. Then\\nlet E\u00c2\u00ab, E5, Ec, etc., be made\\nproportional to the recipro-\\ncals of the apparent diame-\\nters, and be laid down at\\nangles equal to the angular\\nchanges of the sun s place.\\nFig. 28.\\nA line, a b m v, passing through\\ntheir extremities, shows the form of the sun s apparent orbit", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0061.jp2"}, "60": {"fulltext": "46 LINE OF APSIDES,\\nabout the earth, and therefore the form of the earth s real orbit\\nabout the sun.\\nIn this manner, even while ignorant of the size of the orbit,\\nwe learn that its form is an ellipse, and that the sun occupies\\none of its foci.\\n72. Definitions relating to a planetary orbit. Let E be the\\nfocus occupied by the sun, and am the major axis of an ellipti-\\ncal orbit described about it the nearest point, a, is called the\\nperihelion, and the most distant point, m, the aphelion. The\\ntwo p\u00c2\u00a9ints a and m are also called the apsides. The point a\\nis sometimes called the lower apsis, and m the higher apsis.\\nThe varying distance, E E5, E^, etc., is called the radius\\nvector. If the major axis, am, is bisected in C, the ratio of EC\\nto the semi-major axis, aC, is called the eccentricity of the\\norbit. The less EC is, compared with aC, the less is the\\neccentricity, and the nearer does the ellipse approach to a\\ncircle. If E coincides with C, the eccentricity is nothing, and\\nthe orbit is a circle.\\n73. The earthus orbit very nearly circular. The eccen-\\ntricity of the earth s orbit in 1850 was 0.01677, and is very\\nslowly diminishing. This fraction is about -g^, that is, EC\\n(Fig. 28) is eV of aC. As aC, in this figure, is about one inch\\nlong, EC should be only of an inch, in order to represent\\ncorrectly the proportions of the earth s orbit. If it were thus\\ndrawn, it could not be distinguished from a circle in its appear-\\nance for the minor axis, as may be easily computed, would be\\nshorter than the major axis by only to ff o o of an inch.\\n74. Position of the line of apsides. The direction of the\\nmajor axis of the earth s orbit, or the line of apsides, is slowly\\nchanging but at present it passes through the 1 0th degree of\\nCancer and Capricorn, as represented in Fig. 25. The earth\\nis at perihelion on the 1 st of January, and at aphelion on the\\n1st of July. We are therefore nearest to the sun in the winter\\nof the northern hemisphere, and furthest from it in the summer.\\n7 5 Distance from the sun, as affecting the seasons. The", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0062.jp2"}, "61": {"fulltext": "SIDEREAL TIME. 47\\nintensity of the sun s heat at the earth, as well as that of its\\nlight, varies inversely as the square of our distance from it.\\nOn this account, the intensity of heat at perihelion is to that at\\naphelion as 61 2 59 2 which is nearly as 31 29. Therefore,\\nso far as distance is concerned, the earth receives more heat\\non the 1st of January than on the 1st of July. This produces\\na slight effect to mitigate the severity of cold in winter and o*\\nheat in summer, in the northern hemisphere, and to aggravate\\nthe same in the southern hemisphere. But, on account oi\\nchanges going on in the places of the equinoxes and apsides,\\nthis modifying effect will be reversed after the lapse of about\\n10,000 years.\\nCHAPTEK Y.\\nSIDEREAL TIME. MEAN AND APPARENT SOLAR TIME.\\nTHE CALENDAR.\\n76. The sidereal day. This is the interval of time which\\nelapses between two successive culminations of a star (Art. 43).\\nThe length of this interval appears to be invariable, whatever\\nstar is observed, or in whatever season or year the observation\\nis made. On this account, the sidereal day is regarded as the\\ntrue period of the earth s rotation on its axis. In order to\\nreckon by sidereal time, the moment chosen for the beginning\\nof each sidereal day is the moment when the vernal equinox\\nculminates. The sidereal clock, if correct, then points to\\nOh. 0m. 0s. Each sidereal day is divided into 24 sidereal hours,\\neach hour into 60 sidereal minutes, and each minute into 60\\nsidereal seconds.\\n7 7 The w.ean solar day.- -This is the mean interval between\\ntwo successive culminations of the sun. It will be shown pres-\\nently, that these intervals vary throughout the year. As the\\nsun, by the annual motion, is advancing eastward continually\\namong the stars, the solar day must always be longer than the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0063.jp2"}, "62": {"fulltext": "48 INEQUALITY OF SOLAR DATS.\\nsidereal day. For, if the sun and a star were 01 the rnendiafi\\nof a place together, then, while that place passes around east-\\nward till its meridian meets the star again, the sun has ad-\\nvanced eastward nearly a degree, and the place must revolve\\nnearly a degree more than one revolution before its meridian\\nwill reach the sun. This will require nearly 4 minutes of\\ntime; for, in the diurnal motion, 15\u00c2\u00b0 correspond to one hour,\\nand therefore 1\u00c2\u00b0 to y 1 of an hour that is, four minutes.\\n78. The relation of sidereal time to mean solar time. As\\nthe sun, in its apparent annual motion, describes 360\u00c2\u00b0 in\\n365.24 days, it will, in one day, on an average, pass over 360\u00c2\u00b0\\n-7- 365.24 59 8.35 or nearly 1\u00c2\u00b0, as before stated. But, by\\nthe diurnal motion, a given place on the earth in one solar day\\ndescribes 360\u00c2\u00b0 plus the above arc. Therefore, 360\u00c2\u00b0 59 8.35\\n59 8.35 24h. 3m. 55.9s. of solar time. This is the excess\\nof the mean solar day above a sidereal day. And one sidereal\\nhour, minute, or second is to one solar hour, minute, or second\\nas 360\u00c2\u00b0 360\u00c2\u00b0 59 8.35 that is, as 1 1.0027379. Therefore,\\nto reduce a given period of time from the mean solar to the\\nsidereal reckoning, multiply by 1.0027379 and to reduce side-\\nreal time to mean solar time, divide by the same number.\\n79. The apparent solar day. This is the actual interval\\nbetween two successive culminations of the sun. And this in-\\nterval changes its length from day to day through the entire\\nyear, being sometimes greater, and sometimes less than the\\nmean solar day.\\nIn keeping solar time by clocks and watches, it is customary,\\nfor convenience, to aim to keep the mean rather than the\\napparent time, and to regard the sun as going alternately too\\nfast and too slow.\\n80. First cause of inequality in apparent solar days. One*\\ncause of inequality of days, as measured by the sun, is found\\nin the elliptical form of the earth s orbit, and the consequent\\nunequal increments of longitude made by the sun from day to\\nday. At P (Fig. 25) the sun is nearest to us, and at A it is\\nmost distant. The motion in the parts of the orbit near P", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0064.jp2"}, "63": {"fulltext": "INEQUALITY OF SOLAR DATS. 49\\nwould therefore appear greater than in the parts near A, even\\nif it were uniform in all parts. But, besides this, as will be\\nshown in Chapter Till the motion is really greatest at P and\\nleast at A. For both these reasons, then, the sun, while in the\\nnearer half of its orbit, passes over the longest arcs each day\\nin the ecliptic that is to say, in longitude and the shortest\\narcs, in the half most distant from us. The sun, in fact, occu-\\npies nearly 8 days more time in describing the remote hah\\nthan the nearer one.\\nEecollecting, now, that a solar day consists of a sidereal day,\\nplus the time of describing diurnally the arc which the sun, in\\nthe mean time, advances annually, it is clear that if this daily\\narc is longer, the solar day is longer and if shorter, the solar\\nday is shorter.\\nSo far as this cause is concerned, therefore, the longest solar\\nday would be the 1st of January, and the shortest, the 1st of\\nJuly and about half-way from P to A, and from A to P, the\\napparent days would have their mean length.\\n81. Second cause of inequality in apparent solar days.\\nBut the solar days are unequal for another reason the ob-\\nliquity of the ecliptic to the equator. Time is measured by arcs\\nof the equator. But the sun s daily advance toward the east\\nis made in the ecliptic. Even if the daily increments of the\\nsun s longitude were equal, those of its right ascension would\\nbe unequal, and therefore the solar days unequal.\\nLet Fig. 29 repre ent a portion of the celestial sphere, AF\\na part of the equator projected in a straight line, OH a cor-\\nresponding part of the ecliptic, Q the vernal equinox, S the\\nsummer solstice, and P the north pole. Draw through P a\\nfew meridians, dividing that part of the ecliptic near Q into\\nshort arcs, to represent the daily increments of the sun s longi-\\ntude on CH, and of its right ascension on AF. These meri-\\ndians are oblique to CD, but perpendicular to AB. Hence, as\\nAQC is a right-angled triangle, QC is longer than AQ so also,\\nDQ is longer than BQ and thus each part of CD is longer\\nthan the corresponding part of AB that is, the increment!\\nof the sun s right ascension, near the equinoxes, are less than\\nthose of its longitude. The obliquity, therefore, by short-\\n4", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0065.jp2"}, "64": {"fulltext": "50 INEQUALITY OF SOLAR DAYS.\\nening these increments of right ascension, shortens the soja?\\ndays.\\nBat if meridians are drawn to that part of the ecliptic near S,\\nthe arcs GH and EF are abont parallel to each other, and the\\nincrements on the equator are not shortened, as they are at Q\\nBut, on the other hand, the divergency of the meridians causes\\nEF to be longer than GH, and each part of EF longer than\\nthe corresponding part of GH. At the solstices, therefore, the\\nincrements of right ascension are lengthened by the divergency\\nof the meridians, and hence the solar days are lengthened also.\\nAbout midway between the equinox and solstice, the two\\neffects just described neutralize each other, and the daily arcs\\nof right ascension, so far as this cause is concerned, are at their\\nmean value.\\nFig. 29.\\n82. Location of extreme and mean solar days from each\\ncause. Suppose the first cause alone in operation, and that the\\nsun and a uniform clock agree with each other at P (Fig. 25),\\non the 1st of January. Then, as the solar days are longer than\\ntheir mean, the sun becomes slower, compared with the clock,\\nfrom day to day, for about three months, when the days will\\nhave reached their mean length, at a point near half-way from\\nP to A. Afterward, the days being diminished below the\\nmean, the sun slowly gains on the clock, and catches up with it\\nat A, July 1st. But the days now being shortest of all, the sun\\nis immediately in advance of the clock, and most of all at a\\npoint half-way frcm A to P. The gain and loss compensate", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0066.jp2"}, "65": {"fulltext": "EQUATION OF TIME. 52\\neach other from A to P, as they did from P to A. Thus mean\\nand apparent time would agree twice in a year, at intervals of\\nsix months, if eccentricity of orbit were the only cause of\\nirregularity.\\nAgain, if the second cause alone existed, and we suppose the\\nsun and clock to agree at the equinox Q (Fig. 29), then the sun\\ngains on the clock every day, on account of the short arcs of\\nright ascension near Q. In about 1| months, however, the\\ndays reach their mean length, the sun begins to lose what it\\nhas gained, and at S, June 21st, the sun and clock are again to-\\ngether. But the sun is now losing, falls behind the clock, and\\nis furthest behind midway between the solstice and the next\\nequinox. The autumnal equinox and the winter solstice are, in\\nlike manner, points of time at which the clock and sun agree\\nwith each other. Thus, if the second were the only cause of\\n^regularity, the mean and apparent time would agree four\\ntimes in a year, at intervals of about three months each.\\n83. The equation of time. The difference between mean\\ntime and apparent time, on any given day, is the equation of\\ntime for that day. If the sun is slow, the equation must be\\nadded to the apparent time if fast, it must be subtracted from\\nit, in order to give mean time.\\nWe have seen by the two preceding articles that, on account\\nof eccentricity of orbit, the equation would be reduced to zero\\ntwice in a year and, on account of obliquity of ecliptic and\\nequator, it would be zero four times in a year. The joint effect\\nof these two causes is, to reduce the equation to zero four times\\nin a year, at unequal intervals of time.\\n84. The equation of time represented graphically. The\\nordinates of the curves in Fig. 30 exhibit to the eye the equation\\nof time as depending on each cause by itself, and on the two\\nconjointly. The relative lengths of the ordinates above and\\nbelow AB show the positive and negative equations, as caused\\nby eccentricity, and those on CD the equations as caused by\\nobliquity while the algebraic sum of these on each vertical\\nline, gives the resultant effect on the line EF. The figure\\nshows that the equation reaches its first maximum, 14\\nminutes, on the 11th of February; its first minimum, 4", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0067.jp2"}, "66": {"fulltext": "52\\nTHE JULIAN CALENDAR.\\nminutes, May 14th its second maximum, 6 minutes, July\\n2 6 tli and its second minimum, 16 minutes, November 2d.\\nThe four times of agreement, when the equation is zero, are\\nshown by the intersections they occur April loth, June 15th,\\nSeptember 1st, and December 24th. The sign shows that the sun\\nis on the meridian after mean noon, the sign before mean noon.\\nJan.\\nFeb.\\nMar.\\nApril.\\nMay.\\nFig\\nJune.\\n30.\\nJuly.\\nAug.\\nSept\\nOct\\nNcv.\\nDec.\\nA\\nC\\n14\\n6\\n^-4^\\n16\\n85. Civil and astro?wmical time. The mean solar day, when\\nemployed for civil purposes, is supposed to begin and end at mid-\\nnight, and is divided into hours, numbering from 1 to 12 a. m.,\\nand then from 1 to 12 p. m. But the astronomical day (which is\\nalso the mean solar day) begins and ends at noon, 12 hours\\nlater than the corresponding civil day, and its hours are counted\\nfrom 1 to 24. Thus, the astronomical date, April 12d. 20h., is\\nthe same as the civil date, April 13th, 8 o clock a. m.\\nS6. The Julian calendar. The period in which the sun\\npasses from the vernal equinox to the same point again, is\\ncalled the tropical year. In that period the round of the\\nseasons is exactly completed. The length of the tropical year\\nis 365d. 5h. 48m. 46.15s. This is so near 365i days, that in\\nthe adjustment of the calendar made by Julius Caesar (hence\\ncalled the Julian calendar), three successive years were made\\nto contain 365 days each, and the fourth 366 days. The addi-\\ntional day is called the intercalary day. In this calendar it\\nwas introduced by reckoning twice the 6th day before the", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0068.jp2"}, "67": {"fulltext": "THE GKEGOKIAN CALENDAR. 53\\nKalends of March and hence the year containing this addi-\\ntional day was called the bissextile. The intercalary day is\\nnow the 29th of February and the year containing such a day\\nis called leap-year,\\n87. The Gregorian calendar. By calling the tropical year\\n865^ days, the Julian calendar makes it more than 11 minutes\\ntoo long, and the intercalation of one day in four years is\\ntherefore too great. This excess amounts to more than 18\\nhours in a century. Hence, by dropping the intercalary day\\nthree times in four centuries, the adjustment is nearly complete.\\nThe Julian calendar, thus amended, is called the Gregorian\\ncalendar, because adopted under Pope Gregory XIII. At that\\ntime, 1582, the vernal equinox, by the error of the Julian cal-\\nendar, had fallen back to March 11th. To bring the equinox\\nto its proper date, 10 days were first dropped (the 5th being\\n\u00e2\u0080\u00a2called the 15th), and then the following system was adopted.\\nEvery year, not exactly divisible by 4, has 365 days.\\nEvery year, divisible by 4, and not by 100, has 366 days.\\nEvery year, divisible by 100, and not by 400, has 365 days.\\nEvery year, divisible by 400, has 366 days.\\nThe Gregorian calendar will not be correct perpetually, but\\nthe error will not amount to a day in 4,000 years.\\nThe nation of Eussia has not yet adopted the Gregorian cal-\\nendar, so that there is now a discrepancy of 12 days between\\ntheir dates and those of other nations. The reckoning still\\nused by them is known as old style, and is distinguished by\\nappending the letters O. S. to every date.\\n88. How to compare days of the month and of the week in\\npassing from one year to another. A common year of 365\\ndays contains 52 weeks and one day a leap-year contains 52\\nweeks and two days. Hence, a year usually begins a day later\\nin the week than the year previous. And, generally, any day\\nof any month is one day later in the week than the same day of\\nthe preceding year. Thus, July 4th, 1884, falls on Friday;\\n1885, on Saturday; 1886, on Sunday. But, in leap year,\\nthis rule applies only till the end of February. From that\\ntime to the same date in the year following, every day of a", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0069.jp2"}, "68": {"fulltext": "54 CENTRIFUGAL FORCE.\\nmonth falls two days later in the week than in the previous\\nyear. Thus, July 4th, 1883, is Wednesday 1884, Friday. And\\nFebruary 2d, 1884, is Saturday; 1885, it is Monday.\\nTable I., at the end of the volume, contains a complete cal-\\nendar for 77 centuries.\\nCHAPTEE YI.\\nCURVILINEAR MOTION. SPHEROIDAL FORM OF THE EARTH.\\nITS DENSITY. PROOFS OF ITS ROTATION ON AN AXIS.\\n89. Projectile and centripetal forces. Motion in a curve\\nline is always the effect of two forces one, an impuhe which,\\nacting alone, would have caused a uniform motion in a straight\\nline, and whose influence is always retained in the curve\\nmotion the other, a continued force, which constantly urges\\nthe moving body toward some point out of the original line ol\\nmotion. The first is called the projectile force, the other the\\ncentripetal force. If the action of the latter were to cease at\\nany moment, the body by its inertia would from that moment\\ncontinue uniformly in the direction in which it was then mov-\\ning. Such motion in the tangent may be regarded as the\\neffect of an impulse first given in the direction of that tangent.\\nThis supposed impulse is the projectile force for the moment in\\nquestion but it is in truth the resultant of the original im-\\nulse, and the infinite series of actions already produced by the\\ncentripetal force.\\nThe centripetal force may be resolved into two components\\none in the direction of the tangent, the other perpendicular to\\nit. The tangential component will accelerate or retard the\\nmotion in the curve according as it acts with the projectile\\nforce or in opposition to it. When the body moves in the cir-\\ncumference of a circle, the tangential component of the cen-\\ntripetal force is 0, and hence the motion is un form.\\n90. Centrifugal force, When a body moves in a curve,", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0070.jp2"}, "69": {"fulltext": "CENTRIFUGAL FORCE. 55\\nsince by its inertia it tends to proceed in the tangent at that\\npoint, there is a continual outward pressure directed from the\\ncenter of force: this is called the centrifugal force. It is\\nalways opposed to the centripetal force, and in circular motion\\nis always equal to it. It must not be viewed as a third force\\nintroduced to explain curvilinear motion, but as that compo-\\nnent of the projectile force which acts in opposition to the cen-\\ntripetal force.\\n01. First law of centrifugal force in circular motion.\\nWhen a body moves in a circular path, its centrifugal (or cen-\\ntripetal) force varies as the square of the velocity divided by the\\nradius. Let Ab (Fig. 31) v, the space passed over in one\\nsecond. The projectile force is then represented by AB, and\\nthe body would move in that line uniformly,\\nwere it not for the centripetal force acting\\ntoward E, and thus deflecting it into Ab. Aa\\nbeing the distance through which the body\\nfalls in one second, 2A# or c represents the\\ncentripetal force. Let AE r. Then Aa\\nv\\nAb Ab AD or ^-c v v 2r, and c\\nAs the centripetal and centrifugal forces are\\nequal in circular motion, c may represent either in value, though\\nthey are opposite in direction. Hence, in a given circle, where\\nr is constant, the force either toward or from the center varies\\nas v 2 the square of the velocity. In whirling a ball, for in-\\nstance, with a string of given length, if the velocity is doubled,\\nthe strain upon the string (the centrifugal force) is four times\\nas great, and the strength of the string (the centripetal force)\\nneeds also to be four times as great. So, if a train of cars goes\\nround a curve with a velocity 1J times that which is intended,\\nits tendency to be thrown from the track is increased 2J times.\\n93. Second law of centrifugal force in circular motion.\\nWhen the path of a body is circular, its centripetal or centrif-\\nugal force varies as the radius of the circle divided by the\\nsquare of the time of revolution.\\nLet t the time of describing the whole circumference 2jtr", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0071.jp2"}, "70": {"fulltext": "56\\nLOSS OF WEIGHT.\\nand let the velocity per second\\n%nr 4tt 2 r 2\\nt\\nr a 2rr 2 r\\nvaries as\\nTherefore 2nr i and\\nv\\n2\\n2\\nAa or ^c\\nBut (Art. 91) c f\\n4tT 2 7\\nwhich\\nHence, if the time of revolution is the same, the attraction to\\nthe center must be increased as the radius is increased for then\\ncoor. Thus, if a string is twice as long, it must have twice\\nthe strength, in order to whirl a ball at the same rate oi\\nrevolution.\\n93. Centrifugal force on the eartKs surface. As the earth\\nmakes its diurnal rotation, all free particles upon it are in-\\nfluenced by the centrifugal force. Let NS (Fig 32) be the\\naxis, and A a particle describing a circle with the radius A(X\\nIf AB, in the plane of that\\ncircle, represent the centrifugal\\nforce, resolve it into AD on\\nCA produced, and AF, tan-\\ngent to the meridian 1STQS.\\nThe effect of AD is to dimin-\\nish the weight of the particle, e\\nwhile the effect of AF is to\\nurge it horizontally toward the\\nequator. If the surface, then,\\nconsists of yielding matter, as\\nwater, the spherical form can\\nnot be retained, but the parts about the poles, N and S, will be\\ndepressed, and those about the equator, EQ, will be elevated.\\nAt each point between the pole and the equator, a particle is.\\nheld in equilibrium, by that component, AF, of the centrifugal\\nforce which urges it toward the equator, and that component\\nof gravity which urges it down the inclined surface toward the\\npole.\\n94. Loss of weight at the equator caused by rotation. Let\\nthe weight of a body, w, be taken to express the force ot\\ngravity, and let \\\\g 16^ feet) be the distance fallen through\\nby this body in one second. Kow, c is the force by which Aa", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0072.jp2"}, "71": {"fulltext": "LOSS OF WEIGHT AT EQUATOR. 57\\n2n 2 r\\n(Fig 31) is described in one second and Aa (Art. 92}\\nHence,\\nw c\\n\\\\g:\\n2ttV\\nc\\nw X\\nj2\\nUsing the values of the letters in the fraction, we obtain c, the\\ncentrifugal force, in terms of w, the weight of the body.\\nThe equatorial radius of the earth, r, is 3962.8 miles\\n20,923,584 feet.\\nThe earth makes one rotation in 24 sidereal hours 86,400\\nsidereal seconds. Reducing this to solar seconds (Art. 78), we\\nfind\\nc w X\\nt 86,164s. Hence,\\n4 x 3.14159 2 x 20,923,58 4 _w_\\n321 x 86,164 2 289*\\nAnd, since the centrifugal force at the equator acts directly\\nfrom the center, a body at the equator loses ^ig of its weight\\nby the rotation of the earth.\\n95. Loss of weight by rotation at other latitudes. Since c\\nvaries as r (Art. 92), the centrifugal force is greatest at the\\nequator, and zero at the poles, and the force at the equator\\nis to that at any latitude A (Fig. 32) as QC AO that is, as\\nrad cos lat. But, except at the equator, the centrifugal force\\ndoes not directly oppose gravity. If AB is the whole centrif-\\nugal force at A, AD is the component of it which acts agains*\\ngravity. But AB AD AC AO rad cos lat. So thai\\nthe loss of weight is diminished again in the same ratio as be-\\nfore. Tlierefore, the loss of weight at the equator is to that at\\nany given latitude, as rad 2 cos 2 of latitude.\\n96. Whole loss of weight at the equator. It is found by\\nobservations made with the pendulum, that the weight of a\\nbody at the equator is y^- less than that at the poles. But the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0073.jp2"}, "72": {"fulltext": "58\\nSPHEROIDAL FORM OF THE EARTH,\\nloss from centrifugal force is only ^ig. Subtracting this from\\nj-jL^, the remainder is very nearly 6 a loss of weight at the\\nequator which must be ascribed to some other cause. This\\ncause is the oblateness itself, by which the equator is more\\ndistant from the center than the poles are.\\n97. Spheroidal form of the earth found by measurement\\nNot only is the oblate form of the earth inferred from its rota-\\ntion on its axis, but the measurement of the length of a degree\\nof latitude, at various distances from the equator, proves that\\nthe meridians of the earth are ellipses, whose major axes are in\\nthe plane of the equator, and their common minor axis a line\\njoining the poles. If the meridians were circles, all the degrees\\nof latitude would be of the same absolute length, but it has\\nbeen ascertained, by numerous and most accurate trigometri-\\ncal surveys, that the length of a degree of latitude is least at\\nthe equator, and increases toward the poles. But if the degree\\nlengthens as we go toward the pole, then the radius must\\nlengthen in the same proportion, and therefore the curve, belong-\\ning to a larger circle, must become more flattened. And this\\nchange of curvature belongs to an ellipse, not to a circle. Thus,\\nat Q (Fig. 33) the degree is shortest, longer at K, still longer at\\nL, and so on to the pole.\\nThe center of the arc Q\\nis at A, nearer than the\\ncenter of the earth the\\ncenter of K is B, of L is\\nD, and of the polar arc\\nit is F, beyond the cen-\\nter C. Thus, the cen-\\nters of curvature of the\\nelliptical quadrant Q~N\\nlie on the curve ABDF,\\nwhich is the evolute of\\nthat quadrant. Each\\nmeridian quadrant is in\\nlike manner the involute of a curve, and their four evolutea\\nform the figure AFG-H about the center. Eo part of a meri-\\ndian has its center of curvature at the center of the earth.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0074.jp2"}, "73": {"fulltext": "MASS OF THE EAKTH.\\n59\\nThe following numbers express both the size and the form of\\nthe earth\\nEquatorial diameter\\nPolar diameter\\nMean diameter\\nDifference of diameters\\n7925.604 miles.\\n7899.100\\n7912.357\\n26.504\\nThe difference of diameters is ^^-g of the equatorial diani\\neter this is called the compression of the poles, or the ellip-\\niicity of the earth.\\nSo slight is the oblateness above described, that an exact\\nmodel of the earth could not be distinguished by sight or touch\\nfrom a perfect sphere.\\nThe volume of the earth (7912.357) 3 x g 259,400,000,000\\ncubic miles.\\n98. The equatorial belt. If we imagine a sphere con-\\nstructed on the polar diameter of the earth, the difference be-\\ntween the sphere and spheroid will be a sort of shell or ring,\\nthirteen miles thick at the equator, and growing thinner on\\nevery side to the poles. This is sometimes called the equa-\\ntorial ring or belt of the earth, and it produces sensible effects\\non the earth s relations to the moon and sun.\\n99. Weight and density of\\nthe earth. The earth s mass,\\nand therefore its density, can\\nbe obtained by comparing the\\neffects produced upon a plumb-\\nline, by the earth and a moun-\\ntain of known weight. Let M\\n(Fig. 34) be an abrupt moun-\\ntain situated alone on a plain,\\nand let a station, B, be selected\\non the north side of it, and an-\\nother, D, in the same meridian,\\non its south side, for measuring\\nthe zenith distances of stars. If\\nFig. 34.\\nB-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0075.jp2"}, "74": {"fulltext": "60 DIUKtfAL KOTAT10N.\\nthe mountain were not present, the plumb-line of the zenith\\nsector would hang in the lines B and D, and would mark E\\nand G as the zeniths of the stations. But the attraction ui\\nthe mountain draws the plumb-line toward it, so as to joint to\\nthe false zeniths E and G When the star S, therefore,\\nculminates, its apparent zenith distance, SE is measured at\\none station, and at another culmination, SG is measured. The\\ndifference, SE SG is the distance between the apparent\\nzeniths. The distance, EG, between the true zeniths, is the\\nsame as the difference of latitude between the stations B and\\nD. Let a trigonometrical survey, therefore, be made around\\nthe mountain, and thus the arc BD, or its equal EG, be found.\\nE G EG the sum of the two angles by which the plumb-\\nline is drawn from a vertical position at the two stations.\\nThe volume and density of the mountain being measured, and\\nthe angle being found, as above, by which it draws a plumb-\\nline from a true vertical, we have the means of determining\\nthe mass of the earth. And, as its volume is known, its\\ndensity is inferred. Observations of this kind were made near\\nMount Schehallien, Scotland, by Dr. Maskelyne, who found\\nthe deviation of the plumb-line to be a little more than 6\\nThe mean density of the earth, as deduced from a great\\nnumber of results, obtained by this and other methods, is 5.46,\\nthat is, the earth, as a whole, is 5.46 times the weight of the\\nsame volume of water. Calling the weight of a cubic foot of\\nwater 62^ lbs., the weight of the earth is somewhat more than\\n6,000,000,000,000,000,000,000 tons.\\n1 OO. Proofs of the earth? s diurnal rotation.\\n1. To suppose the earth to rotate eastward on its axis, is the\\nonly reasonable way of explaining the fact, that all the mill-\\nions of fixed stars, at various and immense distances from us,\\nin large and in small circles of the sphere, perform their ap-\\nparent revolutions about us in precisely the same length of time\\nviz., one sidereal day.\\n2. Without supposing the earth to rotate on its axis, we can\\nnot account for the oblate form, of the waters of the ocean.\\nWhatever form the solid parts might have, the movable portion\\nwould be spherical, if the earth were at rest. Moreover, the", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0076.jp2"}, "75": {"fulltext": "ROTATION OF THE EARTH. 61\\ndegree of oblateness is exactly that which is required on a\\nsphere having the diameter and mass of the earth, if it be sup-\\nposed to rotate once in 24 hours.\\n3. The weight of a body at the equator, compared with that\\nat the poles, is too small to be wholly accounted for by in-\\ncreased distance. Centrifugal force, arising from rotation, can\\nalone explain the remaining difference.\\n4. A body dropped from a great height strikes further east\\nthan the vertical line in which it began to fall. If the earth\\nrotates, the top of a tower moves faster than the base and\\ntherefore a body let fall from the top, retaining the east-\\nward motion of that point, will strike further east than the-\\nbase. At the equator, this distance would be near 2 inches,\\nfor a fall of 500 feet. Numerous experiments on the fall of\\nbodies through great distances have been very carefully made\\nby different individuals, and in different latitudes. And they\\nall concur in proving that a body in falling deviates from a\\nvertical line toward the east.\\n5. It is jxroved by the vibrations of a pendulum that the\\nearth rotates eastward. Let us suppose a weight to be sus-\\npended by a long fine wire, and then made to vibrate in a\\nplane. The plane in which the wire and weight move is ver-\\ntical, and passes through the point of suspension. The weight\\nitself may be considered as describing a straight horizontal line.\\nOn account of inertia, the weight tends to keep always in the\\nsame line, or (if the point of suspension be moved) in a line\\nparallel to itself. And it will always remain strictly parallel tc\\nitself, provided it can at the same time remain horizontal, and\\nin a vertical plane passing through the point of suspension.\\nThus, if at the equator the weight be made to vibrate north\\nand south that is, in the plane of a meridian\u00e2\u0080\u0094 it will continue\\nto do so without deviation, as the earth rotates eastward, be-\\ncause it will thus remain moving horizontally in a plane which\\npasses through the point of suspension, though that plane is\\ncontinually changing. In this case, the lines in which the\\nweight vibrates are all parallel among themselves.\\nIf the experiment be tried at the pole, and the weight be\\nmade to vibrate in the plane of a certain meridian, the point of\\nsuspension does not move from its place, but only revolves in", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0077.jp2"}, "76": {"fulltext": "-62 FORM OF THE SUN.\\nit and while the earth revolves 15\u00c2\u00b0 per hour, the weight pre-\\nserving its own plane of vibration, will seem to shift that plane\\n15\u00c2\u00b0 per honr in the contrary direction, keeping pace with the\\nstars in their diurnal motion.\\nAt localities between the equator and the pole, the line oi\\nvibration remaining horizontal, and in a vertical plane which\\npasses through the point of suspension, can not at the same time\\npreserve its parallelism. But it will come as near fulfilling\\nthis condition as possible. Its north extremity will deviate\\neastward from the meridian more or less, according as it is\\nnearer the pole or the equator. It is proved that the deviation\\nper hour is to 15\u00c2\u00b0 as the sine of latitude to radius.\\nWhen experiments are performed with sufficient care, it is\\nfound that the pendulum actually deviates eastward from the\\nmeridian, and at a rate corresponding well with the calculated\\nresult. The pendulum thus furnishes evidence that the earth\\nrotates on its axis.\\nThe above is known as Foucault s experiment.\\n6. It will be seen hereafter that the motion of the equinoc\\ntial points toward the west, called the precession of the equi\\nnoxes, affords an independent proof of the earth s diurnal\\nmotion.\\nCHAPTEK VII.\\nTHE SUN. SOLAR SPOTS. CONDITION OF THE SUN S\\nSURFACE. THE ZODIACAL LIGHT.\\n101. The form of the sun. The disk of the sun is always\\ncircular. And, as it presents all sides toward us in its rotation,\\nwe infer that its form must be spherical. But since it rotates\\non an axis, and its surface is hi a fluid state, it might be ex-\\npected to reveal a spheroidal form. The reasons why it does\\nnot are, that the force of gravity on the sun is very great, and,\\nin consequence of the slowness of its rotation, the centrifugal\\nforce is small. It appears by calculation that the angle sub\\ntended by the equatorial and the polar diameters can not differ", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0078.jp2"}, "77": {"fulltext": "DIMENSIONS OF THE SUN. 63\\nfrom each other, except by a small fraction of a second. Its\\noblateness is, therefore, too slight to be perceived.\\n102* Distance of the sun, and size of the earth s orbit.\u00e2\u0080\u0094*\\nThe sun s horizontal parallax is 8. 848. Therefore, the distance\\nof the sun from the earth is found (Fig. 4) by the proportion.\\nsin 8. 848 rad 3962.802 92,381,000-;\\nwhich is the distance in miles from the earth to the sun.\\nThe circumference of the earth s orbit, or the distance trav\\neled by the earth each year, is\\n92,381,000 x 2?r 580,447,000 miles.\\n1 03. Velocity of the earth on its axis and in its orbit coin-\\npared. In the diurnal motion, a place on the equator describes\\nnearly 25,000 miles in 24 hours that is, more than 1,000\\nmiles per hour, or about 17 miles in a minute. In the annual\\nmotion, the earth describes 580,447,000 miles in 365J days,\\nthus passing over a distance of 1,589,000 miles each day;\\nwhich is about 1,103 miles in a minute, or 18.393 miles in a\\nsecond. The earth s velocity in its orbit is about 65 times as\\ngreat as that of the equator in the diurnal motion.\\n1 04. To find the dimensions of the sun. The angle sub-\\ntended by the sun s diameter may be measured by instruments.\\nLet AES (Fig. 35) equal one-half the measured angle. Then\\nwe have rad sin AES ES AS, the semi-diameter of the\\nsun. As the sun s mean apparent semi-diameter is 16 2 and\\nES is 92,381,000 miles, we find the sun s radius near 430,855,\\nand therefore its diameter 861,710 miles.\\nFig. 35.\\nThe sun s diameter is about 109 times that of the earth.\\nAnd, since spheres vary as the cubes of their diameters, tho\\nvolume of the sun to that of the earth is as\\n109 3 l 3 1,295,000 1, nearly.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0079.jp2"}, "78": {"fulltext": "64 DIURNAL ROTATION OF THE SUN.\\n1 05. The surfs mass and density. It is found, by methodi\\nto be described hereafter, that the sun does not exceed the\\nearth in mass nearly so much as it does in volume. While\\nthe volumes are as 1,295,000 1, the masses are about as\\n326,800 1.\\nThe density of the sun, therefore, is to that of the earth a?\\n326,800 1,295,000 1 4, nearly.\\n106. Force of gravity at the surface of the sun. \u00e2\u0080\u0094When\\nthe relative masses and diameters of bodies are known, it is\\neasy to find the relative force of gravity on their surfaces. For\\nG oo (TS at. Phil., Art. 16), where G represents gravity, Q\\nthe mass of the body, and D its semi-diameter. Let W repre-\\nsent weight at the earth, and W at the snn, and we have\\nW W -1 S 1 27.5. Hence, the weight of a body\\nat the sun is 27.5 times as great as at the earth, and a body\\nwould fall 442 feet in the first second of its descent.\\n107. Diurnal rotation of the sun. By observations on the\\nsolar spots, it is found that the snn rotates on its axis nearly in\\nthe same direction in which the earth revolves about the sun.\\nIn general, a spot which appears on the edge of the disk passes\\nacross, then disappears, and afterward reappears in the same\\nplace as at first in 27^ days. If the earth were at rest, this\\nwonld be the period of the sun s 36\\nrotation on its axis. But, as the\\nearth revolves in nearly the same\\ndirection in its orbit, the appa-\\nrent rotation of the snn is longer\\nthan its real rotation. In Fig.\\n36, suppose the earth to be sta-\\ntionary at E, and that a spot on\\nthe sun appears on the diek at\\nA. Then, after passing through\\nB, D, H, it will appear again at\\nA, at the end of one revolution. ^e F\\nBut, if the earth in the mean time moves on to F, the* the", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0080.jp2"}, "79": {"fulltext": "APPEARANCE OF THE SOLAR SPOTS. 65\\nspot must pass over AB, in addition to one revolution, before\\nit will be seen on the edge of the disk. As EC is perpendicu-\\nlar to AD, and FC to BH, the corresponding arcs on the two\\ncircles are obviously similar. Therefore, EGE EF EGE i\\nADA AB ADA. Instead of the arcs, we may use the\\ntimes of describing them and then we have 1 year -f 27^\\ndays 1 year 2T| days 25 days, 8-J hours, which is the\\nperiod of the sun s rotation. Appendix A.\\n108. Position of the sun s equator. If the solar spots al\\nways described their paths across the disk in apparent straight\\nlines, it would be inferred that the sun s equator coincides\\nwith the plane of the ecliptic. But these lines appear straight\\nonly twice in the year, near the middle of June and of December.\\nAt other times, they appear as semi-ellipses, having the greatest\\nbreadth in March and September. The earth, therefore, passes\\nthe plane of the sun s equator in June and December. The\\ninclination of the sun s equator to the plane of the ecliptic is\\nfound to be about 7i\u00c2\u00b0.\\n109. Appearance of the solar spots. On examining the\\nsun s disk with a telescope, there is usually seen a greater or a\\nless number of dark spots, differing from each other in form\\nand size, and each spot generally consisting of two distinct\\nparts, called the macula, or nucleus, and the umbra. The\\nmacula is black, of irregular form, and commonly surrounded\\nby the umbra, which has a lighter shade. The two parts of\\nthe spot do not often shade into each other, but are each\\nmarked by a sharp, though irregular outline. If watched from\\nday to day, they are seen not only to move slowly across the\\ndisk, as already stated, but they change their form and general\\nappearance. A large spot sometimes divides into two or more\\nsmaller ones and again a group unites into a single large spot.\\nSometimes a spot diminishes and disappears, first the macula,\\nthen the umbra. The reverse also happens a spot is seen in\\nthe midst of the disk, where there was none the day before.\\nThough only a few are commonly in sight at once, yet they have\\nbeen, in some instances, counted by tens and even hundreds.\\nVery rarely a spot is so large as to be seen by the naked eye.\\n5", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0081.jp2"}, "80": {"fulltext": "bb RELATION OF SPOTS TO SURFACE LEVEL.\\nFigure 37 (lower part) shows two views of the same grou|;\\nas seen July 9th and 11th, 1 844.\\nFig. 37.\\n110. The spots are at the surface, and limited to a northern\\nand a southern zone. Each spot appears on the disk during one-\\nhalf the time of its entire revolution. It must, therefore, be at\\nthe surface, and not at any distance from it. For, if it revolved\\nat any distance from the surface, as in the orbit abc (Fig. 35),,\\nthen it would be seen on the disk only from a to h, which is\\nless than half its orbit.\\nBut the spots do not pass across all portions of the disk;\\ntheir paths are limited to a zone which extends not more than\\n35\u00c2\u00b0 on each side of the equator and with very few exceptions,,\\nthey lie in the outer, rather than the central parts of this zone.\\nSpots are very rarely seen within the zone lying between 10\u00c2\u00b0\\nof north and south latitude; and still more rarely in the polar\\nzones above latitudes 35\u00c2\u00b0 north and 35\u00c2\u00b0 south. The macular\\nzones, as they are sometimes called, are represented in Figure\\n37, limited by the dotted lines, EQ being the equator.\\n111. Relation of the spots to the surface level. If the spots\\nwere flat surfaces on the same level with the general surface\\nof the sun, then all their parts would be foreshortened alike,", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0082.jp2"}, "81": {"fulltext": "THE RECEIVED THEORY. 67\\nwhen near the edges of the disk. If they were elevated ob-\\njects, as mountains, rising above the solar atmosphere, then the\\numbra nearest the edge of the disk would be hidden by the\\ndarker part, and on the edge the spot would appear as a pro-\\ntuberance.\\nBut it is proved, by multiplied observations, that the spots\\nmust be degressions below the general surface, and the macula\\na deeper depression than the umbra. For, as a spot approaches\\nthe edge, while it is foreshortened by perspective, the umbra\\nfurthest from the edge disappears first, and then the macula\\nitself, while that part of the umbra nearest the edge is still in\\nsight. As a spot comes from the edge toward the central part\\nof the disk, the order of appearances is* reversed. These\\nchanges are indicated in Fig. 37, upper zone. Appendix B.\\nIIS. The general surface, The luminous part of the sun s\\nsurface is not uniform, nor at rest. Every portion of it is mi-\\nnutely mottled by spots and streaks of unequal illumination.\\nThese are called facidce. And continued observation shows\\nthat these faint inequalities are also undergoing incessant\\nchanges. The faculse are most strongly marked, and indicate\\nthe greatest agitation of surface, where a spot is about to ap-\\npear, or where one has recently disappeared. Appendix C.\\n113. The received theory. No theory so well explains the\\ntelescopic appearances of the sun, as that which in substance\\nwas proposed by Sir William Herschel, in 1801. Whatever\\nmay be the condition of the central mass, the external surface,\\ncalled the photosphere, consists of gas in an incandescent state,\\nwhile below it, within the solar atmosphere, is a cloudy\\nstratum, less luminous than the outer surface. Whenever,\\nfrom any cause, a rent is made in the photosphere, the less\\nluminous stratum below is seen through it, as the umbra of a\\nspot; and a smaller rent in the lower stratum reveals the\\ndenser and darker part of the sun, as the macula of the same\\nspot. The strata in which the rents occur are in a gaseous\\ncondition for the constant motions going on in the outlines\\nof the spots, forbid the supposition that they consist of solid\\nmatter and the extreme rapidity of these motions, often more", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0083.jp2"}, "82": {"fulltext": "68 THE ZODIACAL LIGHT.\\nthan 1,000 miles per day, is inconsistent witA the idea thai\\nthey are liquid.\\n114. The tody of the sun not necessarily dark. The very\\ndark appearance of the macula may be due to its strong con\\ntrast with the intense illumination of the general surface.\\nFor it is found by experiment that the brightest artificial light\\nwhich has been produced, if placed between the eye and the\\nsun, appears as a dark spot compared with the solar surface.\\n115. Cause of the spots. Sir John Herschel has suggested\\nthat there are reasons for considering the equatorial regions of\\nthe sun to be more heated than the other portions, so that there\\nare currents in the solar atmosphere analogous to the trade-\\nwinds on the earth. Resulting from these currents, he sup-\\nposes that occasional local winds are produced, rotating on a\\nvertical axis, and rending the atmosphere and clouds by their\\ncentrifugal force. The ruptures thus occasioned are the spots\\non the sun.\\nThis supposition derives considerable plausibility from the\\nconsiderations, that the spots are limited to narrow zones a little\\ndistance from the equator; that they sometimes differ from\\neach other in their motions across the disk and that, in a few\\ninstances, they have shown signs of rotation about their own\\ncenters. Appendix D.\\n116. Periodicity of the spots. The number and size of\\nspots vary exceedingly in different years. Sometimes for days\\nand weeks none are to be seen and again, for many months,\\nthe disk is never free from them. It is noticed, of late years,\\nthat their frequency alternately increases and decreases during\\na period of 10 or 11 years. The years in which the greatest\\nnumber has been seen of late, were 1870, 1882. And those in\\nwhich there were fewest, were 1867, 1878. Appendix E.\\n117. The zodiacal light. This name is given to a faint, ill-\\ndefined light, extending along the zodiac, either in the west,\\nafter sunset, or in the east, before sunrise. It so much resem-\\nbles the twilight, that it is not ordinarily noticed, because it", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0084.jp2"}, "83": {"fulltext": "KEPLER S LAWS.\\n69\\nappears as a mere upward extension of it. It is projected on\\nthe sky as a triangle, inclined to the horizon at the same angle\\nas the ecliptic (Fig. 38). In the\\nevening it is best seen at the\\nseason when the ecliptic is most\\nnearly perpendicular to the ho-\\nrizon, after twilight has ceased.\\nIt is therefore most conspicu-\\nous at evening in the month\\nof February. When the air\\nis clear, and there is no moon,\\nit is visible till after 9 o clock.\\nFor a like reason, the best\\ntime for seeing it before morn-\\ning twilight is the month of\\nOctober. The apparent extent\\nbreadth and\\nincreased by\\nof it, both in\\nheight, is much\\nindirect vision.\\n118. Its nature. There has been much speculation rela-\\ntive to the nature of the zodiacal light. But astronomers gen-\\nerally regard it as a nebulosity attending the sun, and extend-\\ning beyond the orbits of Mercury and Venus, and even beyond\\nthe orbit of the earth.\\nCHAPTER VIII.\\nKEPLER S LAWS. THE LAW OF GRAVITATION.\\n119. Statement of Kepler s laws. From a long and labo-\\nrious examination of the recorded observations of Tycho Brahe,\\nKepler deduced three laws relating to the movements of the\\nplanets about the sun. They are hence called Kepler s laws,\\nand may be stated as follows.\\n1. The areas described about the sun by the radius vector of\\nan orbit, vary as the times of describing them.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0085.jp2"}, "84": {"fulltext": "70\\nLAW OF AREAS.\\n2. The orbit of every planet is cm ellipse, having the sup. in\\none focus.\\n3. The squares of the periodic times of the several planets\\nvary as the cubes of their mean distances.\\nTo render the language of the third law strictly correct, the\\ncube of the distance should be divided by the sum of the masses\\nof the sun and planet. But the mass of even the largest planet\\nis so small, compared with the sun, that the omission intro-\\nduces an error which is scarcely appreciable.\\nKepler established these three laws as facts in the solar\\nsystem but Newton afterward demonstrated, by mathematical\\nreasoning, that they are necessarily involved in the laws of in-\\nertia and gravitation.\\n120. Areas described by the radius vector. Whatever path\\na body describes under the influence of a projectile and a cen-\\ntripetal force, the areas described about the center of force vary,\\nas the times of describing them.\\nLet S (Fig. 39) be the center of attraction, and suppose the\\nprojectile force in the line YE, to be such as to cause the body\\nto pass over the equal spaces PQ, QR, etc., each in a certain", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0086.jp2"}, "85": {"fulltext": "LAW OF VELOCITY IK AN ORBIT. 71\\nemit of time. When the body reaches Q, let the action\\ntoward S be sufficient to move it over QY in the same time\\nin which by the original impulse it would describe QR. Then\\nit will in the same time describe the diagonal QC of the par-\\nallelogram. Jo\u00c2\u00a3n ES and CS. The triangles QSC and\\nQSR are equal but QSR QSP QSC QSP that is,\\nthe areas described in the first and second units of time are\\nequal. In like manner, by supposing a second action toward\\nS to occur at C, a third at D, etc., it is proved that QCS, CDS,\\nDES, etc., which are described in equal times, are equal. This\\nis true, however small the unit of time between the successive\\nactions toward S, and is therefore true when the central force\\nacts incessantly and causes curvilinear motion. As all the\\nareas are equal, which are described in the several units of\\ntime, therefore the areas vary as the times.\\nAs the diagonal of each parallelogram is in the same plane\\nwith its two sides, it is obvious that the whole orbit lies in one\\nand the same plane.\\nConversely, if areas described about a point vary as the\\ntimes, the deflecting force acts toward that point. For\\nPSQ QSE, as before (Fig. 39) and by supposition, PSQ\\nQSC QSC QSR hence CR is parallel to QS, and QC is\\nthe diagonal of a parallelogram, whose side QY, in which the\\ndeflecting force acts, is directed toward S.\\nSince it is an established fact, agreeably to Kepler s first law,\\nthat the radius vector of each planetary orbit describes areas\\nabout the sun, which vary as the times; therefore, the cen-\\ntripetal force, acting on the planets, is directed toward the sun.\\n121. The law of velocity in an orbit. The velocity at any\\npoint varies inversely as the perpendicular from the center of\\nforce to the tangent at that point.\\nLet ST (Fig. 39) be perpendicular to PQ then the area\\nrSPQ =iPQ x SY, which varies as PQ x SY; PQ oo\\nBut PQ oo Y, the velocity at P and the area SPQ is constant;\\nV* oyj or the velocity varies inversely as the perpendicu-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0087.jp2"}, "86": {"fulltext": "72\\nLAW OF GKAVITATICXN.\\nlar from S, upon the line in which the body is moving; in\\nother words, upon the tangent of its path, if it describes a\\ncurve.\\n122. Law of gravitation in an orbit, as related to dis-\\ntance. If a body describes an elliptical orbit, by a centripetal,\\nforce which acts toward the focus, that force varies inversely a\\nthe square of the distance.\\nFig. 40.\\nLet the body be at M (Tig. 40), and MF the radius vector at\\nthat point. Let MO be the radius of curvature at M, and.\\ntherefore perpendicular to the tangent and suppose M^N to be\\nan infinitely small arc described in a given small portion o\u00c2\u00a3\\ntime. Draw FP perpendicular to the tangent MP, KK to\\nFM, and NH to MO then PFM, MHI, KNI are similar tri\\nangles. ME considered as a straight line, is described by the\\njoint action of the centripetal force in the line MI, and the\\nprojectile force which is parallel to IN. The motion in MI\\nmay be regarded as uniformly accelerated, because in the in-\\nfinitely small time of describing it, the centripetal force may\\nbe considered constant. Hence, 2MI may be taken as the\\nmeasure of the centripetal force f (ISTat. Phil., Art. 28).\\nTherefore, f c\u00c2\u00a9 MI. It is to be proved that MI qo r^.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0088.jp2"}, "87": {"fulltext": "LAW OF GKAVITATION. 73\\n123. By similar triangles, MI MH XI NK;\\nNI\\nflow, the chord MN is a mean proportional between tha\\nTVTNT 2\\nversed sine MH and the diameter 2MO or MH oiuTj\\nNil 2\\nbut, as the arc is infinitely small, NH MIST MH o]v/r(V\\nAgain, the versed sine MH, and therefore HI, is infinitely\\nsmall compared with NH, and NI may be substituted for NH\\nMH Sro-\\n124. Now it is shown in conic sections, that r\\nmKJ 2 V FP/\\nFM NI\\ntherefore, since by similar triangles -^p -Sxt??\\nM0 =*ffiY\\n2VJSTK/\\nSubstituting this for MO in the equation for MH above, we have\\nMH m\\nNI\\nHence, in the equation for MI we have\\nEK 3 NI 1_ T _\u00e2\u0096\u00a0\\nMI T x NK.\\nj? ]NI M jp\\nNow, the sector FMN is measured by JFM NK NK\\nJackson s Conic Sections. The same may be derived from Coffin s Conic\\n(FM MV) 3\\nSections, Pr. V., Curvature, R 2 or MO v a and b being tlie semi-\\n1 3 3\\naxes; MO x (FM. MV) 2 Multiply by 2 2 and divide by its equal\\n(FP VL)s JkenMO L 2 (|^j 2 since FMP and VML\\nare similar. But MO f f p", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0089.jp2"}, "88": {"fulltext": "74 LAW OF GRAVITATION.\\n2FMN AT1Z2 4FMN 2 __. 4FMN 2 _ t \u00e2\u0096\u00a0_\\n-^j- and NK 2 -j^-; MI w But as the\\nareas described by the radius vector vary as the times, FMN ia\\nconstant. Therefore,\\nMI(=/)co^;\\nthat is, the centripetal force in the orbit varies inversely as the\\nsquare of the distance.\\n125. Applicable to every conic section. It is thus proved\\nthat, in any elliptical orbit described about the focus as the\\ncenter of attraction, the intensity of that attraction varies in-\\nversely as the square of the radius vector. As there is nothing\\nin the foregoing demonstration to limit the conclusion to the\\norbits which are nearly circular, like those of the planets, we\\nare at liberty to apply it to orbits of extreme eccentricity, as\\nthose of the comets. And it is proved by Newton, in his Prin-\\ncipia, that the same law of force is necessary, in order that a\\nbody may describe any one of the conic sections about its focus\\nas the center of attraction.\\n126. Law of gravitation as to distance, in different or-\\nbits. And not only does this law prevail in all parts of any\\none orbit, but it is true also that all the different bodies of a\\nsystem, describing orbits about the same center of force, are\\nurged toward that center by attractions which vary, from one\\norbit to another, inversely as the square of the distance.\\nLet a be the semi-major, and b the semi-minor axis of any\\nelliptic orbit. Then a is the mean distance of all points of the\\norbit from the focus. By a rule of mensuration, the area of\\nthe ellipse nab. If s the area described by the radius\\nvector in a unit of time, as one second, and t the number of\\nseconds in the whole period of revolution, then the ellipse also\\nts. Therefore, nab is and t and f By\\n27 2 7 2\\nKepler s third law (Art. 119), tfao a 3 \u00e2\u0080\u00945- 00 a z op s\\\\\\ns a\\nBut, because the semi-parameter is a third proportional to", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0090.jp2"}, "89": {"fulltext": "LAW OF GRAVITATION.\\n75\\nthe semi-axes a and\\nfoes.\\nHence, substituting\\nfor s 2 that is, FMN 2 in the equation for MI (Art. 124), we\\nfind MI\\n4FMN 2 2/y 2\\n^.FM^FM 2\\n.-./.oo\\nOr, the\\njp FM 2 jp. FM 2 FM 2 J FM 2\\nforce varies inversely as the square of the distance, in different\\norbits, as well as in different parts of the same orbit.\\nThe satellites which revolve about the planets are found to\\nconform to Kepler s laws, and therefore the force which urges\\nthem toward their respective primaries varies in each case in-\\nversely as the square of the distance.\\n127. Law of gravitation within small distances. But the\\ninquiry still remains, does the law of gravity, as demonstrated\\nin the foregoing articles, hold good at the smallest distances\\nalso For example, do the tendencies of bodies resting on the\\nearth, and of those elevated in the air, and of the moon toward\\nthe earth s center, come under the same general law This is\\nthe very question which presented itself to the mind of New-\\nton, after he had discovered that the force which deflects the\\nplanets from their lines of motion toward the sun, varies in-\\nversely as the square of their distance from it. As he noticed\\nthe fall of an apple, the inquiry arose, may not this fall be of\\nthe same nature as the lending of the moon s path toward the\\nearth, and may not the force in the two cases be as the squares\\nof the distances inversely\\nThe distance through which the\\nmoon actually descends in one second\\nmay be represented by Ka (Fig. 41),\\nA o being the arc described in the same\\ntime. For, as the moon was going\\ntoward B, it would not have deviated\\nfrom the line AB, if some force had\\nnot turned it aside. This influence\\nmust be directed toward the earth, E,\\nbecause it is about E that the radius\\nis known to describe areas propor-\\ntional to the times (Art. 120). There*-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0091.jp2"}, "90": {"fulltext": "76 LAW OF GKAVITATTON.\\nfore, Bh, or the versed sine Aa (which may be considered equal\\nto it), is the distance fallen through in one second. Now, the\\ncircumference of the moon s orbit, divided by the number of\\nseconds occupied in describing it, gives the arc Ah. This arc\\nand its chord may be considered the same, and by geometry\\nwe have 2 AE Ah Ah Aa 0.0535 of an inch.\\nAt the surface of the earth, a body falls 1 6^ feet in the\\nfirst second. On the supposition that gravity varies inversely\\nas the square of the distance, we find the fall in one second at\\nthe moon, by the proportion, the square of the moon s dis-\\ntance square of the earth s radius 16^ feet 0.0536 of an\\ninch, agreeing very accurately with the distance which the\\nmoon actually falls from a tangent in one second. Therefore,\\na body falling at the surface of a planet, and a satellite revolv-\\ning about it, are both subject to the same law of centripetal\\nforce.\\n128. The law prevails throughout the solar system. As\\nwill appear hereafter, there are numerous disturbances pro-\\nduced upon the motion of each body in the system by the\\nattraction of every other. Every one of these disturbing influ-\\nences is measured, by applying the law of distance already men-\\ntioned. If a planet or comet moves toward a plauet for a\\ncertain length of time, it is accelerated and its acceleration is\\ngreater, as the square of the distance is less and it is retarded*\\naccording to the same law, when departing from it.\\n129. The law of gravitation, as related to the quantity of\\nmatter. The force of gravity varies directly as the quantity ot\\nmatter. In Mechanics, we infer the existence of this law from\\nthe fact that all bodies, light and heavy, and of every kind ot\\nmaterial, fall with equal velocity toward the earth. So, in the\\nsolar system, a planet and all its satellites, when at equal dis-\\ntances from the sun, are urged toward it by forces proportional to\\ntheir masses, or they could not maintain their mutual relations\\nas they do. And it is found that every disturbing influence in\\nthe system is accounted for only by applying both parts of the\\nlaw of gravity that it varies directly as the quantity of matter\\nand, inversely as the square of the distance.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0092.jp2"}, "91": {"fulltext": "PATHS OF PROJECTILES.\\n77\\n130. Paths of projectiles considered as orbits. When a\\n6tone is thrown, or a ball is fired, its path (undisturbed by the\\natmosphere) is part of an elliptic orbit, one of whose foci is at\\nthe center of the earth. In Mechanics, the path of a projectile\\nis proved to be a parabola (Nat. Phil., Art. 44) but, in that\\ndemonstration, the vertical lines were assumed to be parallel\\nto each other, and the force of gravity a constant force, neither\\nof which is strictly true. Knowing the distance and period of\\nthe moon, the time in which a projectile would complete its\\nrevolution if. found by Kepler s third law. Any force, which\\nman could apply, would carry the lower extremity of the orbit\\nso little beyond the center of the earth, that the mean distance\\nmight be. called one-half the radius of the earth. Therefore,\\ncalling the moon s distance 60 radii, and its period 27J days,\\nwe have (60) 3 3 (27J) 2 x% from which x is found to be\\nabout 31 minutes. Every projectile, then, if it were free to\\ncomplete its orbit unobstructed, and according to the law of\\ngravity which prevails outside of the earth, would make an en-\\ntire revolution, and return to its place, in about half an hour.\\n131. Effect of increased velocity of projection. Suppose\\nthat P (Fig. 42) is a point near the earth, ADE, and that the\\nvelocity of projection, in the direction PB, is so greatly in-\\ncreased that the projectile strikes the earth at D. By a still\\ngreater increase of velocity\\nit might meet the earth at E.\\nIn these cases the earth s\\ncenter would be in the most\\nremote focus of the orbit.\\nBut if we suppose the velo-\\ncity so much increased that\\nthe centrifugal force just\\nequals the force of gravity,\\nthen the body would de-\\nscribe the circular orbit PFG\\n(Art. 90). As the mean dis-\\ntance now equals the radius\\nof the earth, the time of revolution is found, by Kepler s third\\nlaw, to be lh. :4m. 39s. Any increase of the velocity of pro-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0093.jp2"}, "92": {"fulltext": "78 MOTIONS OF SUN AND PLANET.\\njection beyond this will again produce an ellipse, as PK.\\nwhose nearer focus is at the earth s center. And we can\\nimagine the velocity increased till the ellipse becomes one ol\\nextreme eccentricity, and then changes into the branch of a\\nparabola, and then of a hyperbola, in which last cases the body\\nwill never commence a return toward the earth.\\n132. Orbit motion and diurnal rotation by one impulse.\u00e2\u0080\u0094\\nIf we suppose the projectile motion of the earth, or any other\\nplanet, to have been produced by a single impulse, that im-\\npulse may also have caused the diurnal rotation of the body.\\nIf the impulse had been directed in a line passing through the\\ncenter of gravity of the planet, then it would have caused a\\nprogressive motion without rotation on an axis. But, if the\\nline of impulse did not pass through the center of gravity,\\nthere would be rotation as well as progression. It has been\\ncalculated that the two existing rotations of the earth might\\nhave been produced by one impulse, applied in a line which\\npasses 24 miles from the earth s center, on the side most\\nremote from the sun.\\nHad it been directed through a point lying on the side\\nnearest the sun, the diurnal motion would obviously have been\\nretrograde.\\n133. Motions of sun and planet, resulting from an impulse\\ngiven to the planet. Suppose that the sun at S (Fig. 43), and\\nthe earth at E, mutually attract each other, and that an im-\\npulse is given to E in a line perpendicular to ES. S can not\\nremain stationary and E revolve about it for it is proved (Nat.\\nPhil., Art. 89) that their center of gravity will move precisely\\nas the sum of the bodies would move if united at the center,\\nand the same impulse were applied to them. Suppose, for the\\nsake of simplicity, that the weights of the bodies and the\\nstrength of the impulse are so related that the center, C, will\\npass over each unit of space, Ga, ab, bo, etc., while E advances\\n45\u00c2\u00b0 in a circle about the moving center. Then, when the\\ncenter is at a, E is at 1, 45\u00c2\u00b0 from a perpendicular at a. But S\\nmust be on the opposite side of a, and as far from it as from\\nbefore. Therefore, by the impulse given to E, and the mutual", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0094.jp2"}, "93": {"fulltext": "A PLANET AT APHELION OR PERIHELION. 79\\nAttraction between E and S, the latter has been drawn along\\nfrom S to 1/. Again, when the center is at b, E is at 2, and S\\nat 2 While E was on the upper side of CA, S was drawn\\ntoward that line, and now crosses it, and by its inertia con-\\ntinues upward, although E is now below the line. In this\\nmanner the bodies revolve about the moving center, describing\\ncircles relatively to that, but curves of a totally different char-\\nacter in space. These curves are always some variety or other\\nof the class of curves called epicycloids. In the case repre-\\nsented in the figure, the planet describes an epicycloid which\\nforms a series of loops, intersecting its own path at every revo-\\nlution, while the path of the heavier body is of a waving form.\\nThe body E retrogrades on the lower part of the loop from 3\\nto 5, while S advances continually, but with unequal velocities,\\neach body being alternately drawn forward and held back by\\nthe other.\\nFig. 43.\\n-E\\nThe only way in which two separate bodies could be made to\\nrotate about a fixed center of gravity, would be to give an\\nequal impulse to each body, and in opposite directions. Two\\nsuch forces would constitute a couple (Nat. Phil., Art. 54),\\nwhose effect is to produce rotation merely.\\n134. Why a planet at aphelion begins to return, or at peri-\\nhelion begins to depart. It might be thought that a planet at", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0095.jp2"}, "94": {"fulltext": "80\\nPRECESSION OF EQUINOXES.\\nits aphelion, C (Fig. 44), being less attracted toward the sun\\nthan at any other point, wonld continue to withdraw, instead\\nof commencing to return and that when at its perihelion, G-,\\nbeing more attracted than else-\\nwhere, it would continue to ap-\\nproach till it falls to the sun. The\\nreason why a planet begins to re-\\nturn after reaching the aphelion is\\nto be found in its diminished ve-\\nlocity. As the plauet recedes\\nthrough. H, K, and A, the centrip-\\netal force toward S draws it back,\\nand causes continual retardation,\\ntill at C the velocity is so much\\ndiminished that the attraction of S,\\nthough less than elsewhere, is still\\nsufficient to curve the path so that it falls within a circle about\\nthe centre S, and the planet begins to approach the sun.\\nAgain, as the planet passes through D, E, and F, the at-\\ntraction toward S partly conspires with its inertia, and it is\\ncontinually accelerated, till, at G, its velocity has become so\\ngreat that its path strikes outside of a circle about the center,\\nS, and it begins again to depart as before.\\nCHAPTEK IX.\\nPRECESSION OF EQUINOXES. NUTATION. ABERRATION OF\\nLIGHT. APSIDES OF THE EARTH S ORBIT.\\n135. Precession of equinoxes described. The points in\\nwhich the equator intersects the ecliptic on the celestial sphere\\nare not stationary, but have a slow retrograde movement that\\nis, they revolve from east to west. The sun, therefore, in its\\nannual progress eastward, crosses the equator each year a little\\nfurther west than it did the year previous This motion is", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0096.jp2"}, "95": {"fulltext": "CAUSE OF PEECESSION. 8 J\\nealled the precession of the equinoxes, either because the time\\nof the equinoxes precedes the time in which the sun would have\\npassed them if they had remained at rest, or because, in\\nthe daily transit of the meridian, the equinoxes precede those\\nstars which crossed at the same time with them the preceding\\nyear.\\nThe equinoctial points retrograde about 50i A each year. At\\nthis rate, it will require 25,800 years to make a complete circuit\\nof the heavens.\\n136. Signs of the ecliptic displaced from the signs of the\\nzodiac. The want of coincidence between the signs of the\\necliptic and the signs of the zodiac was noticed (Ait. 61). They\\ncoincided at the time the division was made, about 2,000 years\\nago and the precession daring this period has moved the equi-\\nnoxes backward 2,000 x 50i 28\u00c2\u00b0, nearly. Hence, Aries of\\nthe zodiac almost coincides with Taurus of the ecliptic, Taurus\\nof the zodiac with Gemini of the ecliptic, etc.\\n137. Motion of the north and, south poles. Considering\\nthe plane of the ecliptic as fixed, its poles of course occupy\\nfixed positions among the stars. But this is not true of the\\npoles of the equator. Their distance from the polefi of the\\necliptic is equal to the obliquity of the two circles that is,\\n23\u00c2\u00b0 27 As this angle remains nearly constant, and the points\\nof intersection move around westward, the poles of the equator\\nmust likewise move round those of the ecliptic in the ^ame\\ndirection, and occupy the same period, 25,800 years in com-\\npleting their revolution. The north pole of the equator is row\\nnear the star in Ursa Minor, known as the pole-star. Accord-\\ning to the earliest catalogues, the pole was 12\u00c2\u00b0 distant from the\\npole-star. It is now somewhat more than 1\u00c2\u00b0 distant, and will,\\nat the nearest, pass within of it. In about 13,000 years the\\npole will be on the opposite side of the pole of the ecliptic, near\\nthe bright star a Lyrse, which will then be the pole-star.\\n138. Cause of precession. The precession of the equinoxes\\nis a disturbance produced by the sun s and moon s attraction\\nupon the equatorial ring of the earth, as it rotates on its axis.\\n6", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0097.jp2"}, "96": {"fulltext": "82\\nCAUSE OF PKECESSION.\\nThe sun being in the ecliptic, while the equatorial ring is inclined\\n23\u00c2\u00b0 27 to it, the sun s attraction is oblique to the plane of the\\nring; and one component of this force is perpendicular to the\\necliptic. In most positions of the ring in relation to the sun,\\nthis component acts on one part to press it towards the ecliptic,\\nand on another part to move it from the ecliptic. But the first is\\nin excess so that, on the whole, the ring tends to turn on the\\nline of equinoxes towards the plane of the ecliptic. And this\\ntendency, compounded with the inertia of the ring in its diurnal\\nrotation, moves the equinoxes backward.\\nFig. 45.\\nLet EC (Fig. 45) represent the plane of the ecliptic, ana\\nQR the equatorial ring of matter. A particle, A, of the ring,\\nby its inertia of rotation, tends to move toward T in the plane\\nQR. Let AB represent this force, and AF the pressure toward\\nEC, produced by the sun then the resultant will be the diag-\\nonal AD, shifting the equinox back to T All the particles\\nare subjected to this influence, except at the moment (each day)\\nof crossing T and so long as the sun itself is not in the line\\nT=^ produced, which occurs in March and September. The\\neffect is then interrupted for a time.\\nAs the moon is always near the ecliptic sometimes on\\none side of it, and sometimes on the other its action on the\\nwhole conspires with that of the sun. And as it is compar-\\natively near, though it is so small a body, its effect is more\\nthan twice as great as that of the sun. The planets produce a", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0098.jp2"}, "97": {"fulltext": "THE TROPICAL AND SIDEREAL YEAR. 83\\nvery minute effect on the ring, tending to diminish the amount\\nof precession. The joint effect of all the bodies mentioned is,\\nas stated above, 50J\\n139. Law of composition of rotations. The case of pre-\\ncession of equinoxes is classed under the general law for the\\ncomposition of two rotations, which is analogous to that for\\nthe composition of two rectilinear motions (Nat. Phil., Art.\\n38). It may be stated thus if two forces are applied to a\\nbody, which, separately, would cause rotation on two different\\naxes, their joint action will produce rotation on a third axis\\nlying in the plane of the other two, and making angles with\\nthem, whose sines are inversely as the forces. In precession,\\nthe earth rotates on the diurnal axis by one force, and the sun\\nand moon tend to rotate it on the line of the equinoxes. As\\nthe latter force is minute compared with the other, the new\\naxis is shifted by a very small angle each year from the diurnal\\naxis toward the line of equinoxes. And this line slides along\\nthe ecliptic, so that the two axes remain perpetually at right\\nangles with each other.\\nThe rotascope, a modification of Foucault s gyroscope, may\\nbe used to exhibit a very perfect illustration of the precession\\nof equinoxes.\\n140. Cause of the slowness of precession. If the equatorial\\nring were a separate body rotating about the earth in its own\\nplane, its points of intersection with the ecliptic would retro-\\ngrade very rapidly by the action of the sun and moon. The\\nreason why the precession is exceedingly slow is, that while\\nthe disturbing action is exerted only on the ring, the force\\naround the diurnal axis consists of the inertia of the entire\\nearth. The ring can not move by itself, but must carry the\\nwhole mass of the earth with it.\\n141. The tropical and sidereal year. The fact of preces-\\nsion shows that the year has two different values, according as\\nwe reckon from a star or from an equinox. Hence, the side-\\nreal year is defined to be the period occupied by the sun in", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0099.jp2"}, "98": {"fulltext": "\u00c2\u00a34 NUTATION.\\npassing eastward around the heavens from a star to the same\\nstar again and the tropical year, the time of passing around\\nfrom an equinox to the same equinox again (Art. 86). As the\\nequinox moves westward, the sun reaches it sooner than if it\\nwere stationary, and thus makes the tropical year shorter than\\nthe sidereal, by the time required to pass over 50y, which is\\n20m. 22.9s. As the tropical year is 365d. 5h. 48m. 46.15s.\\n(Art. 86), the sidereal year, therefore, is 365d. 6h. 9m. 9s.\\nThough the sidereal year is the true period of the earth s\\nrevolution about the sun, yet the tropical year possesses by far\\nthe greatest interest, because it is the period in which the\\nseasons are completed.\\n142. Nutation. By precession alone, the pole of the\\nequator would move in the circumference of a circle about the\\npole of the ecliptic. But this motion is modified by a minute\\nvibration from side to side, as it\\nadvances, so that the line described Fi g- 46.\\nby the pole is a delicate wave lying\\nalong on the circumference, as rep-\\nresented in Fig. 46, where P repre-\\nsents the pole of the ecliptic, and\\nMN the path of the pole of the\\nequator around it. This vibratory\\nmotion is called nutation. It is\\nprincipally due to the unequal ac-\\ntion of the moon upon the equa-\\ntorial ring.\\nThe moon s action, at any given\\ntime, tends to revolve the ring into\\nthe plane of its orbit. But, on\\naccount of the retrograde motion of\\nits nodes, the angle between the\\nring and the moon s orbit varies\\nfrom 1 8J\u00c2\u00b0 to 28^-\u00c2\u00b0, going through all the changes every nine-\\nteen years. Owing to these changes of position, the equinoxes\\nvrill recede sometimes faster, and sometimes slower while the\\ninclination of the equator to the ecliptic will also increase and\\ndecrease, causing the poles of the equator to oscillate, a? stated", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0100.jp2"}, "99": {"fulltext": "ABERRATION OF LIGHT. 85\\nabove. The amount, by which the pole of the equatoi moves\\nto and from the pole of the ecliptic is IS\\nThe waves in the figure are exceedingly exaggerated The\\narc MN being about T V of the circumference, the waves, if\\ntruly represented, would be small enough to cross the arc 270\\ntimes.\\n143. Aberration of light. The heavenly bodies suffer a\\nminute apparent displacement, on account of the progressive\\nmotion of light, combined with the earth s motion in its orbit.\\nSuppose the earth to move from C to E (Fig.\\n47), while the light, coming from S, describes\\nthe line I)E. If they arrive together at the\\npoint E, the impulse on the retina of the eye\\nwill not be in the same direction as if the\\nobserver had been at rest but the light will\\nappear to come in the direction S E, the body\\nbeing apparently thrown forward from S to T\\nS For, make EA DE, and complete the\\nparallelogram CA and suppose, according\\nto the principle of equal action and reaction,\\nthat the light has the motion EC given to it,\\nin place of the earth s motion, CE then the\\ntwo motions, EA and EC, will produce the resultant, EB, as\\nthough the light had come from S instead of S.\\n144. Aberration illustrated. The apparent direction of\\nany kind of impulse is modified in the same way, by the\\nmotion of the person who receives it. For instance, if the\\nwind drives drops of rain in a person s face, at a certain inclina-\\ntion, while he is standing still, when he comes to move toward\\nthe wind, they will strike him at a less inclination with the\\nhorizon, as though the source of the drops was further forward.\\nFor, when the person moves, the effect is the same as if he\\nremained at rest, and the wind were to receive an increment\\nof velocity equal to his motion.\\n145. Greatest and least aberration. The greatest aberra-\\ntion occurs when the body, from which the lis;ht comes, is in a", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0101.jp2"}, "100": {"fulltext": "86 ADVANCE OF APSIDES.\\ndirection at right angles to the line of the earth s motion\\nThe displacement is then 20 5. When the earth is moving\\ndirectly toward or directly from the body, the aberration is\\nzero. Therefore, a star in the plane of the ecliptic is seen in its\\ntrue place once every six months bnt three months before\\nand three months after either of those times, it is displaced\\n20 .5 in opposite directions, making the total arc of displace-\\nment 41 But a star at the pole of the ecliptic, being always\\nthrown forward of its true place by 20 5, will seem to de-\\nscribe each year a circle, whose diameter is 41 Between the\\necliptic and its poles, the apparent orbit of aberration is an\\nellipse, whose major axis is 41 and whose minor axis increases\\nwith the latitude of the body.\\n146. Velocity of light computed by aberration. In the\\ntriangle AEB (Fig. 47), AB represents the velocity of the\\nearth, AEB the observed aberration, and EAB the angle\\nbetween the line of the earth s motion and the direction of\\nlight. When EAB=90\u00c2\u00b0, the aberration is found to be 20 .4451.\\nTherefore,\\ntan 20 .4451 rad 18.393 miles 185,600\\nmiles per second, which is about the velocity of light.\\n147. Advance of the apsides of the earth s orbit. It was\\nintimated in Art. 74 that the line of apsides is not stationary.\\nIf the exact place of the perihelion among the stars be noted,\\nit will be found the next year 11 .5 further east that is, the\\napsides advance 11 5 per year. But in longitude, the advance-\\nis much faster, since the vernal equinox, from which longitude\\nis reckoned, retrogrades 50^ per year. The perihelion, there-\\nfore, increases its longitude nearly 62 each year.\\nAs the longitude of the perihelion in 1800 was 279\u00c2\u00b0 30 8\\n(that is, 9\u00c2\u00b0 30 8 past the winter solstice) it must have been\\njust at the solstice in the year 1247. For, 9\u00c2\u00b0 30 8 -f- 61f\\n553 years; and 1800 553 1247. In a similar manner, it\\nis found that the perihelion will be at the summer solstice in\\nthe year 11741. In the course of many centuries, the length\\nand temperature of the seasons are modified by these slo^v\\nmovements of the equinoxes and the apsides (Art. 75).", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0102.jp2"}, "101": {"fulltext": "LONGITUDE OF THE SUN. 87\\n1 48. Cause of the advance of apsides. The apsides of the\\nearth s orbit are made to advance by the attraction of the\\nheavy planets, whose orbits are outside of it. The entire re-\\nsultant of the attractions of these planets upon the earth, is to\\ndiminish a little the earth s tendency to the sun. Hence, as\\nthe earth approaches one of its apsides, its path is not suffi-\\nciently drawn in by the sun to meet the former line of apsides\\nat right angles. But it makes right angles with a radius vec-\\ntor a little further on, which becomes, therefore, the new line\\nof apsides.\\n1 49. Sun s anomaly. The sun s longitude is his distance\\neastward on the ecliptic from the vernal equinox (Art. 15).\\nIts anomaly is its distance eastward, on the ecliptic, from\\nperihelion. The reason for reckoning motion from the peri-\\nhelion is, that the angular velocity depends on it so that, to\\nfind the true longitude of the sun at any time, we need to\\nknow how far it is from the perihelion.\\n150. How to find the true longitude of the sun at a given\\ntime. It is first supposed that the sun moves uniformly in a\\ncircle. And by knowing what its mean motion is, and how\\nlong it is since it passed the vernal equinox, we have its mean\\nlongitude at once. But this needs correction on account of\\nthe variable motion in the ellipse. Let E (Fig. 48) be the\\nearth PCA, the elliptic orbit of the sun and BCF, the sup-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0103.jp2"}, "102": {"fulltext": "8S THE MOuN S DISTANCE.\\nposed circular orbit whose area equals that of PCA. Suppose\\nthe sun s mean place to be at S and the vernal equinox at \u00c2\u00b0P\\nthen its mean longitude is TDS already obtained. The angle\\nBES is its mean anomaly. But as the .sun has been passing\\nthrough the nearest part of its orbit, its true place is further\\nadvanced, as at S. The angle PES is the true anomaly, and\\nthe difference between them that is, S ES is called the equa-\\ntion of the center. This equation, or correction, being found\\nin tables of the sun s motions, and applied to the mean longi-\\ntude, gives the true longitude.\\nIf the mean and true places are considered as agreeing at P,\\nthen the equation of the center immediately becomes positive,\\nand increases to its maximum at C after which it diminishes,\\nand the mean and true places agree again at A. After that,\\nthe sun falls behind its mean place, and the equation is neg-\\native, till the sun reaches P, the greatest value being at D.\\nThe eccentricity of the earth s orbit is so small, that the sun s\\nmean and true places never differ so much as 2\u00c2\u00b0, the greatest\\nequation of the center being 1\u00c2\u00b0 55 27\\n151. The anomalistic year. The perihelion is another\\npoint from which to measure the revolution about the sun.\\nThe time of passing round from perihelion to perihelion again\\nis called the anomalistic year. It is 4m. 40s. longer than the\\nBidereal year, or 365 d. 6h. 13m. 49s.\\nCHAPTEE X.\\nT^\u00c2\u00a5 MOON. ITS REVOLUTIONS. ITS PHASES- -THE\\nCONDITION OF ITS SURFACE.\\n1 52. Distance and dimensions of the moon. The moon is\\na satellite of the earth, revolving about it within a compara-\\ntively small distance, and accompanying it in its orbit around\\nthe sun. The mean horizontal parallax of the moon at the", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0104.jp2"}, "103": {"fulltext": "MONTHS. 89-\\nearth s equator being 57 2 7, its mean distance is found by\\nthe proportion (Fig. 4),\\nsin 57 2 7 rad 3962.8 238,820m.\\nThe moon s angular diameter is 31 6 therefore, rad sin\\n15 33 238,820 1080.3 which is the moon s semi-diameter\\nin miles. Hence, the moon s diameter is 2,160.6 miles.\\nThe surfaces of the earth and moon being as the squares of\\ntheir radii, are as 13 1.\\nThe volumes of the earth and moon being as the cubes of\\ntheir radii, are as 4:9 1, nearly. But the moon s density is so\\nsmall (3.4), that the masses are nearly as 81 1.\\nThe force of gravity on the earth to that on the moon is as-\\nW5Voow ::6:1 nearly\\n153. Revolution about the earth. The slightest attention,\\nto the position of the moon, from night to night, shows that it\\nmoves eastward, among the stars, several degrees every day.\\nIf the instruments of the observatory be employed to measure\\nits right ascension and declination, as in the case of the sun\\n(Arts. 58, 59), it is ascertained that the moon describes nearly\\na great circle, inclined about 5\u00c2\u00b0 to the ecliptic, and occupies-\\n27.32 days in returning to the same place among the stars.\\nThe inclination of the moon s orbit to the ecliptic va~\\nries from 5\u00c2\u00b0 20 6 to 4\u00c2\u00b0 57 22 but its mean value is 5\u00c2\u00b0\\n8 M\\n154. Months. The period just mentioned, in which the-\\nmoon makes a revolution from a star to the same star again, is\\ncalled the sidereal month. The time occupied in making a\\nrevolution relatively to the sun, instead of a star, is called a\\nsynodical month. This is more than two days longer than the\\nsidereal month for the moon s daily progress is about 13\u00c2\u00b0\\nand during the 27 days of its revolution, the sun, at the rate of\\n1\u00c2\u00b0 per day, will advance 27\u00c2\u00b0, requiring more than two addi*\\ntional days for the moon to overtake it.\\nThe mean length of the synodical month is 29.53 days.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0105.jp2"}, "104": {"fulltext": "90 moon s orbit.\\n155. Node*. The points where the moon s }ath cats the\\ncircle of the ecliptic are called the moon s nodes. The ascend-\\ning node is the one through which the moon passes from the\\nsouth to the north side of the ecliptic the other, 180\u00c2\u00b0 from it,\\nis called the descending node.\\n156. The moon? 8 positions in relation to the sun. The\\nmoon is said to be in conjunction with the sun, when both\\nbodies have the same longitude in opposition, when their\\nlongitudes diifer by 180\u00c2\u00b0. The conjunction and opposition\\nare called by the common name of syzygies.\\nWhen the longitude of the moon is 90\u00c2\u00b0, or 270\u00c2\u00b0 greater\\nthan that of the sun, it is said to be in quadrature.\\nThe points midway between syzygies and quadratures are\\ncalled octants.\\nThe period in which the moon passes from any one of these\\npoints to the same point again that is, a synodical month is\\nalso called a lunation.\\n157. To find the synodical month. The synodical month\\nis best obtained by comparing ancient and modern eclipses.\\nAn eclipse of the sun takes place at the time of conjunction.\\nIf then, the whole interval between the recorded date of a\\nsolar eclipse, which occurred before the Christian era, and the\\ntime of another, which occurred recently, be divided by the\\nnumber of intervening lunations, the quotient is a very accu-\\nrate expression of the mean synodical month.\\nThe mean synodical month, as thus obtained, is 29d. 12h.\\n44m. 3s. 29.5306 days.\\n158. To find the sidereal month. Dividing 360\u00c2\u00b0 by\\n365.25635, the number of days in a sidereal year, we have\\n0\u00c2\u00b0.9856, the mean daily progress of the sun. Multiplying this\\nby 29.53, the number of days in a synodical month, we find\\n29\u00c2\u00b0.105, the arc passed over by the sun in that time. Now,\\nthe moon passes over 360\u00c2\u00b0 29\u00c2\u00b0.105 in a synodical month,\\nbut only 360\u00c2\u00b0 in a sidereal month. Hence, we have the pro-\\nportion, 360\u00c2\u00b0 29\u00c2\u00b0.105 360\u00c2\u00b0 29.53d. 2T.32d.\\nThe sidereal month, more exactly, is 27d. 7h. 43m. lis.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0106.jp2"}, "105": {"fulltext": "LIBRATION TN LONGITUDE. 91\\n159. Form of the moon s orbit. It is ascertained by the\\njame method as was described (Art. 71), that the moon s orbit\\nis an ellipse, one of whose foci is at the eirth. The moon s\\napparent diameter varies from 33 f 31 to 29 21 Therefore,\\nthe greatest and least distances of the moon from the earth are\\nin the ratio of these numbers, or as 8 7, nearly and the ec-\\ncentricity or 0.067, which is about four times as great as\\nthe eccentricity of the earth s orbit (Art. 73). Yet a figure in\\nthe exact form of the moon s orbit could not be distinguished\\nfrom a circle, since the major axis would exceed the minor by\\nless than T qVo of its length.\\nThe point of the moon s orbit nearest the earth is called the\\nperigee, the most distant point the apogee.\\n160. The moon s diurnal motion. The moon not only re-\\nvolves about the earth, but also on its own axis in the same\\nlength of time that is, once in 27.32 days and its axis is\\nnearly perpendicular to the plane of its orbit. This rotation\\nis indicated by the fact that the same side of the moon is al-\\nways presented toward the earth. If it should pass around the\\nearth, and not turn upon an axis, it would obviously present\\nall sides to us in the course of each revolution.\\nBut though it keeps the same side toward the earth, it pre-\\nsents all sides to the sun once in each synodical month there-\\nfore, the days and nights on the moon are nearly 30 (29.53)\\ntimes the length of those on the earth.\\n101. The moon s librations. Though the same side of the\\nmoon is turned toward us on the whole, yet there are slight\\napparent oscillations, by which narrow portions of the other\\nhemisphere alternately come into view. These are called\\nlibrations. They are of three kinds the libration in longi-\\ntude, the libration in latitude, and the diurnal libration.\\n162. The libration in longitude. By this libration we ex-\\ntend our view a little further round upon the moon s equator,\\nfirst on one side, then on the other, every sidereal month.\\nIt arises from the fact that while the moon rotates uni-\\nformly on its axis, it revolves in its elliptical oibit with un-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0107.jp2"}, "106": {"fulltext": "92 REVOLUTION ABOUT THE SUN.\\nequal angular velocity. Near the apogee, where it moves\\nslowest, it rotates more than 90\u00c2\u00b0 on its axis, while passing just\\n90\u00c2\u00b0 around us, and thus reveals a little of the remote hemi-\\nsphere on the eastern side. Near the perigee, on the other\\nhand, where the orbit motion is rapid, it makes less than one-\\nfourth of a rotation, while going 90\u00c2\u00b0 around the earth. This\\nbrings into view a little of the other hemisphere on the western\\nlimb.\\nIf the moon s orbit were a circle, there would be no libra-\\ntion of longitude.\\n163. The libration in latitude. As the name implies, this\\nlibration extends our view alternately north and south on the\\nmoon s meridian. As the moon s equator is a little inclined\\nto the plane of its orbit, its north and south poles are brought\\nalternately toward us, just as the earth s poles are presented in\\nturn toward the sun every year. The mean value of the incli-\\nnation of the moon s equator to its orbit is 6\u00c2\u00b0 39\\nIf the moon s equator and its orbit were in the same plant,\\nthere would be no libration of latitude.\\n164. The diurnal libration. This is the effect of diurnal\\nparallax. When the moon is on the meridian, we view it\\nnearly as from the center of the earth but when it is at the\\nhorizon, we see it, as it were, from a position near 4,000 miles\\nhigher, and extend our vision a little distance over its western\\nlimb at rising, and its eastern at setting.\\n165. Apparent diameter on the meridian and at the hori-\\nzon. The distance of the moon from the earth is about 60\\ntimes the radius of the earth. Therefore, when the moon is on\\nthe meridian, as it is nearer than when at the horizon, its\\napparent diameter is greater. This change, equal to about\\n30 is too small to be perceived by the eye, but can be meas-\\nured by instruments.\\n166. The moon s revolution about the sun. While the\\nmoon revolves about the earth, the earth revolves about the\\nsun, at a distance 387 times as great. For, 238,820 x 387\\n92, 423,0u0.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0108.jp2"}, "107": {"fulltext": "WHAT FOECES CONTROL THE MOON. 93\\nTherefore, the moon really has a third revolution namely,\\nthat in company with the earth around the sun. And this is\\nfar greater than its other revolutions, which have been de-\\nscribed. A point of the moon s equator, in its diurnal motion,\\n\u00c2\u00a3oes only 10 miles per hour. Around the earth, the moon s\\nvelocity is nearly 2,300 miles per hour but around the sun, it\\nis more than 66,000 miles per hour.\\n167. Form of path around the sun. Whenever a body re-\\nvolves about a center, while that center is itself in motion, the\\nbody describes a species of curve, called an epicycloid. The\\nmoon s path about the sun is a leaving epicycloid. Let the\\nsmall circles at A, B, etc. (Fig. 49), represent the size of the.\\nFig. 49.\\nmoon s orbit, and let AE be an arc of the earth s orbit, the\\nsun being at the intersection of the dotted lines when pro-\\nduced. While the moon describes one half of its orbit, the\\nearth goes over ^j of its annual circuit that is, from A to E.\\nTherefore, the earth being at A, suppose the moon in quadra-\\nture on the left, beginning to describe the semicircle nearest the\\nsun. When the earth reaches B, the moon has passed to the\\noctant m at C, the moon is in conjunction at D, it is at the\\nnext octant and at E, it is again in quadrature on the right,\\nhaving described a semicircle relatively to the earth. But, in\\nrelation to the sun, it has passed over the curve inside of the\\nearth s path, from Ammm E. At E, it crosses the earth s path,\\nand while describing the outer semicircle, it advances with the\\nearth a distance equal to AE, on the outside. Thus, the\\nmoon s path around the sun consists of 25 undulations, so\\nBlight that, if represented alone, the whole would scarcely be\\ndistinguished from the earth s orbit.\\n168. By what forces the moon is mainly controlled. Since\\nthe moon describes around the sun an orbit at the mean d;s-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0109.jp2"}, "108": {"fulltext": "94 moon s phases.\\ntance of the earth s orbit, and in the same time, it must be\\nsubject to the same projectile and centripetal forces. It the\\nearth, therefore, were to be annihilated, the moon s path about\\nthe sun would not be essentially disturbed the waves only\\nwould cease, and the orbit become an exact ellipse.\\nThe relative attractions of the earth and sun, exerted on\\nthe moon, are estimated by the formula proved in Art. 92,\\nc oo Considering the radius of the moon s orbit 1, that\\nof the earth s orbit is about 387; and the times are 27.32d. and\\n365. 25d., respectively. Hence, attraction to the earth that\\ni ^87\\nto the sun 3 pgijgy 2 2 near1 Therefore,\\nthe sun, though so very far frpm the moon, exerts upon it\\n2 J times more attraction than the earth does.\\n169. How the earth s action causes the waves in the moon s\\npath. When the moon is in conjunction, as at C, the earth\\ndraws it away from the sun, so that it begins to move further\\noff, as at D, E, etc., till it reaches opposition. But, at opposi-\\ntion, the earth is on the same side as the sun, and increases the\\nmoon s tendency toward it, so that the moon begins to move\\ntoward the sun, and continues approaching till it reaches con-\\njunction again. But, in describing the wave line, the moon\\nsometimes gets in advance of the earth in its orbit, as at A,\\nand then falls behind, as at E. For, the earth at A draws the\\nmoon backward, and it falls further and further back, till it is\\nbehind the earth in its motion, as at E, where the earth, having\\novercome the backward motion, draws it forward, till it passes\\nby, and is again in advance of the earth. Thus, in the moon s\\ngreat revolution around the sun, we may regard its path as\\nthrown into the waving line by the small disturbing influences\\nof the earth.\\n170. Phases of the moon. The moon is not self-luminous,\\nand is seen only as it reflects to us the light which falls upon\\nit. The several forms which the part illuminated by the sun\\npresents to our view, are called phases.\\nThe circle of illumination, or the terminator, is the circle", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0110.jp2"}, "109": {"fulltext": "MOON S PHASES.\\n95\\nwhich separates the hemisphere enlightened by the sun from\\nthe dark hemisphere, and is perpendicular to the sun s rays\\nwhich fall on the moon. The circle of the disk is that which\\nseparates the hemisphere turned toward the earth from the op-\\nposite one, and is perpendicular to our line of vision. The\\nphase depends on the size of the angle formed at the moon,\\nbetween the solar ray and our visual line.\\nFig. 50.\\nO\\nLet the earth be at E (Fig. 50), and the moon in several po-\\nsitions, A, B, etc., and let the lines AS, BS, etc., be directed\\ntoward the sun. At A, the moon is in conjunction, and wholly\\ninvisible this is called new moon; and the angle SAE, be-\\ntween the solar ray and visual ray, is 180\u00c2\u00b0. From A to\\n(as at B), the phase is called crescent and the angle, SBE, is\\nobtuse. The first quarter occurs at C, the quadrature, where\\nSCE is a right angle. From C to F (as at D), the phase is\\ncalled gibbous in this phase, the angle, SDE, is always acute.\\nAt F, the moon is in opposition, and wholly illuminated. This\\nis called full moon the angle, SFE, is 0\u00c2\u00b0. From F to A,\\nthe phases are repeated in reverse order, the last quarter being\\nat H. The outer figures at B, C, etc., show the corresponding\\nphase", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0111.jp2"}, "110": {"fulltext": "t)6 INEQUALITIES OF THE MOON S SURFACE.\\n171. The meridian altitudes of the moon at a given phase.\\nIt is generally observed that at a given age of the moon, foi\\ninstance at the full, its meridian altitude is very different at\\ndifferent seasons of the year. This is readily explained, by\\nnoticing the moon s relations to the sun. As the moon s path\\nis everywhere near the ecliptic, the new moon will culminate\\nat a high point when the sun does that is, in the summer.\\nBut, in the same season, the fall moon, being opposite to the\\nsun, will culminate low. On the contrary, when the sun is in\\nthe most southern part of the ecliptic, and culminates low, as\\nis the case in winter, the new moon will do so likewise but\\nthe full moon will culminate at a high point. In the polar\\nwinter, therefore, wdien the sun is absent for months, the moon,\\nwhenever near the full, circulates round the sky without\\nsetting.\\n1 T 2. The harvest moon. This name is given to the full\\nmoon which occurs nearest to the autumnal equinox, Septem-\\nber 2 2d, and which rises from evening to evening with a less in-\\nterval of time than the full moon of any other season.\\nThe sun being at the autumnal equinox, the moon is near\\nthe vernal equinox, and at sunset, the southern half of the\\necliptic is above the horizon, and makes the smallest possible\\nangle with it. It is this small angle, made by the ecliptic, and\\ntherefore by the moon s orbit with the horizon, which causes\\nthe small interval in the time of the moon s rising from one\\nevening to another; for, as the moon advances 13\u00c2\u00b0 each day\\nin its orbit, this arc is so oblique to the horizon that its two\\nextremities rise with only a few minutes difference of time\\nbut the place of rising moves rapidly northward.\\nThe harvest moon attracts most attention in high latitudes,\\nwhere the angle between the ecliptic and horizon is smaller,\\nand therefore the intervals of time are less.\\nThe moon passes the vernal equinox every month, and\\ntherefore rises with the same small intervals. But when the\\nmoon is not full at the same time, the circumstance is un-\\nnoticed.\\n173. Inequalities of the moon s surface. These are clearly", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0112.jp2"}, "111": {"fulltext": "FORMS OF VALLEYS. 97\\nrevealed by the changing direction of the sun s rays. As\\nthe terminator advances over the disk, the light strikes the\\nhighest peaks, which appear as bright points a little way upon\\nthe dark part of the moon. After the terminator has passed\\nover them, they project shadows away from the sun, which\\ncorrespond to the apparent shape of the elevations, and grow\\nshorter as the rays fall more nearly vertical. And again, in\\nthe waning of the moon, the shadows are cast in the opposite\\ndirection, lengthening until the dark part of the disk reaches\\nthem, and the summits once more become isolated bright\\npoints, and then disappear. Fig. 2, Frontispiece, will give\\nsome idea of these appearances.\\n174. Forms of valleys. The most striking characteristic\\nof the moon s surface is its numerous circular valleys. A few\\nare represented in Figs. 1 and 2, Fr. The smaller and more\\nregular ones are of all sizes, from one or two miles in diameter\\nup to sixty miles. These are numbered by hundreds. The\\nmountain ridge which surrounds one of these cavities is a ring,\\nvery steep and precipitous on the inner side but externally it\\nfalls off by a rugged but gradual slope. These ridges are\\ncalled ring-mountains. In the central part of the cavity are\\ngenerally one or more steep, conical mountains. Some of the\\nprincipal ring-mountains are No. 1. Tycho; 2. Kepler; 3. Co-\\npernicus etc. (Fig. 1, Fr.)\\nThere is another class of larger but less regular cavities,\\nsometimes called bulwark plains. Their diameters are often\\nmore than one hundred miles. These are also surround-\\ned bj rough mountain masses arranged in a circle. Over\\nthese plains are sparsely scattered small conical and ring moun-\\ntains.\\nThere are still larger tracts, more level than the general\\nlunar surface, and of a darkish hue, which still retain the name\\nof seas, formerly given them, though they are covered with\\npermanent inequalities, and show no signs of being fluid. Ex-\\namples of these are: A, mare humorum; B, mare nubium^\\nntc (Fig. 1, Fr.)\\nBesides the ridges of mountains inclosing the circular val-\\n7", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0113.jp2"}, "112": {"fulltext": "98 LUNAR MOUNTAINS.\\nleys, there are occasional chains and spurs, having more resem-\\nblance to terrestrial ranges.*\\n175. Luminous radiations. At fall moon, all shadows\\ndisappear, because the light falls in the direction of our line of\\nvision. But at that time another peculiarity presents itself.\\nFrom a few of the large ring mountains there radiate a great\\nnumber of luminous stripes, nearly in straight lines, and ex\\ntending, in some cases, hundreds of miles. They are not\\nridges, as they cast no shadows when the terminator passes\\nthem and the difference of illumination must result from the\\ndifferent nature of their material. They are sometimes called\\nlava-lines. The most extensive system occurs around Tycho,\\nmarked 1, in Fig. 1, Fr.\\n176. Surface rigid and angular. Every part of the moon s\\nsurface has the appearance of rocky hardness. The interior\\nslopes of the ring-mountains are steep, rough, and angular.\\nThe conical peaks within them appear like isolated rocks, re-\\nsembling the needles of the Alps. The surface nowhere gives\\nindication of having been softened down by the action oi\\nwater.\\n17 7. Probable volcanic origin. The circular cavities, with\\nsteep and rugged sides, appear like vast craters, and the moun-\\ntains within them like volcanic cones, more recently thrown\\nup. Nearly every part of the hemisphere presented to our\\nview exhibits these indications of former volcanic action, on a\\nscale far beyond any thing on the earth. But there is no evi-\\ndence of volcanic action at present.\\n178. Height of lunar mountains. One method of measur-\\ning the height of a lunar mountain is the following. Let the\\nlight from the sun, S (Fig. 51), pass the moon s surface at O, and\\nilluminate the summit of the mountain, MF. To the observer\\non the earth at E, M is seen as a bright point beyond the ter-\\nThe lunar map of Beer and Madler, 2$ feet in diameter, contains a very\\nperfect delineation of the mountains and valleys of the moon, accompanied\\nbv their names.", "height": "4361", "width": "2640", "jp2-path": "introductiont00olms_0114.jp2"}, "113": {"fulltext": "NO ATMOSPHERE OR VAPOR.\\n90\\nminator O. Let OEM, subtended by OM, be measured with\\na micrometer; also, OEB, between the terminator and the\\nopposite edge of the disk. From the latter subtract CEB, the\\nsemi-diameter, and OEC is known which, with OC and EC,\\nwill give EO and EOC. The supplement EOA, plus 90\u00c2\u00b0,\\nequals EOM. Then EO and the angles E and O, will furnish\\nOM from which and 00, CM is computed. FC, subtracted\\nfrom CM, leaves FM, the height required.\\nFig. 51.\\nThe height of a mountain may also be determined by meas-\\nuring the length of its shadow, and the inclination of the solar\\nray which casts it.\\nThe highest of the lunar mountains have an elevation of 4^\\nmiles, and great numbers of them exceed three miles. Thus,.\\nthe mountains of the moon are proportionally much greater\\nthan those of the earth. For, while the diameter of the mooD\\nis not much more than one-fourth as great as the earth s diam\\neter, its mountains are about equal in height to the mountains\\non the earth.\\n179. No atmosphere or vapor. If any kind of atmosphere\\nwere spread over the disk of the moon, it would reflect the\\nsun s light so strongly as to dim the features of the solid sur-\\nface. Nothing of the kind is ever perceived. No terrestrial", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0115.jp2"}, "114": {"fulltext": "100 NO ATMOSPHERE OR VAPOR.\\nobjects, however near, ever exhibit greater sharpness of outline\\nthan the inequalities of the moon and they never vary in this\\nrespect, except in a manner which is obviously occasioned by\\nour own atmosphere.\\nBut the severest test of a perceptible atmosphere would be\\nthe effect on a star at the beginning and end of its occultation\\nby the moon. Let AB (Fig. 52) be the edge of the moon s\\nFig. 52.\\ndisk, and CD that of the atmosphere around it. The light\\nfrom the star S will, according to the laws of optics, be re-\\nfracted toward the moon in entering its atmosphere, and as\\nmuch more in the same direction in leaving it so that it will\\nreach the observer at E, appearing to come from S when the\\nstar is really behind the moon at S. Thus, it will appear to be\\ndetained in its diurnal motion as it approaches the edge of the\\nmoon, and to arrive only to S when it has really reached the\\nposition S. So, also, in reappearing at the opposite limb, the\\nstar will seem to have advanced to the edge, when it is\\nstill behind the moon so that, after coming into view, and\\nbefore passing by the atmosphere, it will again appear to be\\ndetained in its diurnal motion. Since it disappears too late,\\nand reappears too early, the duration of occultation is too\\nshort.\\nBesides this irregularity in its motion, its brightness will\\nalso be a little dimmed by the obstruction of the atmosphere,\\njust before disappearing, and just after reappearing.\\n]STow, the nicest observations have failed to show either oi\\nthese effects. The diurnal motion is uniform up to the very\\nedge of the disk, and the actual continuance of occultation is\\nequal to the calculated duration. And, as to loss of light,\\nthe star at its full brightness disappears all at once, with a\\nsuddenness which is startling. Its reappearance is equally\\nsudden, and without any change of intensity in its light. The\\nmoon, therefore, has no appreciable atmosphere.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0116.jp2"}, "115": {"fulltext": "VIEW OF EARTH FROM MOOJN T 101\\n180. Changes of temperature on the moon. The moon s\\nequator makes an angle of only 1J\u00c2\u00b0 with the ecliptic, and\\ntherefore experiences no perceptible change of seasons but its\\ndiurnal rotation is so slow, that the extremes of heat and cold\\nduring each day are excessive. A place on the moon is ex-\\nposed to the full power of the sun s rays for about two weeks,\\nand then is for as long a time turned away from the sun, with-\\nout clouds, or even air, to prevent the free radiation of heat.\\n181. View of the earth from the moon.\\n1. As to magnitude. The apparent dimensions of the two\\nbodies, as seen one from the other, are proportional to their\\nreal dimensions. Hence, in diameter, the earth as seen from\\nthe moon is 3} times as large as the moon viewed from the\\nearth, and in area is about 13 times as large.\\n2. As to phase. It is obvious, from Fig. 50, that when the\\nfull moon is presented to the earth, the earth s dark side is\\ntoward the moon, and the reverse. Also, that when we see\\nthe gibbous phases of the moon, a spectator on the moon would\\neee crescent phases of the earth for the angle SED or SEG\\nwould then be obtuse. In like manner, the relative phases are\\nin every case supplementary to each other. This relation ex-\\nplains the w T ell-known fact that near the time of new moon,\\nthe part of the moon not directly enlightened by the sun is\\ndistinctly visible. It is then illuminated indirectly by the\\nearth, which is nearly full as seen from the moon, and reflects\\na strong light upon it.\\nFor the same reason, the moon can be faintly seen in a total\\nsolar eclipse.\\n3. As to position in the sky. The earth seen from the moon\\nhas no apparent diurnal rotation, as all other heavenly bodies\\nhave, but remains nearly fixed in the same part of the sky.\\nThis is owing to the fact that the moon s monthly motion and\\nits diurnal motion are at the same rate in the same direction,\\nso that one apparent motion of the earth neutralizes the other.\\nHence, a spectator occupying the middle of the moon s disk\\nsees the earth perpetually near his zenith. Another, at the\\nedge of the disk, sees it always near the same point of the\\nhorizon.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0117.jp2"}, "116": {"fulltext": "102 moon s gravity disturbed.\\nThe first ana second librations of the moon, since they vary\\nthe spectator s position a little in relation to the disk, merely\\ncanse small oscillations of the earth s place in the sky.\\n4. As to surface -The earth, by its rotation, presents all its\\nparts to the view of the nearer hemisphere of the moon once in\\n25 hoars. To the other hemisphere it never appears at all.\\nOn account of its nearness, and its great size, we might sup-\\npose that the geographical features of the earth would be\\nvery conspicuous to a spectator on the moon, and that the\\nnature of its surface in nearly all respects could be thoroughly\\nobserved. But the deep and dense atmosphere of the earth\\nwould reflect an intense light, so as probably to render the in-\\nequalities of the terrestrial surface nearly invisible and when-\\never clouds prevail over a country, that portion of the earths\\nsurface would, of course, be entirely hidden from view.\\nCHAPTER XI.\\nDISTURBANCES OF THE MOON S MOTION CAUSED BY THE SUN..\\n182. Why the sun disturbs the moon s revolutions around\\nthe earth. If the sun were at an infinite distance from the\\nearth and moon, however great its attraction might be, it\\nwould not disturb their mutual relations, because it would act\\non both exactly alike. Though the sun s distance from them\\nis very great, being 387 times their distance from each other,\\nyet the difference of action is sufficient to produce sensible dis-\\nturbances. These disturbances are caused in part by difference\\nof distance, and in part by difference of direction,\\n183. The moon s gravity diminished at syzygies, and in-\\ncreased, at quadratures. When the moon is in conjunction,\\nthe sun attracts it more than it does the earth, in the ratio of\\n387 2 386 2 and thus diminishes the moon s tendency to the\\nBarth. In opposition, the sun attracts the moon less than it\\nJoes the earth in nearly the same ratio, which, as before, di-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0118.jp2"}, "117": {"fulltext": "THE SUN S DISTUEBING EFFECT.\\n103\\nsmnishes the moon s tendency to the earth. Therefore, at the\\nsyzygies, the moon s gravity to the earth is diminished. And\\nthe diminution is computed to be about g\\\\ of the whole.\\nIn quadrature, the sun attracts the moon in a line slightly\\noblique to that in which it attracts the earth. Hence, there is\\na small component of its action directed toward the earth.\\nTherefore, at the quadratures, the moon s gravity to the earth\\nis increased. This increase is proved to be about t -1q of the\\nwhole, or one-half as great as the diminution at syzygies.\\nAs the diminution at syzygies is more than the increase at\\nquadratures, the entire effect of the sun s influence is to dimin-\\nish the moon s gravity to the earth, and thus cause it to revolve\\nin a larger orbit than it would do if the sun did not exist.\\nThe moon s gravity to the earth is diminished by 3-J0, in con-\\nsequence of the sun s action.\\n184. The sun s disturbing effect repre-\\nsented geometrically. Let ABCD (Fig.\\n53) be the moon s orbit described about\\nthe earth E, and S the place of the sun.\\nSuppose the moon at M. Let ES rep-\\nresent the attraction of the sun upon the\\nearth. Then (Art. 128), SM 2 SE 2 SE\\nSF 3\\n^rp the attraction of the sun upon M,\\nin the direction MS. Make MG\\nSM 2\\ndraw MF equal and parallel to ES, and\\ncomplete the parallelogram MFGH.\\nEesolve the force MG- into MF and MH.\\nSince the component MF is equal and\\nparallel to ES, which is the sun s attrac-\\ntion on the earth, it produces no disturb-\\nance and the only force which can dis-\\nturb the relations of M and E is the\\nother component MH. This line lies\\nin various positions, and is of various\\nlengths, according to the place of M. It\\nis convenient to reduce it to two ele-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0119.jp2"}, "118": {"fulltext": "104\\nEVECTION.\\nments called the radial and the tangential disturbing forces\\nDraw MO tangent to the orbit, and EM joining the earth\\nand moon then, ME may be resolved into the radial force\\nMP, increasing or diminishing the moon s gravity to the earth,\\nand the tangential force MO, which increases or diminishes\\nthe velocity of the moon. In the figure, the position of MH\\nis such, that MP increases the gravity, and MO accelerates.\\nNear the quadratures, MP acts toward E and near the\\nsyzygies, it acts away from E. MO accelerates on the quad-\\nrants DA and BC, and retards on AB and CD.\\n185. Equations for correcting the moorts place. The\\nmoon s path being elliptical, and its motion being subject to\\nseveral disturbances, its true longitude for a given time can\\nnot be found, except by applying various corrections.\\n186. TJie equation of the center, First suppose the moon\\nto revolve uniformly in a circular orbit, and then, as in the\\ncase of the sun (Art. 150), apply the equation of the center to\\nchange its place for the variable motion in the ellipse. The\\nmoon s orbit being more eccentric than the earth s, its great-\\nest equation of the center is 6\u00c2\u00b0 18 17 while the sun s is less\\nthan 2\u00c2\u00b0.\\n187. Evection. A cor-\\nrection must be applied on\\naccount of the change of ec-\\ncentricity caused by the\\nsun s disturbance. This\\nchange of eccentricity is\\ncalled evection. It is caused\\nby the radial disturbance\\nMP (Fig. 53), which pro-\\nduces greater or less effect,\\naccording to the position of\\nthe line of apsides in re-\\nlation to the line of syzy-\\ngies. Let FH (Fig. 54)\\nbe the line of apsides of the moon s orbit about the earth,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0120.jp2"}, "119": {"fulltext": "VARIATION. 105\\nE, and suppose the sun to be in the direction A. Then AC\\nis the line of syzygies, and the two lines coincide. The\\nmoon s gravity toward E is diminished at F and H, as it always\\nis when in the line of syzygies. But at F, it is diminished less\\nthan ever, because there is the least difference of distances, AE\\nand AF while at H, it is diminished more than ever, because\\nthe difference of distances AE and AH is the greatest possible.\\nHence, F is less separated from E, and H more separated from\\nE, than in any other situation. The same would be true, if the\\nsun were in the direction of C. Therefore, when the line of\\napsides coincides with the line of syzygies, the moon s orbit is\\nmost eccentric.\\nAgain, suppose the sun to be in the direction B or D in\\nother words, that the line of apsides is in quadrature. Then,\\nthe gravity of the moon toward E is increased at F and H, as\\nit always is when in quadrature. But at F, its increase is the\\nleast possible, because the obliquity of FB to EB is the least\\npossible while at H, the increase is the greatest, because the\\nobliquity of HB to EB is the greatest. Hence, HE is less,\\ncompared with FE, than in any other position. Therefore, the\\neccentricity is least when the line of apsides is in quadrature.\\nThe greatest correction for evection is 1\u00c2\u00b0 12\\n188. Variation. Another correction is applied on account\\nof the alternate changes of velocity caused by the sun. This\\nchange of velocity is called variation. It is produced by the\\ntangential disturbance MO (Fig. 53). From D to A, it con-\\nspires with the motion of the moon, and accelerates it. From\\nA to B, it is directed backward, and retards the moon s motion.\\nFrom B to C it accelerates, and from C to D it retards. It\\nmight be supposed that because the sun attracts toward S, this\\nwould act against the moon s motion in going from B to 0,\\nand thus retard it and with it from C to D, and accelerate it.\\nBut the disturbing action is not the absolute, but the relative\\nattraction. From B to C, the sun attracts the moon less than\\nit does the earth and the effect is the same as if it exerted no\\nattraction on the earth, and urged the moon in the opposite\\ndirection that is, toward C. Hence, the moon s velocity is\\nalternately accelerated and retarded in the successive quad", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0121.jp2"}, "120": {"fulltext": "i06 KETKOGRADATION OF THE MOON S NODES.\\nants, causing the greatest equation about 45\u00c2\u00b0 from the quad\u00c2\u00ab\\nratures B and D. The variation at its maximum is about 37\\n189. Annual equation. This is a change in the moon s\\nmotion, arising from the greater and less distance of the sun at\\ndifferent seasons of the year. The disturbing action of the sun\\nis greatest when it is nearest that is, at perihelion and it is\\nleast when it is most distant, or at aphelion. This inequality\\nis called the annual equation, since it passes through all its\\nchanges in a year. It amounts to about 11\\n190. Smaller equations. The foregoing are the largest in-\\nequalities of the moon s motion, which require corrections to\\nbe made for finding its true place. There is a large number of\\nsmaller ones, for which allowance must be made, in order to\\nobtain the moon s longitude for a given time, with the utmost\\nexactness. By the most complete tables of the moon now in\\nuse, its place can be determined within 3\\n191. Apsides of the moon s orbit. The line of apsides ad-\\nvances that is, moves forward from west to east. This is a\\ndisturbance produced by the sun, and is explained in the same\\nmanner as the advance of the earth s apsides (Art. 148). The\\nattraction of a body external to the orbit always tends to pro-\\nduce this effect. Though the sun makes the moon s gravity to\\nthe earth sometimes greater, and bometimes less, yet it, on the\\nwhole, diminishes it (Art. 183). Without any disturbing in-\\nfluence, the moon would always describe the same elliptic\\norbit. But as it approaches one of its apsides, it is, in general,\\nnot sufficiently drawn in toward the center to cut the former\\nline of apsides at right angles but it makes right angles with\\na radius vector a little further on, which, therefore, becomes\\nthe new line of apsides. The apsides of the earth s orbit ad-\\nvance with exceeding slowness (Art. 147); but the sun s dis-\\nturbing power is so great, that those of the moon s orbit shift\\ntheir place more than 3\u00c2\u00b0 in each sidereal month, and, therefore\\nmake a complete revolution in about 9 years.\\n199. Betrogradation of the moon s nodes. In the pre-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0122.jp2"}, "121": {"fulltext": "RETROGRADATION OF THE MOON S NODES.\\n107\\nceding articles we have considered the disturbing force of the\\nsun upon the moon in the plane of its orbit, one component\\nbeing the radial, and the other the tangential. As the moon s\\norbit does not coincide with the ecliptic, the sun exerts another\\ndisturbing force namely, out of the moon s orbit either to or\\nfrom the ecliptic. This third force is called the orthogonab\\ncomponent. It causes a motion of the nodes, and a change of\\ninclination.\\nFig. 55.\\nLet MN (Fig. 55) represent a short arc of the ecliptic, AB\\nan arc of the moon s orbit, and ANM the inclination of their\\nplanes. When the moon is at L, moving toward the node, N,\\nthe sun attracts it in a line slightly oblique to its orbit. There-\\nfore, while one component of this disturbing force lies in the\\nplane of the orbit, the other is perpendicular to it. Let 12 be\\nthe distance through which the latter would move the moon in\\nthe time of its describing ~La in its orbit. The resultant is Le,\\ncutting the ecliptic in W. Again, after passing the node, let the\\northogonal component move the moon over Ud, while it would\\ndescribe Ue in its own plane. Then, by the joint action of Ue\\nand Ud, it describes Uf which produced makes the node at W.\\nIn the case here described, the line of nodes is supposed to lie\\nperpendicular to the line joining the earth and sun, and we see\\nthat the node is made to move backward, both when the moon\\napproaches it, and when it is leaving it. But in other posi-\\ntions of the line of nodes, it can be shown that the orthogonal\\ncomponent is directed sometimes toward the ecliptic and some-\\ntimes from it. In the former case the nodes retrograde, in the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0123.jp2"}, "122": {"fulltext": "108 ACCELERATION OF THfi MOON.\\nlatter they advance. In any revolution, however, the latter\\neffect is less than the former so that on the whole, the nodes\\nhave a retrograde motion.\\nThe nodes of the moon s orbit retrograde at the rate of 19\u00c2\u00b0\\n35 each year, thus completing a revolution in 18.6 years.\\n193. Disturbance of the inclination of the moon s orbit.\\nWhen the moon approaches a node, the inclination of its orbit to\\nthe ecliptic is generally increased for LN M is greater than the\\ninterior angle LNM. And it is generally diminished as the\\nmoon leaves a node, since ZN 1$ is less than the exterior angle\\n\u00c2\u00a3N !N These alternate changes nearly balance each other, and\\nleave the mean value of the inclination almost constant\u00e2\u0080\u0094\\nnamely, 5\u00c2\u00b0 8 44 (Art. 153).\\n1 94. Periodical and secular inequalities. The inequalities\\nin the moon s motion, which have been described, pass through\\nall their changes in a short period, as a month, a year, or a\\nfew years at most. These are called periodical. But there are\\nothers, whose periods extend through many centuries or ages.\\nThese are called secular. Some minute secular disturbances in\\nthe solar system run on in the same direction for an indefinite\\nnumber of centuries.\\n195. The acceleration of the moon s mean motion. This is\\nan interesting example of secular inequality. The period of a\\nlunation is now sensibly shorter than it was before the Chris-\\ntian era. This is ascertained by comparing the recorded date\\nof an eclipse which occurred in 720 before Christ with the\\ntime of any recent eclipse. The whole interval, if divided by\\nthe present mean length of a lunation, leaves a considerable\\nremainder. The acceleration amounts to about 10 in a cen-\\ntury.\\n196. Its cause. It has been stated that the sun diminishes\\nthe moon s gravity toward the earth (Art. 183). The amount\\nof this diminution depends, in part, on the eccentricity of the\\nearth s orbit. From the time of the earliest observations, the\\nearth s orbit has been slowly approaching a circle, and will", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0124.jp2"}, "123": {"fulltext": "ECLIPSE MONTHS. 109\\ncontinue to do so for many centuries to come. So long as the\\neccentricity of the earth s orbit is diminishing, the sun s dis-\\nturbing action on the moon diminishes also. The moon, there-\\nfore, being less drawn away from the earth, describes a smaller\\norbit, and, consequently, in a shorter time. In the course ot\\nages, the earth s orbit will reach the limit of its change, and\\nbegin to grow more eccentric. The moon s orbit will then\\ncommence to enlarge, and will, therefore, require a longer\\ntime to be described.\\nCHAPTER XII.\\nECLIPSES OF THE MOON. ECLIPSES OF THE SUN.\\n197. General relations in eclipses. The moon is eclipsed,\\nwhen it is obscured wholly or in part by the earth s shadow.\\nIt can occur, therefore, only at opposition, or full moon. The\\nsun is eclipsed, when it is either wholly or partially concealed\\nfrom view by the moon coming between it and the earth. This\\ncan happen only at conjunction, or new moon.\\nIf the moon s orbit and the ecliptic were coincident planes,\\nthere must be an eclipse of the moon at every full moon, and\\nan eclipse of the sun at every new moon for at those times\\nthe three bodies would be in a straight line. But as the moon s\\norbit and the ecliptic make an angle of 5\u00c2\u00b0 with each other, the\\nmoon generally passes opposition and conjunction so far north\\nor south of the sun, that there is no eclipse. That an eclipse\\nmay occur, the syzygies must happen near the line of nodes, so\\nthat, as the moon comes into conjunction or opposition, some\\nparts of the three bodies may be in a straight line.\\n198. Eclipse months. As there are two nodes on opposite\\nsides of the heavens, the sun in its annual progress must pass\\nthrough both of them every year, at intervals of about six\\nmonths. And as the moon comes into the line of syzygies\\nevery two weeks, the sun will certainly be near enough to a", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0125.jp2"}, "124": {"fulltext": "110 earth s shadow.\\nnode for one or two eclipses, and possibly for three, every six\\nmonths. Thus, the eclipses of any year always occur in clus-\\nters, at opposite seasons. If two or three are in January, the\\nothers are in July. These are called the node months of that\\nyear. In 1884, for example, the node months are parts ol\\nMarch and April, and parts of September and October. On\\naccount of the rei/ograde motion of the nodes, the sun passes\\nfrom a node to the same one again in less than a year, so\\nthat the node months occur earlier each successive year per-\\npetually.\\n*199. Eclipse of the moon. When the moon is eclipsed,\\nthere is nothing interposed to hide it from our view but it\\nmerely falls into the shadow of the earth, and is obscured.\\nThis obscuration may possibly continue for several hours.\\n200. Form and angle of the earth? s shadow. As the sun\\nis larger than the earth, and both are spheres, the tangents\\ndrawn from one to the other, along the corresponding edges,\\nwill converge and form a cone. Thus (Fig. 56), let AA be\\nthe sun, and BB the earth then BB C is the conical shadow\\nand rays of light from AA moving in straight lines, can not\\nenter any part of it. The axis of the shadow, EC, is the ex-\\ntension of the line joining the centers of the sun and earth.\\nSince the light is entirely excluded from the cone BB C, it is\\noften called the total shadow.\\nFig. 56\\nIToin AE; then the exterior angle AES ACE EAC;\\nACE AES EAC. But AES is the sun s apparent\\nsemi-diameter, and EAC is the sun s horizontal parallax.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0126.jp2"}, "125": {"fulltext": "LUNAR ECLIPTIC LIMIT. Ill\\nTherefore, the semi-angle of the earth s shadow is equal to th6\\nsun s apparent semi-diameter diminished by its horizontal\\nparallax. Calling the sun s semi-diameter d, and its horizontal\\nparallax^?, the semi-angle of the shadow is 6 p. d 16 2\\nand p 8 .8; 6 \u00e2\u0080\u0094p 15 53 .2, the mean value of the\\nsemi-angle of the shadow.\\n201. Length of the earth s shadow. In the triangle ECB\\nright-angled at B, as we know EB and ECB, EC is found by\\nthe proportion, sin {p p) rad 3956 856,050, the length\\nof the earth s shadow in miles.\\nSince the moon is 238,820 miles from the earth, the length\\nof the earth s shadow is more than 3 i times the distance from\\nthe earth to the moon and the moon, when eclipsed, passes\\nthrough the broader part of it.\\n202. Angular breadth of the section traversed by the moon.\\nLet h h be a part of the moon s orbit supposed to pass\\nthrough the axis of the shadow at M. Then Mm is the semi-\\ndiameter of the section, and MEm its angular semi-diameter,\\nwhich is to be found. The exterior angle EmB ECm\\nCEra CEra EmB ECm. But EmB is the horizontal\\nparallax of the moon, and ECm the semi-angle of the shadow.\\nCall the moon s parallax P, then the angular semi-diameter of\\nthe shadow P (6 p\\\\ or P p 6.\\nP 57 3 and 6 p 15 53 P p S 41 10\\nthe mean semi-diameter of the section.\\nSince the moon s semi-diameter is 15 r 33 the breadth of\\nshadow where the moon crosses it is 2f times the breadth of\\nthe moon.\\n203. Lunar ecliptic limit. The distance of the center or\\nthe earth s shadow from the node, when the moon at opposi-\\ntion would only touch the shadow, is called the lunar ecliptic\\nlimit. Let GN (Fig. 57) be an arc of the ecliptic, MN an arc\\nof the moon s orbit, N the node, Ca the semi-diameter of the\\n6hadow, and aM that of the moon when it only touches the\\nshadow at opposition. Then CK is the ecliptic limit. In the\\nspherical triangle CMN, right-angled at M, N being known.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0127.jp2"}, "126": {"fulltext": "112 DIMENSIONS OF PENUMBRA.\\nand also Qa and f/M, we have, by Napier s rule, rad x sin CM\\nsin CN x sin N from which CN is obtained. Since N\\nC\u00c2\u00ab, and aM are all variable, CX must also vary. Its greatest\\nvalue is 12\u00c2\u00b0 24/, beyond which an eclipse is impossible. Its\\nleast value is 9\u00c2\u00b0 2i r within which an eclipse can not fail to\\nccur.\\nFig. 57.\\n204. Magnitude of eclipse. The mere contact of the moon\\nand earth s shadow at the ecliptic limit is called an appulse.\\nIf the moon is obscured only in part, the phenomenon is called\\na partial eclipse. It is a total eclipse when the moon is en-\\ntirely enveloped in the shadow. If its center passes through\\nthe axis of the shadow, there is a central eclipse.\\n205. The earth? s penumbra. If tangents be drawn across\\nthe opposite sides of the sun and earth, as Ah, A!h (Fig. 56),\\nthey diverge, and inclose a space around the total shadow,\\ncalled the penumbra, or partial shadow. Its form is the frus-\\ntum of a cone, and it extends to an infinite distance beyond\\nthe earth. Within the penumbra, and outside of the shadow,\\nthere is light from a part of the sun only, while the other part\\nis conceaJed by the earth. Thus, at a point between BC and\\nBh produced, it is obvious that the limb of the sun near A\\ncould not shine, because the light would be intercepted by the\\nopposite side of the earth near B. The vertex of the penumbra\\nis between the earth and sun, at C.\\n206. Dimensions of the penumbra. The semi-angle of the\\npenumbra is h Q C (Fig. 56), which is equal to AC S. And the\\nexternal angle AC S EAC C EA. But EAC is the sun s\\nhorizontal parallax p and C EA is the s tin s apparent semi-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0128.jp2"}, "127": {"fulltext": "SOLAR AND LUNAR TABLES. 113\\ndiameter d; therefore, the semi-angle of the penumbra\\nThe semi-diameter of the section of the penumbra through\\nwhich the moon passes is AM, and its angular or apparent\\nsemi-diameter is AEM. And AEM, being external to the tri-\\nangle AEC, equals EC A EAC. But EAC is the moon s\\nhorizontal parallax P and EC A p d therefore, the\\napparent semi-diameter of the earth s penumbra P p 6\\nAt mean values, this equals 1\u00c2\u00b0 13 14 which is nearly 5 times\\nthe semi-diameter of the moon.\\n207. Effect of the penumbra. On account of the penum-\\nbra, the edge of the total shadow is not sharply denned, but\\nshades off into the full light by slow degrees, so that the moon\\npasses over rather more than its own breadth after entering the\\npenumbra, before it reaches the total shadow. This circum-\\nstance renders the exact moment of the observed beginning\\nor end of a lunar eclipse uncertain.\\n208. Effects of the earth s atmosphere. It is found, by cal-\\nculation, that the sun s light which traverses the lowest parts\\nof the earth s atmosphere would be so much refracted as to\\nmeet the axis of the shadow before reaching the moon. Hence,\\nthe whole disk of the moon is visible, even in a central eclipse,\\nand appears of a dull red color.\\nAnother effect is the enlargement of the shadow. The light,\\nwhich passes the earth near its surface, and would immediately\\nsurround the shadow if there were no atmosphere, is, in part,\\nobstructed, and in part diffused through the whole breadth of\\nthe shadow, as just stated. Therefore, the boundary of the\\nshadow is enlarged. To make its computed diameter agree\\nbest with the observed diameter, it is necessary to add\\n209. Solar and lunar tables. In order to determine the\\ncircumstances of any particular eclipse, tables are needed which\\nwill give for that time the sun s and moon s hourly motions,\\ntheir parallaxes, and their apparent semi-diameters. Such tables,\\nof the most accurate kind, are published in the Nautical Alma-\\nnac for each year, and several years in advance.\\n8", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0129.jp2"}, "128": {"fulltext": "114 LUNAR ECLirSE.\\n210. The moon? 8 relative orbit. The center of the earth 9\\nshadow moves in the ecliptic at the same rate as the sun, about\\n1\u00c2\u00b0 per day while the moon moves in its orbit about 13\u00c2\u00b0 per\\nday. To reduce these two motions to one, the relative orbit is\\nsubstituted for the real one, in the following manner. Let 1STG\\n*Fig. 58) be an arc of the ecliptic, ~Ng an arc of the moon s\\nDrbit, E the ascending node, A the place of the shadow s cen\\nier, and a that of the moon s center, at the time of opposition\\nWhile A, in one hour, moves to A suppose a to move to g.\\nThen A!g represents the distance and relative direction of the\\ncenters at the end of an hour after opposition. If gd be drawn\\nequal and parallel to A A, then Ad has the same length and\\ndirection as A!g. We may, therefore, suppose A, the center oi\\nthe shadow, to have remained at rest, and a, the moon s center,\\nto have moved to d in one hour in which case, Yad would be\\nthe relative orbit, id hg) is the moon s hourly motion in lati-\\ntude, and ai ah AA is the difference of hourly motions\\nIn longitude.\\nFig. 58.\\nDA A F^TS*^\\nThe inclination of the relative orbit to the ecliptic is found\\nby the right-angled triangle dai, in which ai and di being\\nknown, the angle dai, or its equal, dFD, is computed.\\nThe change from the true to the relative orbit is greatly ex-\\naggerated in the tigure. If truly represented, ag would be 13\\ntimes as long as A A\\n211. Times of beginning, middle, and end of a lunar\\neclipse, by projection. Let ND (Fig. 59) represent an arc of the\\necliptic, and A the center of the shadow at opposition. With\\nany convenient scale of equal parts, lay off from A the minutes\\nof hourly motion of the moon from the sun namely, AB, BC,\\nAD, etc., and divide them into as small fractions of an hour as\\nis desired. Then draw a circle with the radius Ao, equal tc", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0130.jp2"}, "129": {"fulltext": "MIDDLE AND OPPOSITION.\\n115\\nthe minutes in the semi-diameter of the shadow. Lay off Aa\\nperpendicular to CD, equal to the moon s latitude at opposi-\\ntion. Then a is the moon s center at that time. Through a\\ndraw N/j making N equal to the inclination of the relative\\norbit. Draw Amo perpendicular to N/1 At the middle oi\\nthe eclipse, the moon s center is at m, because Am bisects the\\nchord of the circle. From m draw ml perpendicular to ND.\\nThe parts of hourly motion between M and A show how long\\nbefore opposition the middle of the eclipse occurs.\\nFig. 59.\\nTake a line equal to the sum of the semi-diameters of the\\nshadow and the moon, place one end at A, and mark the points\\nc and/, with the other end on the moon s path. With a radius\\nequal to the semi-diameter of the moon, draw the circles around\\nc and/ which will touch the shadow. The eclipse begins\\nwhen the moon s center is at c, and ends when at f. Next\\ndraw the perpendiculars c-F, /G, and we have on the scale of\\ntime the interval FA between the beginning and opposition,\\nand AG between opposition and the end.\\nFinally, if the latitude is so small that the moon falls entirely\\ninto the shadow, making Ac A/ each equal to the difference\\nof the two semi-diameters, mark the points c and/ as before.\\nThen the perpendiculars, c K andy K, mark the times of the\\nbeginning and end of the total eclipse.\\n212. The middle of the eclipse, how related to the opposi-\\ntion. In the projection just described, N is the ascending", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0131.jp2"}, "130": {"fulltext": "116 ECLIPSE OF THE SUN.\\nnode, and the moon passes the node, 1ST, before it reaches the\\nopposition, a in which case, the middle of the eclipse at m\\nprecedes the opposition at a. This is true at either node the\\nmiddle of the eclipse precedes opposition, if the passage of the\\nnode precedes it but the middle is later than opposition, if the\\npassage of the node is later.\\n213. Times of beginning, middle, and end of a lunar\\neclipse by computation. The same results may be obtained\\nwith greater accuracy by trigonometry.\\nAs Aa and Am are perpendicular respectively to NT) and\\n~Nf, the angle a Am is equal to AN a, the angle of the relative\\norbit. The moon s latitude, Aa, being known, and the angle\\na Am, compute Am then by Am and AmM aAm) find AM,\\nand change it into time by the proportion, hourly motion in\\nlongitude of moon from shadow MA 1 hour time of pass-\\ning over MA. Thus, the time of the middle of the eclipse is\\nobtained.\\nAm and Ac being known, the angle mAc is calculated;\\nwhich subtracted from mA M (complement of aAm) leave*\\ncAE. Hence, in the triangle AcF, Ac and the angle cAF fur-\\nnish FA, which, changed to time as before, determines the time\\nwhen the eclipse begins. In the same manner, by the triangle\\nAc H, the time of the beginning of the total eclipse is found.\\nISTo additional calculation is necessary for the end for the in-\\nterval between the beginning and middle is equal to that be-\\ntween the middle and the end.\\n214. Digits eclipsed. The magnitude of an eclipse, is\\nusually expressed in digits, or 12ths of the moon s diameter.\\nThe distance from n, the inner edge of the moon, to the edge\\nof the shadow, is divided into parts, each equal to of nl.\\nThe number of such parts contained in no expresses the digits\\n\u00e2\u0080\u00a2eclipsed. If the digits eclipsed equal or exceed 12, the eclipse\\nis total.\\n215. Eclipse of the sun. An eclipse of the sun is of a dif\\nferent character from an eclipse of the moon. When the moon\\nis eclipsed, it is obscured by the earth s shadow falling on it", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0132.jp2"}, "131": {"fulltext": "LENGTH OF MOON S SHADOW.\\n117\\nThe moon itself is affected. But the sun is said to be eclipsed\\nwhen the moon intervenes between it and the earth, and hides\\nit from our view. The sun itself suffers no change, but we are\\nplaced in circumstances which prevent our seeing it. The\\nphenomenon would more properly be called an occultation of\\nthe sun.\\n216. Form and angle of the moon s shadow. The moon s\\nshadow, like the earth s, is a cone, surrounded by a penumbra\\nof infinite extent. Let AR (Fig. 60) be the sun, BC the moon,\\nand K, the vertex of its conical shadow. The exterior angle\\nSDK DEK DKR; DKK SDE DEK. JS T ow,\\nSDE is readily found, being the apparent semi-diameter of the\\nsun as seen from the moon. It is larger than as seen from the\\nearth, in the inverse ratio of distances, or as 387 386, nearly.\\nThe angle DEK is the sun s horizontal parallax at the moon.\\nOn account of distance, it is larger than at the earth, nearly in\\nthe ratio of 387 386 but on account of the moon s size, it is\\nless in the ratio of their diameters, 2161 7912. The sun s\\nhorizontal parallax at the earth, when thus modified, gives the\\nangle DEK. Therefore, DKE, the semi-angle of the moon s\\nshadow, is found. Its mean value is 16 1 .6, about the same\\nas the sun s apparent semi-diameter.\\nFig. 60.\\n217. Length of the moon s shadow. In the triangle DKC,\\nright-angled at C,\\nsin DKC rad DC DK,\\nthe length of the moon s shadow. Its mean length is 231,690\\nmiles, not quite sufficient to reach to the earth s surface.\\nWhen the moon is nearest to the earth, and the earth at the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0133.jp2"}, "132": {"fulltext": "118 SOLAR ECLIPTIC LIMIT.\\nsame time is furthest from the sun, the shadow is long enough\\nto reach about 14,500 miles beyond the earth s center.\\n218. Greatest breadth of section on the earth. In the case-\\njust mentioned, if the shadow is directed toward the earth s-\\ncenter, its section at the surface is the greatest possible. To\\nfind its diameter en, compute the angle eTd, thus:\\neT TK sin eKT sin TeK,\\nand eKT TeK eTd. Then,\\n360\u00c2\u00b0 eTd earth s circumference ed.\\nThis, when greatest, is about 85 miles, and therefore the-\\ndiameter of the section is 170 miles. Within this circle there\\nis witnessed a total eclipse of the sun.\\n219. The moorfs penumbra, and its greatest section on the\\nearth. The crossing tangents, ACH, RBG, etc., include the\\npenumbra. Its semi-angle is BID, which is equal to IKD -f-\\nIDR. But IRD is the sun s horizontal parallax at the moon,,\\nand IDR is the sun s apparent semi-diameter at the moon.\\nTherefore, BID is known. To this add IGD, the moon s appa-\\nrent semi-diameter, and the sum equals GDT. Hence, in the tri-\\nangle GDT we have GT, TD, and the angle GDT, by which\\nGTD is computed. From this, GH, the diameter of the pe-\\nnumbra on the earth, is obtained, as in the preceding article.\\nIts greatest diameter is 4,500 miles.\\n220. Solar eclijrtic limit. The distance of the sun s center\\nfrom the node, when the moon s penumbra at conjunction\\nwould only touch the earth in passing, is called the solar eclip-\\ntic limit. It is obtained by first finding the distance between\\nthe sun s and moon s centers at the given time. Let S (Fig.\\n61) be the sun s center, E the earth s, and M the moon s. It is\\nobvious that the limit occurs when the moon s disk just touches\\nAB, the extreme solar ray that meets the earth. The angular\\ndistance between the centers of the sun and moon at that time\\nis the angle SEM. But SEM SEA AEC OEM. SEA\\nis the sun s semi-diameter 6. OEM is the moon s semi-diame\\nter d. The angle AEC (in the triangle EAC) ECB OAK.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0134.jp2"}, "133": {"fulltext": "MAGNITUDE OF ECLIPSE. 119\\nBut ECB is the moon s horizontal parallax P and CAE is\\nthe sun s horizontal parallax jp. Therefore, the distance be-\\ntween the centers, SEM 6 d+Y p that is, the sum\\nof the semi-diameters of the sun and moon, added to the differ-\\nence of their parallaxes.\\nFig. 61.\\nEepresenting this distance by CM (Fig. 57), CN is computed\\nas in Art. 203. At the maximum, it is found to be 18\u00c2\u00b0 36\\nand beyond that, an eclipse is impossible. Its minimum value\\nis 15\u00c2\u00b0 20 and within that, there cannot fail to be an eclipse.\\n221. Magnitude of eclipse. If the eye of the observer were\\nat the vertex of the total shadow of the moon, it is plain that\\nthe moon s disk would exactly cover the sun s. And as the\\nmoon appears to our unaided vision to be of the same size as\\nthe sun, this., of itself, shows that the cone of the shadow has a\\nlength sufficient to reach about to the earth, as proved (Art.\\n217). But the moon s semi-diameter is sometimes greater than\\nthe sun s, and sometimes less. When greater, the eclipse is\\ntotal to all those places which fall within the section of the\\nshadow as it crosses the earth. When less, the eclipse is annu-\\nlar to places lying sufficiently near the path of the axis of the\\nshadow. It is called annular, because a ring of the sun s disk\\nis seen about the moon (Fig. 62). An eclipse, whether total oi\\nannular, is central at all places where the axis of the shadow\\nfalls, or to which it points. If only the penumbra passes a\\nplace, the eclipse there is part ial. The annular eclipse belongs\\nto the class of partial eclipses.\\nIf the total shadow reaches the earth at all, yet its section is\\nsmall, compared with that of the penumbra (Arts. 218 and", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0135.jp2"}, "134": {"fulltext": "1*20 VELOCITY OF THE SHADOW.\\n210). Hence, at a given place, while partial solar eclipses-\\noccur frequently, probably one or two every year, a total\\neclipse is extremely rare, perhaps not one in a century.\\nFicr. 62.\\nIt is possible for an eclipse to be annular to those places\\nwhere it is seen in the morning or evening, and total to those\\nin which it is seen near noon for on the meridian, the moon\\nappears about gV larger than at the horizon (Art. 165), and\\nmight cover the sun in one case, when it would not in the\\nother. If an eclipse thus changes its magnitude from annular\\nto total, and then to annular again, while crossing the earth, it\\nresults from the fact that the moon s shadow is too long to\\nreach the nearest part of the earth s surface, and not long\\nenough to reach its center.\\n222. Velocity of the thadovj. The hourly motion of the\\nmoon from the sun is about 30 This arc equals 2,080 miles\\nof absolute motion of the moon in its orbit. The shadow may\\nbe considered as having the same velocity as the moon. There-\\nfore, the absolute velocity of the moon s shadow on the earth is\\n2,08 miles per hour, which is sufficient to carry it across the\\nearth s disk in a little less than 4 hours. Relatively to the sur-\\nface, the velocity is much less than this. At the equator, the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0136.jp2"}, "135": {"fulltext": "SOLAR AND LUNAR ECLIPSES. 12\\nvelocity of surface is about 1,040 miles per hour, one-half that\\nof the shadow, and both motions are from west to east. Hence,\\nat the equator, the shadow passes a place at the rate of about\\n1,040 miles per hour, when it falls perpendicularly. When in-\\nclined, as at morning and evening, it passes more swiftly, in\\nthe proportion of radius to the sine of obliquity. The relative\\nmotion is also greater as the latitude increases, on account ot\\nthe slower motion of the surface. When an eclipse falls within\\npolar circle, the shadow and the observer may possibly move\\nin opposite directions, so that the relative motion would be the\\nsum, instead of the difference, of the real motions.\\n223. Duration of total and a?inular eclipses, The sun\\nand moon differ so little in apparent size, and the velocity of\\nthe shadow is so great, that the duration of total and annular\\neclipses is necessarily short. It is seen by the preceding article\\nthat the rotation of the earth generally reduces the relative ve-\\nlocity it therefore increases the duration. The greatest con-\\ntinuance of a total eclipse of the sun is about 8 minutes. An\\nannular eclipse may continue more than 12 minutes.\\n224. Number of solar and lunar eclipses. If an eclipse of\\nthe sun occurs in passing each node in a certain year, the lunar\\necliptic limit is so small, that the moon may escape an eclipse\\nat both the previous and the subsequent oppositions. In this\\ncase, there would be but two eclipses in a year, both solar.\\nThis is the least number.\\nIf, however, a lunar eclipse occurs very near a node, the\\nsolar limit is so large, that there must be one, and there may\\nbe two solar eclipses at the preceding and following conjunc-\\ntions. Thus, there may be as many as six eclipses while the\\nsun passes the two nodes. Another one may possibly occur\\nbefore twelve months have elapsed, in consequence of the back-\\nward motion of the nodes. Thus, the greatest number in a\\nyear is seven, of which five are of the sun, and two of the\\nmoon.\\n225. Relative number of solar and lunar eclipses. Solar\\neclipses are more numerous than lunar, in the proportion o", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0137.jp2"}, "136": {"fulltext": "122 THE SAROS.\\ntheir ecliptic limits that is, nearly as 3 2. But, because one\\nis really an eclipse, and the other an occultation, eclipses oi\\nthe moon at a given place are more frequent than those of\\nthe sim. An eclipse of the moon is visible to all on the hem-\\nisphere nearest to it, without regard to locality. But an\\neclipse of the sun is not seen at a place, unless the moon s\\nshadow falls at that place.\\n226. Solar and lunar eclipses begin on opposite sides. As\\nthe moon moves toward the east much faster than the sun or\\nthe earth s shadow, we determine on which side of the body\\na solar or a lunar eclipse begins, by simply considering the\\nmotion of the moon. In a lunar eclipse, the moon overtakes\\nthe shadow of the earth, and, of course, its eastern limb enters\\nthe shadow first. Hence, a lunar eclipse always begins on\\nthe east side of the moon, and ends on the west side. But\\nin a solar eclipse, the moon, in its eastward motion, overtakes\\nthe sun, and conceals its western limb first so that a solar\\neclipse begins on the west side of the sun, and ends on the\\neast side.\\n227. The Saros. This name is given to the cycle of 18\\nyears and 10 days, within which there is a return of the\\neclipses of preceding cycles, in the same order, and of nearly\\nthe same magnitude. The reason for this return of eclipses is,\\nthat the sun, moon, and node, return to very nearly the same\\nrelations to each other in the period just named.\\nThe return of the moon to the sun (a lunation) occurs 223\\ntimes, and the return of the sun to the node (a synodical rev-\\nolution of the node) occurs 19 times, in this period of 18 years\\nand 10 or 11 days, the two periods differing less than 12\\nhours from each other. As the sun, moon, and node, do not\\nresume their exact relation to each other, the series of eclipses\\nin one cycle will vary a little from those of the preceding;\\nand, therefore, after a number of cycles, their magnitude will\\nbecome essentially changed, and at length, one after another,\\nthey will disappear from the cycle entirely.\\nThis period was used by the Chaldeans for predicting the\\nreturns of eclipses, and by them called the Saros.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0138.jp2"}, "137": {"fulltext": "PHENOMENA OF A SOLAR ECLIPSE. 123\\n228. Phenomena of a total eclipse of the sun.\\n1. The corona. This is a luminous halo surrounding tho\\nmoon when the snn is entirely hidden, and sometimes presents\\na radiated appearance, and extends from the moon s edge out-\\nward a distance equal to one-third of its diameter, fading\\ngradually to the shade of the sky. It is concentric with the\\nsun, rather than with the moon, and is thought to indicate\\nan extensive solar atmosphere.\\n2. Bailtfs heads. At the instant when the fine thread oi\\nthe sun s edge is just appearing or disappearing, it is often\\ndivided up into a series of separate bright points. Being first\\nnoticed by Sir Francis Baity, they are known as Baily s beads.\\nThe appearance is by some attributed to the light of the\\nsun s edge coming through between the mountain summits\\nof the rough outline of the moon s disk. That they are not\\nalways seen, may arise from the fact that the limb in con-\\ntact may, in some cases, be much less serrated by mountains\\nthan in others.\\n3. Flame-colored protuberances. Another phenomenon, very\\nvariable in its aspect, consists of irregular projections, which\\nappear here and there around the disk of the sun, after it is\\nwholly in occultation. They are sometimes broad, and of small\\nelevation at others, they extend out nearly a tenth of the di-\\nameter of the sun that is, to the height of 80,000 miles, and\\nare often bent at a considerable angle. Occasionally, they are\\nentirely detached from the disk. These flame-colored or rose-\\ncolored prominences, when first discovered, were not supposed\\nto be sufficiently luminous to be seen except when the sun was\\nwholly covered by the moon. But improved instruments have\\nmore recently rendered them visible at other times. They are\\nfound to consist mainly of red-hot hydrogen thrown violently\\nupward from the fiery surface of the sun.\\nA total eclipse of the sun is one of the most Sublime and im-\\npressive phenomena of nature. The darkness is such, that the\\nlarger planets and stars appear and yet it is surprisingly sud-\\nden in coming and going for within a few seconds before and\\nafter the total darkness, the light is equal to that of hundreds\\nof full moons. A chill is felt like that of night. It is not\\nstrange that people of barbarous countries are filled with con-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0139.jp2"}, "138": {"fulltext": "124 CALCULATION JF ECLIPSES.\\nsternation and fear by the occurrence of a total eclipse of the\\nsun. Appendix D.\\n229. Eclipses at the moon. When we witness a solar\\neclipse, a spectator at the moon would notice only a small,\\ndimly-defined circular shadow passing over the earth s disk.\\nIt would be a partial eclipse of the earth.\\nBut when we see a total lunar eclipse, the phenomenon at\\nthe moon would be one of great interest, and of very strange\\nappearance. A dim red light from all parts of the sun s disk\\nis spread over the moon, being refracted thither by the earth s\\natmosphere (Art. 208). Hence, a spectator there would see the\\nsun expanded out into a thin dull-red ring, surrounding the\\nearth, and, therefore, having nearly four times the usual diam-\\neter of the sun s disk.\\n230. True form of shadows. It is impossible, in ordinary\\ndiagrams, to present the shadows of the earth and moon in\\ntheir true proportions. The distance of the sun is so very\\ngreat, compared with its diameter, that the shadows are ex-\\nceedingly slender, having a length about 11 times the diame-\\nter of the base. Fig. 63 is intended to exhibit them in their\\ntrue forms. A is the earth, and B the moon, having just\\nemerged from an eclipse. Only one-half of the whole length\\nof the shadow of each is presented. Again, on another scale,\\nC is the moon, and D the earth, on which its shadow is falling\\nin a solar eclipse.\\nFig. 63.\\nA B l\\nI\\n231. Calculation of eclipses.\u00e2\u0080\u0094 -Particular instructions are\\ngiven in various works on practical astronomy for calculating\\nall the circumstances of a solar or a lunar eclipse. Such in-\\nstructions, with examples for illustration, may be found in\\nLoomis s Practical Astronomy and Coffin s Solar and Lunar\\nEclipses.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0140.jp2"}, "139": {"fulltext": "LONGITUDE BY THE CHRONOMETER. 125\\nCHAPTEE XIII.\\nMETHODS OF DETERMINING TERRESTRIAL LONGITUDE.\\n232. Local time. Time is reckoned at every place from\\nthe moment when the sun crosses the meridian at either the\\nupper or the lower culmination. This is called local time for\\nat the same absolute instant, the time thus reckoned at any\\nplace differs from that on every other meridian.\\n233. Connection between longitude and local time. The\\nearth turns uniformly on its axis toward the east through 15\u00c2\u00b0\\nevery hour. Therefore, a place lying eastward of another will\\nhave the sun earlier on its meridian, and consequently, in\\nrespect to the hour of the day, will be in advance of the other\\nat the rate of one hour for every 15\u00c2\u00b0. Thus, to a place 15*\\neast of Greenwich observatory, it is 1 o clock p. m. when it is\\nnoon at Greenwich and to a place 15\u00c2\u00b0 west of that meridian,\\nit is 11 o clock a. m. at the same instant. Hence, the differ-\\nence of local time at any two places indicates their difference\\nof longitude.\\n234. Longitude by the chronometer. If a person leaves\\nLondon with a chronometer accurately adjusted to Greenwich\\ntime, and travels eastward till he finds his own time slower\\nthan the local time of the place by lh. 30m., then he know?\\nthe place to be 22\u00c2\u00b0 30 E. longitude. For 15\u00c2\u00b0 x 1\u00c2\u00a3 22^\u00c2\u00b0.\\nOn the contrary, if he travels westward, and at length finds\\nhis time-piece at 6h. 44m., when the local time is 4h. 32m. in\\nother words, that his Greenwich time is 2h. 12m. too fast then\\nthe longitude of the place is 33\u00c2\u00b0 W. In the same manner,\\nthe longitude of any two places may be compared with each\\nother.\\nFor the use of navigators, chronometers are made which run\\nwith very great accuracy, and may be relied on during long", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0141.jp2"}, "140": {"fulltext": "126 LONGITUDE BY A SOLAE ECLIPSE.\\nvoyages. There is always a probability, however, that a chro-\\nnometer may change its rate somewhat, when it comes to be\\ntransported from place to place. It is therefore safer on long\\nvoyages to nse several chronometers, and employ the mean of\\nall their indications.\\n235. Longitude by a lunar eclipse. In one respect, a lunar\\neclipse is very favorable for the comparison of longitudes. It\\nis a distant phenomenon, seen at the same absolute instant by\\nall. Hence, any difference of time in the observations at dif-\\nferent places is entirely due to difference of longitude.\\nBut in another respect, it is quite unfitted for the purpose.\\nOn account of the penumbra, there is no definite edge to the\\nshadow which passes over the moon s disk, and consequently\\nthere is great uncertainty as to the time of beginning or end of\\nthe eclipse. This method is but little depended on for accurate\\nresults.\\n236. Longitude by a solar eclipse. In both the above par-\\nticulars, a solar eclipse differs from a lunar. It is not an evenl\\nat a distance, seen at once by all, but on the earth s surface,\\nhappening to one place at one instant, and to another place at\\nanother. The time of beginning or end of a solar eclipse de-\\npends on the position of the observer.\\nOn the other hand, the phenomenon is very definite, and\\nthe moments of immersion and emersion of the sun s limb can\\nbe quite accurately fixed by observation.\\nTo compare longitudes by a solar eclipse, the observations\\nmade on the beginning and end at a given place are used as\\nmeans of calculating the time of conjunction that is, the time\\nwhen the sun and moon are in the same secondary of the\\necliptic. But that event occurs at a certain absolute instant.\\nThis computation being made for each place, the time of con-\\njunction ought to be exactly the same, so that the difference in\\nthe results is wholly due to a difference in the longitude of the\\nplaces. This method of obtaining the longitude of a place is\\naccurate, but laborious.\\nOccultations of stars by the moon are much more frequent\\nthan the occultation of the sun and these are phenomena of", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0142.jp2"}, "141": {"fulltext": "LONGITUDE BY THE TELEGRAPH. 127\\nthe same general character, and may be used in the same way\\nfor finding the longitude of a place.\\n237. Longitude by eclipses of Jupiter s satellites. The sat-\\nellites of Jupiter fall into the shadow of that planet, as the\\nmoon does into the shadow of the earth. Every such eclipse\\noccurs at a certain time and all who see it, see it at the same\\ninstant. Hence, these eclipses are favorable for determining\\nlongitudes. Moreover, they are occurring every day, while\\neclipses of the sun and moon are rare.\\nBut, on account of the penumbra of the planet, and the con-\\nsiderable diameter of the satellites, they disappear and reappear\\ngradually. There is difficulty, therefore, in observing accu-\\nrately the beginning and end of these eclipses. In order to\\nobtain the best results, the telescopes used by different ob-\\nservers ought to be alike in aperture and power.\\n238. Longitude by the lunar method. This is a method\\nparticularly useful to navigators, because the observations are\\nmade by the sextant. It consists in measuring the angular\\ndistance between the moon and some conspicuous heavenly\\nbody, as the sun, or a large planet or star, and then correct-\\ning the observation for parallax and refraction, so as to have\\nthe true distance between the bodies, as seen from the center\\nof the earth. The observer must also note the local time\\nwhen this measurement is made.\\nHaving with him the Nautical Almanac, in which the dis-\\ntances, as seen from the earth s center, are predicted for every\\n\u00e2\u0080\u00a2lay and hour of Greenwich time, he looks for the Greenwich\\ntime at which the distance agrees with the distance as he has\\nobtained it. The absolute time is the same hence, the dif-\\nference of time shows his longitude from Greenwich.\\nThe bodies, whose angular distances from the moon the\\nNautical Almanac gives for every three hours, with propor-\\ntional numbers for interpolation, are the sun, Yenus, Mars,\\nJupiter, Saturn, and nine bright fixed stars.\\n239. Longitude ~by the telegraph. Since the invention oi\\nthe magnetic telegraph, it has been employed to determine the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0143.jp2"}, "142": {"fulltext": "12S VELOCITY OF ELECTRIC CURRENT.\\ndifferences of longitude between fixed stations on land with a\\nprecision which was before altogether unattainable. Suppose\\ntwo stations to be connected by the telegraphic line, and that\\nthere is at each a clock keeping the local time. The observ-\\ners agree beforehand at what time, by his own clock, the one\\nat the most easterly station shall commence giving signals\\nand also at what time the other shall commence giving another\\nseries according to his clock. The interval between successive\\nsignals is also previously determined. When the moment ar-\\nrives, the first observer strikes the telegraphic key at the ex-\\nact beat of the clock, and the second observer records the\\ntime of the signal as shown by his own clock and thus they\\ncontinue to do till the full series is recorded. The second ob-\\nserver then commences sending signals, which are in like\\nmanner recorded by the first. The velocity of the electric\\ncurrent is so great, that the absolute time of making a signal\\nat one station, and of perceiving it at the other, may be con-\\nsidered identical so that the difference which is indicated\\nby the two clocks in each case is wholly due to difference\\nof longitude. Still greater precision is attained by causing\\nthe signal key at each station to record its own movement on\\nthe line of second-marks made by the clock at the other sta-\\ntion (Art. 46).\\n240. Velocity of the electric current. The method just de-\\nscribed is susceptible of such accuracy, that it has led to the\\ndiscovery of the velocity of the current. For, if the moment\\nof its arrival at the distant station is not identical with that\\nof the signal given, it will indicate a difference of longitude\\nless than the true difference when sent westward, but greater\\nthan the true difference when sent eastward. By this discrep-\\nancy, if it is appreciable, the velocity of the current becomes\\nknown. It is found to be about 16,000 miles per second.\\n241. Change of days in circumnavigating the earth. While\\na person travels westward, he lengthens his days by one hour\\nfor every 15\u00c2\u00b0, or 4 minutes for every degree, since he moves\\nalong with the apparent diurnal motion of the sun. In travel-\\ning eastward, on the contrary, he shortens the days at the same", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0144.jp2"}, "143": {"fulltext": "DAYS IN THE PACIFIC OCEAN. 129\\nrate, by moving in opposition to the sun s daily progress. Ii\\nwe suppose him to go westward entirely round the earth to the\\nsame meridian again, whether he takes a longer or a shorter\\ntime for the journey, he will lengthen the individual days suf-\\nficiently to make the whole number just one day less than if he\\nhad remained where he was. The 5th of a month is fo him the\\n4th and Tuesday, according to his reckoning, is Monday.\\nThe reason is obvious for during his journey, the earth has\\nmade a certain number of diurnal revolutions from west to\\neast but he, by going round from east to west, has, in respect\\nto himself, diminished that number by one.\\nAll this is exactly reversed when one goes round the globe\\nfrom west to east. He gains just a day by making all the days\\nof his travel a little shorter. It is plain that he makes one\\nmore diurnal revolution from west to east than the earth\\ndoes.\\nOf course, if these two individuals meet at their place of\\nstarting, they differ from each other just two days in their\\nreckoning.\\n242. Ambiguity as to days among the islands of the Pacific\\nOcean. If an island in the Pacific were settled by navigators,\\nwho had gone westward around Cape Horn, and also by others,\\nwho had sailed eastward around the Cape of Good Hope, the\\nreckoning of these two parties would differ by one day. To\\nthe former, a day will be the first of a month when it is the 2d\\nto the latter. It is, in fact, true that there are islands lying\\ncontiguous to each other which have this difference of reckon-\\ning.\\nIf inhabited land extended entirely round the earth, it would\\nbe necessary to Hx arbitrarily on some meridian on which the\\nchange of day should be made. For it is impossible that the\\nreckoning of days should go on unbroken around the earth.\\nThe arbitrary meridian would separate between places which\\ndiffer a day from each other so that, on the west side of it,\\nthe time is one day later, both in the month and the week,\\nthan on the east side.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0145.jp2"}, "144": {"fulltext": "180\\nWATER ACTED OX BY THE MOON.\\nCHAPTEE XIV.\\nTHE TIDES.\\n243. Definitions. The tides are the dailj rising and fall-\\ning of the waters of the ocean. When the water, in this datt,\\noscillation, has reached its highest point, it is called high-\\nwater at its lowest point, it is called low-water. While the\\nwater is rising, it is called flood; and while falling, ebb.\\nA lunar day is the time between two successive culmina-\\ntions of the moon. Its length is about 24h. 52m., being nearly\\nan hour longer than a solar day on account of the rapid east-\\nward motion of the moon. The tides make their revolutions\\nwithin the lunar day.\\nTwice in a lunation high-water is at a maximum, and twice\\nit is at a minimum; the former are called spring tides the\\nlatter, neap tides. The spring tides occur near the time o+\\nsyzygies, the neap tides near the time of quadratures.\\n244. Opposite tides. There are two tide-waves on opposite\\nsides of the globe, moving around it from east to west, and ar-\\nriving at any place at intervals, whose mean value is 12h.\\n26m., or half a lunar day. Since the mean diurnal motion of\\neach of the two opposite tides is the same as that of the moon,\\nthe action of the moon must be regarded as the principal cause\\nof the tides.\\n245. Form of the water acted on\\nby the moon. If the earth were cov-\\nered with water, and no force were\\nexerted except gravitation toward the\\nearth itself, its form would be exactly\\nspherical, as represented in Fig. 64.\\nBut if a distant body, as the moon,\\nshould also attract it, the sphere would\\nbe changed into a prolate spheroid\\nthat is, into a form produced by re-\\nvolving an ellipse about ts major axis.\\nLet the moon be id", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0146.jp2"}, "145": {"fulltext": "JOINT ACTION OF THE SUN AND MOON. 131\\nihe direction of CE produced, and suppose the center of gravity\\nof the nearer half of the water, DEF, to be at A, and that 01\\nthe remote half at B, while the center of the earth, as a whole,\\nis at C. Since A is more attracted than C, and C more than\\nB, the form of equilibrium must be disturbed, and some of the\\nwater will flow toward E, and other parts toward G, till the\\nparticles are in equilibrio between their unequal tendencies to\\nthe moon, and their gravity on the inclined surface of the\\nspheroid. E and G are the highest points of the spheroid, and\\nall points on the circle DF (perpendicular to EG) are the\\nlowest. Every section through EG is an ellipse, whose major\\naxis is EG, and whose minor axis is equal to DF. The ellip-\\nticity of the section will obviously depend not only on the\\nstrength of the moon s attraction, but also on the difference be-\\ntween the attractions on the nearer and remoter parts.\\nIn the case of the earth and moon, it is computed that the\\nmajor axis would exceed the minor by 5 feet that is, the tides\\nwould be only 2\\\\ feet high, and on opposite sides of the\\nearth, one directed toward the moon, the other from it. The\\ntide on the side nearest the moon is sometimes called the direct\\ntide the one on the remote side, the opposite tide.\\n246. Tides oy the sun. The same kind of effect is pro-\\nduced by the sun as by the moon. But the distance of the sun\\nis so great, that though it attracts the eartb more than the\\nmoon does, yet the difference of its attractions on the several\\nparts is less. The power of the moon to raise a tide is to that\\nof the sun about as 5 to 2.\\n247. Joint action of the sun and moon. At the time of\\nconjunction, the moon and sun attract in the same direction,\\nand therefore the tides are equal to the sum of the lunar and\\nsolar tides. The same is true at opposition, because each body\\nproduces two tides at once and the direct lunar tide coincides\\nwith the opposite solar tide, and vice versa. These are the\\nspring tides which occur at the syzygies.\\nAt quadratures, each body raises a tide at the expense of\\nthat raised by the other. For if the moon is in the direction\\nof EG produced (Fig. 64), it causes high-water at E and G,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0147.jp2"}, "146": {"fulltext": "132\\nDIURNAL INEQUALITY.\\nand low-water at D and F. And if the sun is in the direction\\nof DF produced, it causes high-water at D and F, and low-\\nwater at E and Gr, As the lunar tides are the highest, E and\\nG are the neap tides, made less by this action of the sun, than\\nif the moon had acted alone.\\n248. Effect of the inertia of water. If the moon and earth\\nwere at rest, the tides would be directed exactly to and from\\nthe moon. But while the waters are flowing toward these\\npoints, the moon, by the diurnal motion, passes westward, and\\ncauses them to change the places at which they tend to accu-\\nmulate. Thus, even if the wave were unchecked by the shores\\nof continents and islands, the summit would be two or three\\nhours behind the moon in passing a given meridian.\\n249. Diurnal inequality. At a given place, the two tides\\nwhich follow the culmination of the moon will vary in height,\\naccording to the relation between the latitude of the place and\\nthe moon s declination. If the moon, M. (Fig. 65), is on the\\nequator, it is clear that the tides on the equator, EQ, are great-\\nest, and that in other places they are less, as the latitude is\\ngreater. But the two successive tides at any place are equal\\nfor, by the rotation on NS, the tide at B in 12 J hours will\\ncome round to A, and be equal to the tide now there. The\\nsame is true of the tides C and D, or F and Gr. Hence, when\\nthe moon has no declination, there is no diurnal inequality.\\nBut suppose the moon has a northern declination, as in Fig\\n66. Then the highest points of the tide are at A in north lat", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0148.jp2"}, "147": {"fulltext": "COTIDAL LINES.\\n133\\nitude, and D in south. At A, where the direct tide is large,\\nthe opposite tide now at B will arrive in 12\u00c2\u00a3 hours, and will\\nbe small. But at C, this is reversed the direct tide is small,\\nand the opposite one (now at D, and arriving at C 12J hours\\nlater), is large. Therefore, when the decimation and the lat-\\nitude are both north, or both south, the direct tide that is, the\\ntide which first succeeds the upper culmination of the moon\\nis larger than the opposite tide but if one is north, and the\\nother south, the direct tide is smaller than the opposite tide.\\nThis difference in the height of the two successive tides is\\ncalled the diurnal inequality.\\n250. Change of direction and velocity caused by coasts.\\nThe tide-wave, which would move regularly westward around\\nthe earth, if it were wholly covered by deep water, is exceed-\\ningly broken up and changed, both in direction and velocity,\\nby coasts and shoals. Its general direction is westward but\\nas it can pass the continents only at their southern extremities,\\nit bears to the northwest, and then to the north, in the Atlan-\\ntic and Pacific oceans and when it enters seas or channels, i1\\nusually bends its course in the direction of their length.\\nFig. 67.\\n251. Cotidal lines. These are lines drawn on a chart ol\\nthe oceans, showing the posi-\\ntion of the summit of the tide-\\nwave for each hour of a day.\\nSuch a system of lines expresses\\nto the eye the direction and ve-\\nlocity of the tide at all places.\\nThus, on the open ocean, the\\nfigures 1, 2, 3, 4 (Fig. 67) show\\nthe situation of one and the\\nsame tide-wave at those hours,\\nrespectively. And in the chan-\\nnel which extends northward,\\nthe wave, having separated from\\nthe ocean tide, advances north-\\nward, and occupies the places\\nmarked at the hours indicated. The wave advances most rap", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0149.jp2"}, "148": {"fulltext": "134 ESTABLISHMENT OF A PORT.\\nidly in the deepest water. Hence, the front is generally convex\\nas in Fig. 67, since it moves fastest in the central part, where\\nthe water is deepest. For this reason, also, the tide may occu-\\npy as long a time in running through a long channel of shal-\\nlow water as in advancing half round the earth. The greatest\\nvelocity of the tide in the deep, open ocean, is near 1,000 miles\\nper hour. Some channels are affected by tides entering at both\\nextremities. For example, the German Ocean and English\\nChannel receive the Atlantic tide both at the north and at the\\nsouth end. As a consequence, the tide system is doubled,\\ncausing, at some points, four tides per day.\\n252. Modification in the height of the tide caused by\\ncoasts. The relation of coast lines to each other also very\\nmuch affects the height of the tide at particular places. When\\nthe tide directly enters a broad-mouthed bay, it grows higher\\nas the bay contracts in breadth and at the head of the bay,\\nthere is usually found the greatest height of all. One of the\\nmost remarkable examples is the Bay of Fundy. The western-\\nextremity of the Atlantic tide-wave, after entering this bay, is\\ngradually contracted by the shores as it advances, till, at the\\nhead of the bay, it sometimes rises to 70 feet.\\nThe height of the tide on the coast is generally greater than in\\nthe open ocean, owing to the effect of shoal water. The most\\nadvanced part of the wave moves slower than the hinder por-\\ntion so that the cross-section of the ridge becomes shorter y\\nand therefore higher, as the depth of water diminishes.\\nThe mean height of the spring tides at any place is called\\nthe unit of altitude for that place.\\n253. Establishment of a port. This phrase signifies the\\nmean interval between the culmination of the moon and the\\narrival of the tide at a given place. At every meridian, the\\ntide arrives later than the body which causes it but the delay\\nvaries exceedingly at different localities, on account of shoal\\nwater, direction and length of channel, etc. Even at the same\\nplace, the delay during a lunation varies according as the\\nsmall solar tide precedes or follows the large lunar one for\\nthe summit lies between them. It is the mean interval at", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0150.jp2"}, "149": {"fulltext": "TIDES MODIFIED BY DISTANCE. 135\\na given port, which is called the establishment of that\\nport.\\n254. Tides of lakes and inland seas. In general, the tides\\nof lakes and inland seas are scarcely perceptible. The reason\\nis, their extent is so small, that all parts are to be considered as\\nalmost equidistant from the moon. There is little opportunity\\nfor water to be attracted from the more distant to the nearer\\npart. The largest North American lakes have tides but an\\ninch or two in height. In the Mediterranean, however, which\\nderives no tide from the ocean, the tide-wave reaches 1J or 2\\nfeet.\\n25 5. Tides modified by the sun s and moon s change of dis-\\ntance. The difference of the moon s attraction on the several\\nparts of the earth is greatest when the moon is nearest, and\\nleast when it is most distant. The same is true of the sun.\\nHence, the tides of each month have a periodical increase and\\ndecrease as the moon passes through its perigee and apogee.\\nThey have a like, though much smaller, change each year, at\\nthe perihelion and aphelion of the earth s orbit. By the revo-\\nlution of the apsides of the moon s orbit, these maxima and\\nminima will alternately coincide once in 9 years. Combining\\nthese changes with those at syzygy and quadrature, the height\\nof the greatest possible spring tide, to that of the least possible\\nneap tide, is as 10 to 3.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0151.jp2"}, "150": {"fulltext": "L36 CLASSIFICATION OF THE D LANETS\\nCHAPTEK XV.\\nTHE PLANETS. TABULAR STATEMENTS. MERCURY. VENU\\nMARS.\\n256. Names and classification of the planets. \u00e2\u0080\u0094The planets\\nare solid spherical bodies revolving about the sun in orbits\\nwhich are nearly circular. The name planet signifies a\\nwanderer, and was given to these bodies because they con-\\ntinually change their places among the fixed stars, generally\\nmoving from west to east, but sometimes from east to west.\\nThese apparently irregular motions are fully explained by our\\nown annual motion, the earth on which we live being one of\\nthe planets.\\nThe planets are naturally arranged in three classes.\\n1. Four small planets near the sun, of which the earth is the\\nlargest namely, Mercury, Venus, Earth, Mars.\\n2. The planetoids, an indefinite number of bodies, too smal\\nto be measured with certainty, and occupying a ring outside*\\nof the first class. They are also called asteroids, and minor\\nplanets.\\n3. Four large planets, moving outside of the ring of plan-\\netoids, widely separated from each other, and at vast distances-\\nfrom the sun. These are Jupiter, Saturn, Uranus^ Neptune.\\nTwo planets of the first class, Mercury and Yen us, revolve\\nin orbits within the earth s orbit. These are called inferior\\nplanets, being lower down in the solar system than the earth\\nis. All the others, including the planetoids, are called superior\\nplanets because, in relation to the sun, the great center of at-\\ntraction, they are higher than the earth, and revolve in orbits\\nexterior to the earth s orbit. Appendix F.\\n257. Satellites. There is another class of spherical bodies,\\nholding a subordinate place in the solar system, since they re-\\nvolve around the planets as centers. These are called satel-\\nlites The moon, already described in Chapter X,, is a satellite", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0152.jp2"}, "151": {"fulltext": "PERIODIC TIMES OF PLANETS.\\n137\\nof the earth. They are distributed as follows the Earth has 1\\nMars, 2; Jupiter, 4; Saturn, 8 Uranus, 4 Neptune, 1. Mercury\\nand Venus have no satellites.\\nThe satellites are also called secondary planets and the\\nplanets, in distinction from them, primary planets.\\n258. Distances of the planets from the sun. The follow-\\ning table presents the mean distances of the planets from the\\nsun in millions of miles, and also their relative distances, the\\nearth s being called 1.\\nMean Distances.\\nRelative\\nDistances.\\nMercury\\n36,000,000\\n67,000,000\\n92,000,000\\n141,000,000\\n250,000,000\\n481,000,000\\n881,000,000\\n1772,000,000\\n2775,000,000\\n0.39\\n0.72\\n1.00\\n1.52\\n2.67\\n5.20\\n9.54\\n19.18\\n30.05\\nVenus\\nEarth\\nMars\\nPlanetoids\\nJupiter\\nSaturn\\nUranus\\nNeptune\\nIt appears by this table, that the remotest planet is 77 times\\nas far from the sun as the nearest. Hence it is that orreries,\\nunless of inconvenient size, always fail of truly representing\\nthe planetary distances. The same is generally true of dia-\\ngrams.\\n259. Periodic times of the planets, The following table\\ncontains the length of the sidereal revolutions in months and\\nyears, which is the most convenient form for the memory\\ntheir length in days and decimals, for calculations their mean\\ndaily motion and the time of their diurnal rotations, so far as\\nknown, in hours and decimals.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0153.jp2"}, "152": {"fulltext": "138\\nMAGNITUDES.\\nII.\\nMercury.\\nYenus\\nEarth\\nMars\\nPlanetoids\\nJupiter\\nSaturn\\nUranus\\nNeptune\\nSidereal Revolu-\\ntion.\\n3 months,\\n7J\\n1 year.\\n2\\n4.1 a\\n12\\n29\\n84\\n165\\nSidereal Revolu-\\ntion in Days.\\n87.969\\n224.701\\n365.256\\n686.980\\n4332.554\\n10759.104\\n30686.246\\n60228.072\\nMean Daily\\nDiurnal Ro-\\nMotion.\\ntation.\\n4\u00c2\u00b0\\n5 32 .5\\n24.09 h.\\n1\u00c2\u00b0\\n36 7 .7\\n23.35\\n0\u00c2\u00b0\\n59 8 .3\\n23.93\\n0\u00c2\u00b0\\n31 26 .5\\n24.66\\n0\u00c2\u00b0\\n4 59 .l\\n9.92\\n0\u00c2\u00b0\\n2 0 .5\\n10.24\\n0\u00c2\u00b0\\n0 42 .2\\n0\u00c2\u00b0\\n0 21 .5\\nIt will be found, by comparing the squares of any two periods\\nin Table II, and the cubes of the corresponding distances in\\nTable I, that their ratios are nearly the same and this should be\\ntrue according to Kepler s third law (Art. 119). Thus, for Nep-\\ntune and the earth, 30 3 I 3 27,000 and 165 2 l 2 27,225.\\nSo also, while Neptune is 77 times as far from the sun as Mer\\ncury is, its period of revolution is 685 times as long. For\\n77 3 l 3 685 2 l 2 nearly.\\nSince the periods increase more rapidly than the radii of the\\norbits, the velocities of the planets must become less, the fur\\nther they are from the sun. The distance described by Mer-\\ncury in a day is nearly nine times that which Neptune passe9\\nover in the same time.\\nIll\\nDiameters.\\nApparent\\nDiameters.\\nVolumes.\\nSun\\n860,000\\n2,992\\n7,660\\n7,918\\n4,211\\n86,000\\n70,500\\n31,700\\n34,500\\n32 4\\n0 7\\n17\\n9\\n37\\n16\\n4\\n3\\n1,295,000.000\\n0.054\\n0.880\\n1.000\\n0.248\\n1,350.000\\n689.000\\n75.000\\n102.000\\nMercury\\nVenus\\nEarth\\nMars\\nJupiter\\nSaturn\\nUranus\\nNeptune", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0154.jp2"}, "153": {"fulltext": "MAGNITUDES.\\n139\\n260. Magnitudes of the planets. Table III gives the di-\\nameters of the sim and planets in miles, their mean apparent\\ndiameters, and their volumes compared with the earth.\\nIn comparing the n ambers of this table, it is noticeable that\\nin general the planets diminish in size in each direction from\\nthe planetoids. If we suppose Mars to be placed between\\nMercury and Yenus, and Uranus and Neptune to change\\nplaces with each other, this would be strictly true.\\nObserve also that the diameters of the large planets beyond\\nthe planetoids are from eight to eleven times as large respec-\\ntively as those of the small ones within that group. Thus,\\nDiam. of Jupiter\\nSaturn\\nNeptune\\nUranus\\nand the sum\\n11\\n9\\n11\\n10\\nnearly.\\nthat of the earth\\nYenus\\nMars\\nMercury\\nthe sum\\nAnother remarkable fact appears on comparing the diameters\\nin Table III, and the times of diurnal rotation in Table II.\\nThe four small planets all rotate in periods of about 24 hours.\\nBut the large planets, so far as known, revolve in about 10\\nhours. Hence, the equatorial velocity of rotation is far greater\\non the large than on the small planets. That on Jupiter, for\\nexample, is 27 times as great as that on the earth.\\nThe dimensions of the planetoids are not given in the table,\\nbeing too small for measurement. One or two of the largest\\nare thought to be from 100 to 200 miles in diameter.\\nIY.\\nMasses.\\nDensity.\\nSpecific\\nGravity.\\nSun\\n326,800.000\\n0.065\\n0.769\\n1.000\\n0.111\\n311.953\\n93.329\\n14,460\\n16.862\\n0.25\\n1.21\\n0.85\\n1.00\\n0.73\\n0.24\\n0.13\\n0.22\\n0.20\\n14\\n6.8\\n5.2\\n5.5\\n4.2\\n1.3\\n0.8\\n1.3\\n0.9\\nMercury\\nYenus\\nEarth\\nMars\\nJupiter\\nSaturn\\nUranus\\nNeptune", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0155.jp2"}, "154": {"fulltext": "140 DIAMETERS OF PLANETS.\\n261. Masses and densities of the planets. Table IV ex-\\nhibits the masses and densities of the sun and planets, the\\nearth being called 1 also their specific gravities.\\nIt appears from table TV, that the small planets are mnch\\nmore dense than the large planets and the sun.\\n262. The sun and planets compared. By Table III, we see\\nthat the sun has 10 times the diameter, and 1,000 times the\\nvolume of Jupiter, the largest planet in the system. Table IV\\nshows that the mass of the sun is also more than 1 ,000 times as\\ngreat as that of Jupiter, and 700 times greater than the united\\nmasses of all the planets. Its attraction mainly controls the\\nmovements of all the planets, satellites, and comets. Hence,\\nthese bodies describe their various paths about it, scarcely dis-\\nturbing it from a state of rest. For this reason, this system of\\nbodies is called the solar system.\\n263. Diameters of planets, and their distances from the\\nsun. One of the most remarkable facts relating to the planets\\nis brought to view in comparing the distances in Table I with\\nthe diameters in Table III. While the diameters of the planets\\nare only a few thousands of miles, their distances from the sun\\nare many millions. The diameter of Neptune s orbit is more\\nthan 20,000 times the diameters of all the planets added to-\\ngether. To attempt to represent both the distances and mag-\\nnitudes of the planets in their proportions, by an orrery or\\ndiagram, is out of the question.\\n264. Directions of the planetary motions.* It has been\\nIt is desirable that the student should be able to recognize the planets, and\\nbecome familiar with their motions. Some aid can be had by the use of the\\ncommon almanacs. The American Ephemeris and Nautical Almanac, pub-\\nlished annually at Washington, can be purchased for one dollar by applying to\\nthe B i: eau of Navigation. This gives the exact places of the sun, moon, and\\nplanets for each day of the, year.\\nThe orrery, heliotellus, and lunatellus are instruments that explain their\\nmotions. The planisphere is an inexpensive instrument that shows the places of\\nseveral hundred of the more conspicuous fixed stars. It can be readily adjusted\\nfor any hour of the night. The astral lantern is a similar device, of larger size,\\nfor exhibiting maps of the stars on the illuminated sides of a cubical box.\\nAppendix M.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0156.jp2"}, "155": {"fulltext": "APPARENT MOTIONS OF MERCURY.\\n141\\neUteJ in preceding chapters that all the motions of the sun,\\nearth, and moon are from west to east. The same thing ia\\ntrue, in general, of all the planets and satellites and in nearly\\nevery case the inclination to the ecliptic is very small. The\\nonly exceptions are found in the satellites of Uranus and Nep-\\ntune, whose planes of revolution are nearly perpendicular to\\nthe ecliptic, and the motion in them from east to west. All\\nthe planetoids yet discovered revolve from west to east, though\\nthe orbit of one of them has an inclination as large as 34\u00c2\u00b0.\\nSince the motions in the solar system are so generally from\\nwest to east, this is regarded as direct motion and any mo\\ntions, real or apparent, which are from east to west, are called\\nretrograde.\\nMERCURY.\\n265. Tabular statements. Mean distance from the san.\\n35,761,000 miles; periodic time, 3 months; diameter, 2,993\\nmiles; diurnal rotation, 24.09 hours; specific gravity, 6-8.\\nFig. 68.\\n266. Apparent motions.\u00e2\u0080\u0094Mercury is an inferior p!anet,\\nwhose orbit is far within the earth s for it is seen alternately\\neast and west of the sun, and never more than 29\u00c2\u00b0 from it.\\nLet E (Fig. 68) be the earth, supposed, for the present, to be at", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0157.jp2"}, "156": {"fulltext": "142\\nAPPARENT MOTIONS OF MERCURY.\\nrest the circle ABD, the orbit of Mercury S, the sun and\\nB A the sky, on which the bodies are seen projected. When\\nMercury is at B, it is seen at B as it passes through D to A,\\nit appears to advance to A as it is now coming toward the\\nearth, it seems to be stationary at A then from A through C\\nto B, it appears to retrograde from A to B where it is again\\nstationary, as it moves away from us. Since the sun appears at\\nS j the planet passes by it, both when advancing and when\\nretrograding.\\nWhen the planet is at D and C, it is in conjunction with the\\nsun at C, between the earth and sun, it is said to be in the\\ninferior conjunction at D, in superior conjunction. B and A\\nare called the points of greatest elongation. At superior con-\\njunction, the motion of Mercury appears to be forward at the\\ninferior conjunction, backward and if the earth were at rest,\\nas we are now supposing, the planet would appear stationary\\nat the points of greatest elongation.\\nFig. 69.\\n267. The motions of Mercury as modified by the earth s\\nmotion. To simplify the case, it was supposed, in the preced-\\ning article, that the earth is at rest. But the earth moves in", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0158.jp2"}, "157": {"fulltext": "SYNODICAL PERIOD OF MERCURY. 143\\nnearly the same direction as Mercury, making about one rev-\\nolution while Mercury makes four (Table II). The effect is to\\nlengthen the arc of apparent advance, and shorten that of re-\\ntrogradation. Thus, let the earth be at A (Fig. 69), when\\nMercury is at F then it will appear in the sky at L. While\\nthe earth is advancing to B, Mercury passes the inferior con-\\njunction, and arrives at G, and appears at M, having moved\\napparently backward from L to M. As the earth moves to C,\\nMercury describes GKH, and is at superior conjunction ~N.\\nAgain, while the earth moves to D, Mercury passes round to\\nG, still advancing in the sky to O. But while the earth de-\\nscribes DE, Mercury again passes the inferior conjunction from\\nG to K, and apparently retrogrades from O to P after which,\\nit begins once more to advance. Thus, by the earth s motion,\\nthe planet is made to retrograde through a shorter arc, and to\\nadvance through a longer one, than if the earth were at rest.\\n268. Stationary points. If the earth were at rest, as sup-\\nposed in Fig. 68, the points where the planet would appear\\nstationary, in relation to the stars, would be A and B, at which\\ntangents drawn from the earth would meet the orbit. But the\\nearth s motion removes the apparently stationary points a little\\nway toward the inferior conjunction. For, in order to appear\\nstationary, the advance which the earth s motion causes, must\\nbe just neutralized by the retrogradation of Mercury. This\\nplanet appears stationary, when its elongation from the sun\\nis 15\u00c2\u00b0 or 20\u00c2\u00b0, according as it is nearer the perihelion or the\\naphelion.\\n269. The synodical period of Mercury. This is the time\\nin which it goes from a conjunction to the next conjunction of\\nthe same kind that is, describes one revolution relatively to\\nthe earth instead of a star.\\nThe sidereal period having been obtained by observing the\\nplanet s return to its node, the synodical period can be com-\\nputed from it by using the relative motions of Mercury and the\\nearth, just as we find the time in which the minute-hand of a\\nwatch wiL overtake the hour-hand. The synodical period oi\\nMercury can also be found independently, by means of transits", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0159.jp2"}, "158": {"fulltext": "144 TRANSITS OF MERCURY.\\nacross the sun s disk. The synodical period of Mercury is llfi\\ndays, which is nearly a month longer than its sidereal period.\\n270. Form and position of Mercury s orbit. The orbit 01\\nMercury is more eccentric, and more inclined to the ecliptic\\nthan that of any other of the eight planets. While the eccen-\\ntricity of the earth s orbit is only J ff that of Mercury is nearly\\nYet this renders the minor only shorter than the major\\naxis so that the form of the most eccentric of *Jie planetary\\norbits, if correctly drawn, would appear to the eye to be a\\ncircle.\\nThe inclination of Mercury s orbit to the plane of the eclip-\\n271. Phases of Mercury. At the inferior conjunction, C\\n(Fig. 6S). the unilluminated side of Mercury is turned toward\\nthe earth, so that, like the n^w moon, it is invisible. At the\\nsuperior conjunction, D, its illuminated side is toward us, anc\\nit is full. At A or B, where the ray AS, and our line of vis-\\nion, AE, are at right angles, the phase is a semicircle. On the\\narc AOB occur the crescent phases on BDA, the gibbous\\nphases.\\n272. Point of greatest brightness. Mercury is not bright-\\nest when full, because it is then too far distant. It is not\\nbrightest when nearest, because its dark side is toward us.\\nNor is it brightest at the place of greatest elongation but\\nbeyond it, toward the superior conjunction, when about 22\u00c2\u00b0\\nfrom the sun. Its apparent diameter, when nearest the earth,\\nand when most distant from it, is as 2\u00c2\u00a3 to 1.\\n273. Transits of Mercury. As Mercury, at the inferior\\nconjunction, passes nearly between the earth and sun, it may\\npossibly come exactly in a line with them, and thus be seen as\\na black round spot going across the sun s disk. This phenom-\\nenon is called a transit of Mercury. If the plane of its orbit\\nwere coincident with that of the ecliptic, a transit would\\nobviously occur at every inferior conjunction. Since the angle\\nbetween the two planes is 7\u00c2\u00b0, the planet can not.be seen on", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0160.jp2"}, "159": {"fulltext": "APPAEENT MOTIONS OF VENUS. 145\\nthe disk, unless near the node, for its perpendicular distance\\nfrom the ecliptic must be less than the sun s apparent semi-\\ndiameter that is, less than 16 By a simple calculation, like\\nthat in Art. 203, it is found that the limit of transit for Mer-\\ncury is 2\u00c2\u00b0 10\\n274. Node months for Mercury. The nodes of Mercury s\\norbit lie in that part of the heavens which the sun passes\\nthrough in May and November. Therefore, a transit of that\\nplanet can occur only in those months. More transits happen\\nin November than in May, because the planet is nearer peri-\\nhelion in November, and therefore more likely to be projected\\non the sun s disk. After the lapse of ages, the months will\\nchange, on account of the slow retrograde motion of the nodes.\\n27 5. Intervals between transits. -While the earth makes\\n13 revolutions from a node to the same node again, Mercury\\nmakes 54 revolutions, very nearly. Hence, in 13 years after a\\ntransit, the two bodies will return so nearly to the same rela-\\ntions to the node, that another transit is likely to occur. The\\nleast interval between transits at the same node is 7 years, in\\nwhich time Mercury makes very nearly 29 revolutions. As\\nthese are both odd numbers, the period may be halved, and a\\ntransit may occur in 3J years at the other node. This is the\\nshortest interval. The transits of Mercury in the last half of\\nthe present century are the following: November 11, 1861;\\nNovember 4, 1868 May 6, 1878 November 7, 1881 May\\n9, 1891 November 10, 1894.\\nVENUS.\\n276. Tabular statements. Mean distance from the sun,\\n66,822,000 miles periodic time, 7J months diameter, 7,660\\nmiles diurnal rotation, 23.35 hours specific gravity, 4.S.\\n277. Apparent motions. Like Mercury, Yenus appears to\\npass back and forth by the sun, reaching a distance of 47\u00c2\u00b0 at\\nits greatest elongation. This proves it to be an inferior planet,\\nbetween Mercury and the earth. Its sidereal period approaches\\n60 near to that of the earth, that its synodic period is length\\n10", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0161.jp2"}, "160": {"fulltext": "146 TEANSITS OF VENUS.\\nened to nearly If years. Hence, after making an apparent\\nretrograde motion, as LM (Fig. 69), it advances twice and two-\\nthirds round the heavens before it commences the next retro-\\ngrade arc, OP.\\n278. Phases and brightness of Venus. Yenus passes\\nthrough the same changes of phase as Mercury. But its ap-\\nparent diameter, when the crescent phase is narrowest, is more\\nthan 6 times as great as when at full. For its distance from\\nas, in the former case, is 92,000,000 67,000,000 25,000,000\\nmiles and in the latter, it is 92,000,000 67,000,000\\n159,000,000 miles, a distance more than six times as great as\\nthe other.\\nYenus is the brightest of the planets, and has been known\\nfrom ancient times as the morning and evening star, according\\nas it is west of the sun, or east of it.\\nThe place of greatest brightness for Yenus is when about 40\u00c2\u00b0\\nfrom the sun, between the point of greatest elongation and the\\ninferior conjunction. In this situation, it is frequently visible\\nall day.\\n279. Transits of Venus. The orbit of Yenus is inclined\\nto the ecliptic about 3 J degrees. The sun passes its nodes in\\nJune and December; therefore, the transits of that planet\\noccur in those months.\\nYenus makes 13 revolutions in very nearly the same time in\\nwhich the earth makes 8. Hence, a transit of Yenus at either\\nnode is usually preceded or followed by another at the same\\nnode, at an interval of 8 years. But this interval can not be\\nhalved, as in the case of Mercury (Art. 275), to find the time\\nof a transit at the other node because, 8 being an even, and\\n13 an odd number, there would, in 4 revolutions of the earth,\\nbe 6^ revolutions of Yenus, which would bring the two planets\\non opposite sides of the sun.\\nThe interval of 235 years is much more exactly measured by\\n382 revolutions of Yenus. Therefore, after a transit, there is\\nalmost a certainty of another at the same node in 235 years.\\nBut, for the same reason as before, the middle of this interval\\ncan not be taken as the date of a transit at the other node.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0162.jp2"}, "161": {"fulltext": "PARALLAX OF THE SUN. 147\\nThe smaller intervals must be obtained by using the period of\\n227 years, which is 8 years less than 235 years.\\nIn 227 years, there are 369 revolutions of Yenus within\\n1J days. Hence, transits are very likely to occur at the same\\nnode at intervals of 227 years. And at the middle of this in-\\nterval, there will probably be a transit at the other node, since\\n113^ revolutions of the earth, and 184 J of Yenus, bring both\\nbodies to the opposite side of the heavens. This interval oi\\n113^ years may be increased or diminished by 8, to furnish two\\nother intervals. Hence, the ordinary intervals are 8, 105^ r\\n113-J, and 121^ years, as may be seen in the following series of\\ntransits from 1518 to 2004:\\nInterval.\\nJune 5th, 1518\\nJune 2d, 1526 8 years.\\nDec. 7th, 1631 1051\\nDec. 4th, 1639 8\\nJune 5th, 1761 1211\\nJune 3d, 1769 8\\nDec. 8th, 1874 105 J\\nDec. 6th, 1882 8\\nJune 7th, 2004 121J\\n280. Parallax of the sun by a transit of Venus. The\\nplanet Yenus is so near the earth, that its transit across the\\nsun s disk is peculiarly favorable for obtaining the sun s paral-\\nlax. Let E (Fig. 70) be the earth, Y Yenus, and fde the disk\\nof the sun. Suppose observers stationed at A and B, the ex-\\ntremities of that diameter which is perpendicular to the orbit\\nof Yenus. Each one sees the planet describe a chord across\\nthe sun s disk from east to west. A observes it to come on at\\nc, and leave at d while to the view of B, it comes on at e, and\\nleaves at/1 And when it appears at a to the former, it is seen\\nat b by the latter. It is the distance between the two projec-\\ntions at a and b which is to be determined.\\n281. The length of ah in miles. Since the periodic times\\nof the earth and Yenus are known, the ratio of the distances of\\nE and Y from the sun is also known, by Kepler s third law.\\nHence, by subtraction, the ratio of the lengths of the triangles", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0163.jp2"}, "162": {"fulltext": "148 EXTEENAL AND INTEENAL CONTACTS.\\nVA and Ya is known. These triangles may be regarded aa\\nisosceles therefore, as they have equal angles at Y, they are\\nsimilar. Hence, YA Ya AB ab. Thus, from the known\\nratio of YA to Ya, and the length of AB, we have the length\\nof ab in miles.\\nFig. 70.\\nB\\n282. The length of sib in seconds. We next wish to obtain\\nthe angular length of ab. The observers carefully mark the\\nmoment of entering on the disk, and the moment of leaving it.\\nThus, the length of time occupied by the transit, as seen by\\neach observer, is carefully obtained. But since the angular\\nmotion per hour, both of the planet and the sun, is known, the\\ntime of crossing the disk can be changed into an arc and we\\nthus have the number of seconds of a degree in the chord cd,\\nand also the number in ef, and, therefore, in their halves, ca\\nand eh. But the number of seconds in the sun s semi-diameter,\\ncS or dS, is known. Hence, in the right-angled triangles c a,\\ntSb, we readily find the seconds in Sa and 8b, the difference\\nbetween which is the length of ab in seconds. Thus, we find\\nwhat angle is subtended by a line of given length, when placed\\nat the sun, and viewed from the earth or, which is the same\\nthing, placed at the earth, and viewed from the sun. There-\\nfore, we know what angle at the sun is subtended by the\\nradius of the earth and that is the sun s horizontal parallax.\\n283. External and internal contacts. At inferior conjunc-\\ntion, the planet Yenus subtends an angle of more than 1/, and\\ntherefore, in the transit, appears like a small black circle, whose\\ndiameter is f s of the sun s diameter. To observe the beginning\\nand end of a transit, the instant of external contact must first\\nbe noted, and afterward, when the planet has come wholly\\nupon the disk, the time of internal contact also. The mean ot\\nthese is the time at which the center crosses the edge of the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0164.jp2"}, "163": {"fulltext": "APPARENT MOTIONS OF MARS. 149\\ndisk. The duration of the transit is the interval between the\\nmoments at which the center of the planet enters and leaves\\nthe disk.\\n284. Situation of the observers. The observers can not\\nprobably be at points diametrically opposite, nor can they re\\nmain stationary during the transit, on account of diurnal\\nmotion therefore, allowance must be made for these circum-\\nstances. In order that several independent results may be\\nobtained, many stations are chosen, at the greatest possible\\ndistance from each other. In the observations on the transit oi\\n1769, one of a large number of stations was in Lapland, and\\nanother on one of the Sandwich Islands. The result arrived at\\nwas, that the sun s horizontal parallax is 8 5776, which, how-\\never, is now considered to be too small. (See Preface.)\\nMARS.\\n285. Tabular statements.\u00e2\u0080\u0094 Mean, distance from the sun,\\n140,760,000 miles periodic time, 2 years diameter, 4,211\\nmiles; diurnal rotation, 24.62 hours; specific gravity, 4.17.\\n286. Situation of Mars in the solar system. This is the\\nmost remote planet of the first group described in Art. 256\\nnamely, Mercury, Yenus, Earth, Mars. It is also the nearest\\nto the earth of those planets which are called superior.\\nAs Mars revolves in an orbit outside of the earth s, it can\\ncome into opposition to the sun, as well as into conjunction\\nwith it, appearing at every degree of elongation from 0\u00c2\u00b0 to\\n180\u00c2\u00b0.\\n287. Apparent motions. The real motion of Mars is from\\nwest to east; and during most of the year, its apparent motion\\nis in the same direction, sometimes accelerated, and sometimes\\nretarded, by the earth s motion. Near opposition, however,\\nwhen the earth overtakes and passes by Mars, its motion ap-\\npears retrograde. Thus, let the earth make one revolution\\nfrom F to F again (Fig. 71), while Mars describes nearly a hall\\nrevolution from G to 1ST. When the earth is at F, Mars ap-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0165.jp2"}, "164": {"fulltext": "150\\nAPPARENT MOTIONS OF MARS.\\npears in the direction FG when at A, Mars at H, appears iw\\nthe sky at O when the earth is at B, Mars at I, appears at P.\\nThus far, the motion has been in advance, though becoming\\nretarded near P. But as the earth passes from B, through C r\\nto D, Mars, passing over the shorter arc IKX, appears to retro-\\ngrade from P to Q after which it again advances, appearing\\nat E when the earth is at E, and in the direction FN when\\nthe earth is at F.\\nFig. 71.\\nFor the same reason, all the superior planets have a retro-\\ngrade motion at the time of opposition.\\n288. Phases, and changes of apparent size. At opposition^\\nM (Fig. 72), and at conjunction, M it is obvious that Mars\\nappears full, since we look in the same direction in which the-\\nsun shines upon it. In other positions, the angle between the\\nsun s rays and our visual line is acute, and the phase is gibbous\\n(Art. 170). The planet is so near us, that the phase differs\\nperceptibly from the full, when about half-way from conjunc-\\ntion to opposition, as at Q, Q\\nAt opposition, Mars is nearer to us than at conjunction by\\nthe diameter of the earth s orbit. This makes its mean distance\\nat opposition 48,000,000 miles, and at conjunction, 233,000,000.\\nBut on account of the elliptical form of both orbits, the\\nleast distance is 34,000,000 miles, and the greatest, 247,000,000\\nmiles.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0166.jp2"}, "165": {"fulltext": "APPEAKANCE OF DISK.\\n151\\n289. Orbit and equator of Mars, The orbit of Mars is in-\\nclined to the ecliptic nearly 2\u00c2\u00b0, and has an eccentricity equal\\nto T V\\nIn its diurnal rotation, it considerably resembles the earth,\\nhaving about the same length of day, and its equator being in-\\nclined nearly 29\u00c2\u00b0 to its orbit. Hence, the seasons vary some-\\nwhat more than those on the earth.\\n290. Appearance of dish. Mars is remarkable among the\\nplanets for its redness. The telescope reveals some permanent\\ninequalities of surface, by which its diurnal rotation has been\\ndetermined more satisfactorily than in the cases of Mercury\\nand Yenus. And there are other appearances, which change\\nas the relation of the equator to the sun changes. The polar\\nregions, when turned away from the sun, exhibit a whiteness,\\nwhich is supposed to be the effect of ice and snow and thia\\nwhiteness disappears gradually, when the pole is turned again\\ntoward the sun.\\n290a. Satellites. Mars has two satellites, discovered August\\n11-17, 1877, by Prof. Asaph Hall, of Washington. They are\\nremarkable for their small size, and for the proximity of the inner\\none to the planet being but 4,000 miles from its surface, and\\nconsequently revolving in the brief time of 7 hours, 38 minutes.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0167.jp2"}, "166": {"fulltext": "152 CHARACTEEISTICS OF PLANETOIDS\\nCHAPTEE XVI.\\nTHE PLANETOIDS. JUPITER.\u00e2\u0080\u0094 SATURN. URANUS. NEPTUNE.\\n291. The space between the four s?n all planets and the four\\nlarge ones. The large interval between Mars and Jupiter,\\nwhich seemed to break the continuity of the series of planets,,\\nwas noticed by Kepler. About the close of the last century,\\nBode, of Berlin, showed that a series of numbers, following a\\ncertain law, would express pretty accurately the planetary dis-\\ntances from the sun, if only the vacancy between Mars and\\nJupiter were supplied. This led to a special search for new\\nplanets, which was presently rewarded by the discovery of sev-\\neral small bodies, which have been called asteroids, planetoids,\\nor minor planets.\\nTHE PLANETOIDS.\\n292. Their number, and the time of their discovery. Four\\nof these bodies were discovered within the first seven years of\\nthe present century namely Ceres, Pallas, Juno, and Yesta.\\nSince 1845, others have been found nearly every year, till their\\nnumber at the present time (1884) is over two hundred. The\\nwhole number of planetoids may be regarded as indefinitely\\ngreat.\\n293. Characteristics. They are distinguished from the\\neight planets in the following particulars\\n1. By their diminutive size. They are invisible to the\\nnaked eye, and by the telescope can not be distinguished from\\nfaint fixed stars, except by their motion. They are generally\\ntoo small to show a sensible disk, and hence can not be meas-\\nured with any certainty. The largest of them is believed to be\\nonly about 200 miles in diameter. And it is estimated by the\\nslight disturbing influence which they exert, that their entire\\nmass is equal only to a small fraction of the earth.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0168.jp2"}, "167": {"fulltext": "jupiter s magnitude. 153\\n2. By the large eccentricity and obliquity of their orbits.\\nThe eccentricity of most of them is much greater than that 01\\nany of the eight planets.\\nThe obliquity of the orbit of Hebe is 14\u00c2\u00b0, and that of Pallas\\nis 34\u00c2\u00b0, which is the greatest yet discovered.\\n3. By their being clustered in a ring. The orbits vary con-\\nsiderably in size, and therefore the periodic times are various\\nBut as they are generally quite eccentric, nearly every planet-\\noid is nearer the sun at perihelion, than the others at aphelion.\\nThe orbits are therefore all linked together, and pass through\\neach other. Thus, the planetoids are to be regarded as moving\\namong each other about the sun, within the limits of a ring,\\nwhose breadth, in the direction of the radius vector, is more\\nthan 160,000,000 miles. Flora, which moves in the smallest\\norbit yet discovered, performs its revolution in 3-J years\\nHilda, the most remote, in 8 years. Their mean periodic time\\nis 4J years and their mean distance from the sun is 250,000,000\\nmiles.\\n294. Modes of designating them, Feminine mythological\\nnames have been applied to all the planetoids which have yet\\nbeen discovered. But the more convenient method, and the\\none most used, is to express each planetoid by a number, show-\\ning its place in the order of discovery, this number being in-\\nclosed in a circle, which indicates a disk. Thus, Ceres is (T)\\nThetis, Pandora, etc. See Table V., at the end.\\nJUPITER.\\n295. Tabular statements. Mean distance from the sun,\\n480,638,000 miles periodic time, 12 years diameter, 86,657\\nmiles diurnal rotation, 9.92 hours specific gravity, 1.3.\\n296. Jupiter s magnitude and place in the solar system.\\nJupiter is the nearest of the large planets outside of the planet-\\noids, and its orbit is not far from 130,000,000 miles beyond the\\nring which includes them. On account of its great distance\\nfrom the sun, compared with the earth s, Jupiter presents to us\\nno visible change of phase, appearing always full. Its disk, a", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0169.jp2"}, "168": {"fulltext": "154 THE BELTS OF JUPITER.\\npresented to us, is almost the same as if we were at the sun\\nThe same is, of course, true of all the planets still more re*\\nmote.\\nJupiter greatly surpasses all the other planets in magnitude.\\nIn volume, it is about 1| times the sum of all the others, and in\\nmass, more than 2\u00c2\u00a3 times their united mass.\\n297. Its spheroidal form. Though the diameter of Jupiter\\nis 11 times that of the earth, yet it rotates on its axis in less\\nthan 10 hours so that the equatorial velocity is about 27 times\\nas great as the earth s. This rapidity of rotation produces a\\nsensible oblateness of the planet. Its ellipticity is Y and so\\nconsiderable a deviation from the spherical form is perceptible\\nto the eye without measurement.\\n298. The belts of Jupiter. This name is given to bands or\\nstripes of darker shade than the rest of the disk, stretching\\nacross it in the direction of its rotation (Fig. 4, Fr.) They vary\\nfrom time to time in number and in breadth, often covering a\\nlarge part of the surface. A belt usually appears of uniform\\nbreadth entirely across, but not always its edge is occasionally\\nbroken, and sometimes it is much wider on one part of the\\ndisk than on the other, the change of breadth being commonly\\nquite abrupt, and thereby revealing the rotation of the planet.\\nThere are, ordinarily, two conspicuous belts, lying near the\\nequator, one north, and the other south of it.\\n299. Supposed cause of the belts. The belts are considered\\nas affording proof that Jupiter is surrounded by an atmosphere,\\nin which clouds are floating. As a consequence of the exceed-\\ningly rapid rotation of the planet, there would be very power-\\nful currents, analogous to the trade-winds of the earth and\\nthe clouds would be thrown into the form and arrangement of\\nzones parallel to the equator. The clouds would reflect the\\nsun s light to us more strongly than the atmosphere and the\\ndark belts, therefore, are the unclouded portions, through which\\nwe look on the body of the planet.\\n300. Orbit and equator of Jupiter. The orbit rf fupitej", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0170.jp2"}, "169": {"fulltext": "satellites of jupitek. 155\\nis nearly coincident with the plane of the ecliptic, its inclina-\\ntion being only 1\u00c2\u00b0 19 Its eccentricity is ^V? which is three\\ntimes as great as that of the earth s orbit.\\nThe equator of Jupiter is inclined a little more than 3\u00c2\u00b0 to\\nits orbit. There is, therefore, no perceptible change of seasons\\non that planet.\\n301. Satellites of Jupiter. These are four in number, re-\\nvolving in orbits very nearly circular, and in planes which\\nmake small angles, both with the orbit and the ecliptic. They\\nare called the first, second, third, and fourth, reckoning out-\\nward from the planet.\\n302. Their revolutions. On account of the position of the\\norbits, we see the satellites passing back and forth across the\\nplace of Jupiter, nearly in straight lines (Fig. 4, Fr.) From\\ntheir greatest elongation west of Jupiter, they advance to the\\ngreatest elongation on the east, passing behind the planet on\\ntheir way. Then, after remaining stationary a short time, they\\nretrograde to the west side, passing between us and the planet.\\nThese movements prove that they revolve from west to east, as\\nall the primary planets do. At the greatest elongation on\\nthe east side, they are, for a little while, stationary, because\\ncoming toward us and on the west side also, because going\\nfrom us.\\n303. Their size, distance, and periods. The diameters of\\nthe first, third, and fourth satellites are greater than that of the\\nearth s moon, but the diameter of the second is a few miles\\nless. To us, they appear as stars of the 6th or 7th magni-\\ntude but on account of the brightness of the primary, they\\ncan very rarely, if ever, be seen by the naked eye. If two or\\nthree satellites happen to appear very near together, they may\\npossibly be seen by the naked eye, when they of course seem\\nto be one. The first is further from Jupiter than the moon is\\nfrom the earth, and the fourth nearly five times as far. Their\\nperiods of revolution are very short, compared with the moon s\\nfor, on account of the strong attraction of Jupiter, great velocity\\nis requisite to maintain them in their orbits.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0171.jp2"}, "170": {"fulltext": "156\\nECLIPSES AND OCCULTATIONS.\\nSatellites.\\nDiameters.\\nDistances.\\nSidereal Revolutions.\\n1\\n2\\n3\\n4\\n2,365\\n2,123\\n3,471\\n2,966\\n260 ,370\\n414,360\\n660,900\\n1,162,400\\n1 d. 18 h. 28 m.\\n3 13 15\\n7 3 43\\n16 16 32\\n304. Their configurations. Tlie relative positions of Jupi\\nter and the four satellites, as seen from the earth, are inces-\\nsantly varying. We most frequently see two or three on one\\nside, and two or one on the other; rarely all on one Fide.\\nVery often, one or two are invisible, being either behind\\nJupiter, or projected on it. Sometimes, three are thus con-\\ncealed, and in very rare instances, all four.\\n305. Eclipses and occultations of Jupiter and its satel-\\nlites. The great dimensions of Jupiter and its shadow, and\\nthe small inclinations between the ecliptic, Jupiter s orbit, and\\nthose of its satellites, cause very frequent eclipses and occulta-\\ntions. A. satellite of Jupiter is eclipsed when it goes through\\nthe shadow of the planet it suffers occultation when it is\\nhidden from our view by passing behind the planet. The first,\\nsecond, and third satellites pass through both eclipse and oc-\\ncultation at every revolution, and the fourth rarely escapes.\\nBesides these two classes of phenomena, there are two others,\\nnamely, the eclipse of Jupiter, when its satellite casts a\\nshadow upon it and an occultation of Jupiter, when a satel-\\nlite passes between it and the earth. The eclipse is a small\\nblack spot passing over the disk. The occultation is scarcely\\nperceptible, because the planet and satellite are of about equal\\nbrightness. On a belt, the satellite may appear brighter\\nand between two belts it may appear less bright than the\\nprimary.\\n306. Order of eclipses and occultations. When Jupiter is\\neast of opposition, the eclipse always precedes the occultation\\nwhen west of opposition, the occultation precedes the eclipse.\\nFor, let S (Fig. 73) be the sun A, B, C, several positions of\\nthe earth J, Jupiter and EHK, the orbit of a satellite. The", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0172.jp2"}, "171": {"fulltext": "ECLIPSES AND OCCULTATIONS.\\n157\\nOodies are supposed to revolve in the order of the letters. Ii\\nthe earth is at A, SA produced marks the place of opposition,\\nand Jupiter is east of that place. The satellite enters the\\nshadow at E, emerges at F, and then passes behind the planet\\nat G-, and reappears at H. In this case, the eclipse is past be-\\nfore the occultation begins. In the same manner, the eclipse\\nof Jupiter begins when the satellite is at K, and ends when at\\nL and the occultation follows it, while the satellite moves\\nfrom M to N If the earth were at C, Jupiter would be west\\nof opposition that is, west of SC produced. And it is obvious\\nthat the satellite would go behind the planet before entering\\nthe shadow, and also would appear between us and the planet\\nbefore casting a shadow on it.\\nFig. 73.\\nThe earth is not, in general, so situated that one phenom-\\nenon is closed before the next begins; and it is never true oi\\nthe first satellite. The case is represented by the orbit eKkn.\\nThe eclipse begins at e, and the occultation ends at h; but the\\nend of the eclipse and the beginning of the occultation are not\\nseen. In the same manner, the eclipse of Jupiter begins at yfc,\\nand the occultation ends at n. During a part of the interven-\\ning time, the shadow and the body of the satellite are both\\nseen, projected at different places on the primary.\\nAt the time of opposition, the earth being at B, the eclipse", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0173.jp2"}, "172": {"fulltext": "158 Saturn s disk.\\ns f a satellite obviously occurs entirely within its occultation,\\nand the occultation of Jupiter entirely within its eclipse.\\nIt is found that there exists such a relation between the\\nmean motions of the three first satellites, that they can never\\nall be eclipsed at the same time.\\n307. The velocity of light discovered by the eclipses oj\\nJupiter s satellites. In 1675, it was discovered by Roemer\\nthat eclipses occurred earlier than the calculated time, when\\nthe earth is in that part of its orbit which is near to Jupiter,\\nand later, when in the remote part. The eclipses of any one\\nsatellite are so frequent, that the mean interval between them\\nis obtained with great accuracy and by this mean interval,\\nthe times of future eclipses could be calculated. But it was\\nperceived that while the earth moves from the remote side to\\nthe nearer side of its orbit, the real intervals are shorter than\\nthe mean, so that, at the nearest point, an eclipse occurs about\\n8m. 13-^s. too soon. Again, as the earth goes to the side of its\\norbit furthest from Jupiter, the real intervals are all greater\\nthan the mean and at the most distant point, an eclipse is\\nlater than the calculated time by 8m. 13-Js. Roemer attributed\\nthis periodical error of time to the progress of light, and in-\\nferred that light requires 16m. 27s. to cross the earth s orbit.\\nThis makes the velocity of light near 187,000 miles per sec-\\nond which seemed at first quite incredible, and was received\\nwith distrust. But its correctness was soon established by the\\ndiscovery of the aberration of the stars, which gives about the\\nsame result (Art. 146).\\nSATURN.\\n308. Tabular statements. Mean distance from the sun,\\n881,203,000 miles; periodic time, 29 years diameter, 70,500\\nmiles diurnal rotation, 10.21: hours specific gravity, 0.8.\\n309. Saturn s disk. Saturn is the second planet in size\\nand being the second in order beyond the planetoids, is not too\\nfar from the earth to present a large disk. Its form is seen to\\nbe elliptical, and it is faintly striped with belts in the direction", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0174.jp2"}, "173": {"fulltext": "satukn s RItfGS. 159\\nof the major axis. Both these appearances are explained by\\nthe rapid rotation of the planet on its axis, as in the case oi\\nJupiter. Its ellipticity is j 1\\n310. Saturn s rings. The distinguishing feature of this\\nplanet is the system of broad thin rings which surround it.\\nThey lie in a plane inclined about 2S\u00c2\u00b0 to the ecliptic, and\\ntherefore generally present an elliptical appearance to the\\nearth (Fig. 3, Fr.) The ring, as usually seen, consists of two\\nrings, the inner of which is the widest. The inner edge is\\n19,000 miles from the surface of the planet and the diameter\\nfrom outside to outside is 168,000 miles. The line in which\\nthe plane of the ring intersects the plane of Saturn s orbit is\\ncalled the line of the nodes.\\nWithin the double ring already described, there is a much\\nfainter one, which can not be seen with ordinary telescopes.\\nBy careful observations, it is also perceived that there are sev-\\neral concentric divisions of the rings, which vary their number\\nand position from time to time. These fainter divisions are\\ninvisible, except at the ends of the ellipse. The rings lie in\\none plane, and are exceedingly thin. The latest measurements\\nmake their thickness less than 40 miles. A circle of common\\nwriting paper, one foot in diameter, would be too thick to rep-\\nresent it correctly. But the thickness appears not to be uni-\\nform for in the edge view, it often presents the aspect of a\\nbroken line, as though some parts were thick enough to be seen,\\nand others not. There seems to be evidence that the rings\\nconsist either of liquid matter, or else of solid matter in a dis-\\nintegrated condition.\\n311. Rotation of the rings. Such rings of matter around\\nSaturn could no more be sustained without rotation, than the\\nmoon could remain at its distance from the earth without re-\\nvolving about it. They are found to rotate in their own plane\\nwithin the short period of 10J hours, nearly the same as the\\nperiod of the planet itself. The outer edge of the ring must,\\ntherefore, have a velocity of 14 or 15 miles per second.\\n312 The plane of the rings always parallel to itself.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0175.jp2"}, "174": {"fulltext": "160 Saturn s rings.\\nDuring the revolution of Saturn around the sun, occupying\\nabout 29 years, the rings maintain everywhere the same posi-\\ntion in relation to the plane of Saturn s orbit as represented in\\nFig. 74, in which ah is the earth s, and ACEG Saturn s orbit,\\nseen obliquely. While the planet passes through the half revo-\\nlution ACE, the north side of the rings is seen by an observer\\non the earth as an ellipse, more or less eccentric but during\\nthe other half, EGA, the south side is in view. Each of these\\nperiods occupies near 15 years. When Saturn is near A and\\nE, the line of nodes passes across the earth s orbit, and the\\nedge of the rings is therefore directed toward the sun and\\nearth and at those times it fills too small an angle to be seen,\\nexcept by the best instruments.\\nFig. 74.\\n313. Passage of the plane of the rings across the earth? s\\norbit. The motion of Saturn is so slow, that it requires almost\\na year for the plane of its rings to pass by the whole diameter\\nof the earth s orbit. Let DF (Fig. 75) be the earth s orbit, and\\nAC a portion of Saturn s. Suppose these orbits to lie in the\\nplane of the paper, and the plane of the rings to be inclined\\nabout 28\u00c2\u00b0 to the paper, making the common section of the two\\nplanes in the lines AD, BG, etc. Saturn is 9.54 times as far\\nfrom the sun as the earth is. Therefore, SA SD 9.54 1\\nrad. sin SAD; SAD, or its equal, ASB 6\u00c2\u00b0 V ASC\\n12\u00c2\u00b0 2 Knowing Saturn s periodic time, we readily find\\nthat it will describe 12\u00c2\u00b0 2 in 359^ days, near six days less than\\na year. Hence, while Saturn passes from A to C, the earth\\nwill pass very nearly around its orbit, DEFG. But the earth", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0176.jp2"}, "175": {"fulltext": "DISAPPEARANCE OF THE RINGS.\\n161\\nmay be at any point of its orbit when the planet reaches A.\\nThe disappearances of the rings will vary according to the\\npositions of the earth.\\nFig. 75.\\n314. Circumstances of the disappearances. There are three\\nways in which the rings may fail to be visible during the\\nperiod in which the line of their nodes is crossing the earth s\\norbit.\\n1. The ring may present its edge exactly to the earth, when,\\nin common telescopes, it subtends too small an angle to be\\nseen.\\n2. It may present its edge exactly to the sun, so that neither\\nside of the ring is enlightened.\\n3. Its plane may be directed between the earth and sun, when\\nthe dark side is toward us.\\nThe disappearance by either of the two first causes may be\\nconsidered as only momentary; for the line of nodes passes\\nthe breadth of the sun in less than 2 days, and of the earth in\\nabout 20 minutes. But the third cause may conceal the ring\\nfrom our view for weeks or months. This prolonged disappear-\\nance may occur either once or twice, or possibly not at all, while\\nthe line of nodes is passing the breadth of the earth s orbit.\\n315. One disappearance. If the earth is at F when the\\nplanet reaches A, then the earth will go from F nearly to D,\\nwhile the nodal line advances from AD to BS, and the earth\\nwill pass the line between G and D, as at K. Up to that\\npoint, the luminous side is presented toward the earth but\\nfrom K to a point near D, the plane of the rings falls between\\nthe earth and sun, and the rings are invisible, and continue so\\n11", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0177.jp2"}, "176": {"fulltext": "162 DISAPPEARANCE OF THE RINGS.\\nabout two months. When the nodal line has passed the son,\\nthe luminous side of the rings is again toward the earth and\\nbefore the earth completes the half orbit DEF, the nodal line\\nwill pass off at F.\\n316. Ttvo disappearances. If the earth has advanced some\\ndistance on the quadrant FG for example, to the middle L\\nwhen the nodal line touches D, then the earth passes the lint,\\nbetween K and D, and the dark side is toward us. The line\\npasses the sun when the earth is near the middle of DE, after\\nwhich, the rings are seen. But before the nodal line reaches\\nCF, the earth will overtake it, and be on the dark side again.\\nBetween F and L, the earth once more crosses the line, and the\\nrings present to us their bright side. In this case, the rings\\ndisappear twice during the nodal year.\\nThese two periods of disappearance may be so prolonged as\\nto unite in one of about eight months in length. This happens\\nwhen the earth is two or three days past G, at the time when\\nthe nodal line touches D. Then, before reaching D, the earth\\npasses to the dark side of the rings, and continues on that side\\ntill both the earth and the nodal line pass E together. As\\nsoon as that point has been passed, the line is again between\\nthe sun and earth, and continues so mi til it is recrossed by the\\nearth on the quadrant FG.\\n317. No disappearance. It is possible that no disappear\\nance, which has continuance, should happen during the nodal\\nyear. Suppose the earth two or three days past E, when the\\nline of nodes reaches D. Then, while the line moves from AD\\nto BS, the earth will advance to G, all the time on the lumi-\\nnous side of the rings the earth and sun will both be in the\\nline BSG at once, the planet being in conjunction and after\\nthe earth has passed G toward D, the bright side of the rings\\nis in view, as before, and will continue so. Thus, there is only\\na momentary disappearance, and that, when the planet and\\nrings are lost in the blaze of the sun s light.\\nIn general, there are two periods of disappearance within\\nthe nodal year, arising from the third cause, each beginning\\nand ending with a disappearance from the first or second cause.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0178.jp2"}, "177": {"fulltext": "DISCOVERY AND PLACE OF URANUS. 163\\n318. Phenomena of the rings at the planet. On that\\nhemisphere of the planet to which the luminous side of the\\nrings is presented, there is the appearance of splendid arches\\nspanning the sky, having a breadth and elevation according to\\nthe latitude of the place. At latitude 30\u00c2\u00b0, the breadth is about\\n18\u00c2\u00b0, and the elevation of the lower edge on the meridian about\\n22\u00c2\u00b0. E ear the poles, however, it is below the horizon. The\\nluminous side is presented to the northern hemisphere near 15\\nyears, and then the same length of time to the southern hemi-\\nsphere, in regular alternation.\\nA part of the rings is generally eclipsed by the shadow of the\\nplanet falling on it.\\nAlso, during the 15 years in which the dark side of the\\nrings is turned toward a hemisphere, its shadow is cast across\\na zone of it, which causes an eclipse of the sun. And at a\\ngiven place, a total solar eclipse may continue from day to day,\\nwithout interruption, for several years.\\n319. Satellites of Saturn. Saturn is attended by eight\\nsatellites. Their periods of revolution vary from less than one\\nday to 79 days. Their diameters vary from 500 to 2 3 900\\nmiles but on account of their immense distance from the\\nearth, they are seen only with the best instruments. They are\\nall external to the rings, at distances from the planet, varying\\nfrom 122,000 to 2,338,000 miles. Their orbits are nearly in\\nthe plane of the rings, and make an angle of about 28\u00c2\u00b0 with\\nthe orbit of the planet. Hence, they are not very liable to be\\neclipsed. The principal time for eclipses is that at which the\\nrings disappear for then the sun is nearly in the plane of their\\norbits, as well as of the rings.\\nURANUS.\\n320. Tabular statements. Mean distance from the sun,\\n1,772,088,000 miles periodic time, 84 years; diameter, 31,700\\nmiles specific gravity, 1.3.\\n321. Discovery, and place in the system. Uranus was un-\\nknown to the ancient astronomers; and to them, therefore,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0179.jp2"}, "178": {"fulltext": "164 DISCO VEEY OF NEPTUNE.\\nSaturn s orbit was the boundary of the solar system. Uranus\\nwas discovered by Sir William Herschel, in 1781, and has\\nmade but little more than one revolution since that time. It\\nwas, however, repeatedly seen by earlier astronomers, and re-\\ncorded in their catalogues as a fixed star. By this discovery,\\nthe diameter of the known solar system was doubled.\\nUranus is the third of the four great planets in order of dis-\\ntance, but it is least in diameter. Its distance from us is so im-\\nmense that it appears only as a faint star, and presents no in-\\nequalities by which its diurnal motion can be discovered. Its\\norbit is very nearly circular, and is inclined less than a degree\\nto the ecliptic.\\n322. The satellites of Uranus. Sir William Herschel an-\\nnounced the discovery of six satellites belonging to Uranus.\\nBut only four have been identified by later astronomers. The\\nremarkable facts relating to these satellites are, that their orbits\\nare nearly at right angles to the plane of the ecliptic, and that\\nin the orbits, the motions of the satellites are retrograde that\\nis, from east to west. Their periods of revolution vary from\\n2i days to 13J days, and their distances from 123,000 to\\n376,000 miles.\\nNEPTUNE.\\n323. Tabular statements. Mean distance from the sun,\\n2,777,948,000 miles; periodic time, 165 years; diameter,\\n34,500 miles specific gravity, 1.1.\\n324. Discovery. Neptune was discovered in 1846. The\\ncircumstances which led to the discovery were briefly as fol-\\nlows. After the orbit of Uranus had been carefully computed,\\nand corrections made for the disturbing influence of Jupiter\\nand Saturn, the planet was found to depart from the calculated\\npath in a manner not to be accounted for, except by suppos-\\ning some other disturbing force. It was for some time sus-\\npected that there must be a planet superior to Uranus, whose\\nattraction caused the change of its orbit. At length, two\\nmathematicians, Le Verrier, of France, and Adams, of England,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0180.jp2"}, "179": {"fulltext": "ELEMENTS OF ORBITS. .165\\n*jaeh without any knowledge of what the other was attempting,\\nengaged in the arduous labor of calculating what must be the\\nelements of a planet which should produce the given disturb-\\nance of the motions of Uranus. They reached results which\\nagreed remarkably with each other. Le Yerrier communicated\\nto Galle, of the Berlin observatory, the place in the sky in\\nwhich the disturbing body should be situated and in the\\nevening of the same day, Galle found it within a degree of the\\npredicted longitude.\\nThe planet thus discovered explains fully the disturbances in\\nthe motions of Uranus.\\nIt soon appeared that Neptune had repeatedly been entered\\nin catalogues as a fixed star. The earliest of these records, in\\n1795, afforded material aid at once in determining its mean\\ndistance and its periodic time.\\nNeptune is attended by one satellite, which was also dis\\ncovered in 1846. It is nearly as far from the primary as tli6\\nmoon is from the earth, and revolves in 5d. 21h.\\nCHAPTER XVn.\\nELEMENTS OF A PLANETARY ORBIT. QUANTITY OF MATTER\\nIN THE SUN AND PLANETS. PLANETARY PERTURBATIONS.\\nRELATIONS OF PLANETARY MOTIONS.\\n325. Elements of an orbit. These are the quantities which\\nmust be known, in order to calculate the place of a planet at a\\ngiven time. They are seven in number.\\n1. The periodic time.\\n2. The mean distance from the sun, or the semi-major axis\\nof the orbit.\\n3. The longitude of the ascending node.\\n4. The inclination of the plane of the orbit to that of the\\necliptic.\\n5. The eccentricity of the orbit.\\n6. The longitude of the perihelion.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0181.jp2"}, "180": {"fulltext": "166 PERIODIC TIME.\\n7. The place of the planet in its orbit at a given epoch.\\nTwo of these, 3d and 4th, determine the position of the plane\\nin which the orbit lies the second fixes the size of the orbit\\nthe 5th, its form the 6th, the relation of the form to the plane\\nof the ecliptic; the 1st and 7th, the circumstances of the\\nplanet s motion in the orbit.\\nThe orbit of a planet can not be determined by the same\\nmethod as the moon s orbit is (Chap. X.), or the sun s apparent\\norbit (Chap. IV.), because it is not the earth, but the sun, whick\\noccupies the center of the planetary revolutions.\\n326. Geocentric and heliocentric place of a planet. The\\npoint in the celestial sphere which a planet occupies, as seen\\nfrom the earth, is called its geocentric place its place as seen\\nfrom the sun is called its heliocentric place. It has already\\nbeen noticed that the planets, as seen from the earth, have a\\nretrograde motion during a part of every synodical revolution.\\nThis is the effect of the observer s position and motion, and would\\nnot exist if he were stationed at the sun. The place of a planet,\\nas seen from the earth and the sun, can never agree, except\\nwhen the sun and earth are on the same side of the planet, and\\nin the same straight line with it. But after the relations of the\\nearth to the planet and to the sun are obtained, there is no dif-\\nficulty in calculating the heliocentric place of the planet.\\n327. First element the periodic time. This is found by\\nobserving the time that intervenes between the two successive\\nreturns of the planet to the same node.\\nIt may be known when a planet is at a node, because then\\nits latitude is nothing. If, from a series of observations on the\\nright ascension and declination of a planet, the latitudes are\\ncomputed, and one of them is zero, then the exact time of pass-\\ning the node is obtained. But if, as is usually the case, the\\ntwo least latitudes are, one north, and the other south, the time\\nof passing the node between them is readily found by a propor-\\ntion. Similar observations are made when the planet again\\narrives at the same node, and thus the periodic time becomes\\nknown.\\nIt is discovered that a minute correction of the oeriodic time.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0182.jp2"}, "181": {"fulltext": "DISTANCE FROM THE SUN. 167\\nthus derived, must be applied for the retrograde motion of the\\nnode. The periodic time of a planet may also be derived frorc\\nthe observed length of its synodic revolution that is, the inter\\nval between two successive oppositions, or two conjunctions oi\\nthe same kind. The computation is similar to that employed\\nin finding the sidereal period of the moon from its synodical\\nperiod (Art. 158).\\nIn both the above methods, great advantage, in point of ac-\\ncuracy, is gained, if two very distant epochs can be brought\\ninto comparison, such as two distant passages of the node, or oi\\nopposition. For example, a transit of Mercury occurs at in-\\nferior conjunction. Divide the interval between two observed\\ntransits, several years apart, by the number of synodical revo-\\nlutions of Mercury which intervene, and its mean synodical\\nperiod is very accurately obtained.\\n328. Second element the distance from the sun. The dis\\ntance of an inferior planet from the sun is found as follows\\nLet S (Fig. 76) be the sun. E the earth, and C\\nthe planet. Measure the greatest elongation,\\nSEC then, in the right-angled triangle, rad\\nsin SEC SE SC. If the orbit is elliptical,\\nthe value of SC, as obtained at different times,\\nwill be different; and a great number of such\\nobservations should be made, in order to obtain\\nthe mean distance.\\nThe distance of a superior planet may be\\nfound by observations on its retrograde motion\\nat the time of opposition. For, the more dis-\\ntant the planet, the less will the earth s motion\\nthrow it, apparently, backward. Let S (Fig. 77)\\nbe the sun, E the earth, and M a superior planet.\\nLet E pass over ~Ee in a short time, as one day, and let M pass\\nover Mm in the same time. As the periodic times of E and M\\nare supposed to be known, the angles ES and MSm are\\nknown, and, therefore, their difference, eSm, Join em, and\\nproduce it to X in SM produced. Draw ey parallel to SX\\nthe angle ~K.ey is the retrogradation during the day in which\\nthe planets describe the arcs Ee and Mm, and is known by ob-\\nservation. But SXd X.ey and, therefore, in the triangle", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0183.jp2"}, "182": {"fulltext": "163\\nLONGITUDE OF THE NODE.\\neSX, the third angle, XeS, is known. Hence, in the triangle\\nSem we have all the angles, and the side Se, by which 8m ia\\neasily computed. This process may be repeated at every oppo-\\nsition, and thus the mean distance is ultimately obtained.\\n329. Third element longitude of the node. Let S (Fig.\\n78) be the sun, EFG the earth s orbit, OPQ the orbit of a\\nplanet, CL an arc in the plane of\\nthe ecliptic, intersecting the orbit 8\\nin P. SP is, therefore, the line of\\nthe nodes. And let EA, FA and\\nSA be parallel lines, directed to-\\nward the vernal equinox. When\\nthe earth is at E, suppose the plan-\\net is at the node P then E, P, and\\nS are all in the plane of the eclip-\\ntic, and AEP is the longitude of P,\\nand AES that of the sun. These\\nlongitudes being obtained, their dif-\\nference is SEP, which is, therefore,\\nknown. After the planet has per-\\nformed a revolution to the same\\nnode again, suppose the earth to be\\nat F; then we find, as before, its\\nlongitude, ATP, that of the sun,\\nA FS, and their difference, SFP.\\nAs the times are known in which\\nthe earth is at E and at F, we know SE, SF, and the angle ESF,\\nand can compute EF, and the angles SEF and SFE. From\\nthe several angles at E and F, thus obtained, we derive PEF\\nand PFE and these, with the side EF, give us the side FP.\\nThen, in the triangle SFP, from SF, FP, and SFP, compute\\nthe angle FSP. From this, subtract A SF (the supplement of\\nA FS), and there remains A SP, the heliocentric longitude of\\nthe node.\\nIt is by processes of this kind that the slow retrograde mo-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0184.jp2"}, "183": {"fulltext": "INCLINATION TO THE ECLIPTIC. 169\\ntion of the nodes is discovered (Art. 327). It amounts to only\\na few minutes in a century.\\n330. Fourth element inclination of the orbit to the eclip-\\ntic. Select the time of observation, when the sun s longitude,\\nobtained from the tables, is the same as the heliocentric longi-\\ntude of the node and find for that time the geocentric longi-\\ntude and latitude of the planet. Let E (Fig. 79) be the earth\\nS the sun, P the planet, JNO the line of the nodes coinciding\\nwith ES and let EA and SA be the direction of the vernal\\nequinox. Join EP, and, with it as a radius, describe the sur-\\nface of a sphere, cutting the plane of the ecliptic in the arc BC.\\nFrom P draw the arc PQ, perpendicular to BC. AEO is the\\nlongitude of the sun, and A SO, its equal, is the heliocentric\\nlongitude of the node O. AEQ is the geocentric longitude ot\\nthe planet. In the spherical triangle BPQ, right-angled at Q,\\nPQ measures the given latitude, BQ measures the difference\\nbetween AEQ and AES, and PBQ is the inclination to be\\nfound. Then, rad x sin BQ tan PQ x cot PBQ\\np-ro rad s in B Q\\ncot r\u00c2\u00b1 Q dt=t\u00e2\u0080\u0094\\ntan PQ\\nand the inclination of the orbit to the ecliptic becomes known.\\nFig. 79.\\n331. To find the heliocentric longitude and latitude of a\\nplanet. Let S (Fig. 80) be the sun, E the earth, EBC its orbit,\\nP the planet, EA, SA 7 the direction of the vernal equinox.\\nLet PQ be drawn perpendicular to the plane of the ecliptic\\nAEQ is the geocentric longitude of the planet, A SQ its helio-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0185.jp2"}, "184": {"fulltext": "170\\nECCENTRICITY OF THE OEBIT.\\ncentric longitude. Also, PEQ is its geocentric latitude, and\\nPSQ its heliocentric latitude. SEP, the elongation of the\\nplanet from the sun, is known from observation; SE, the\\nradius vector of the earth s orbit, and SP, that of the planet s\\norbit, are also known. Therefore, PE may be computed.\\nKnowing PE, and PEQ in the right- angled triangle, we can\\ncompute EQ. Then, in the triangle QES, EQ, ES, and th(\\nangle QES AES AEQ) being known, QSE and QS are\\nfound. From QSE, subtract ESA (the supplement of AES),\\nand A SQ is obtained, which is the heliocentric longitude of P.\\nAgain, in the right-angled triangle PSQ, having SQ and SP,\\nwe find the angle PSQ, the heliocentric latitude.\\nFig. 80.\\n332. Fifth and sixth elements eccentricity of the orbit,\\nand longitude of the perihelion. A focus and three points in\\nthe curve of a conic section being given, its directrix can be\\ndetermined, and the curve drawn. (Coffin s Con. Sec, Prop.\\nII.) Tims, let SM, SjST, and SP (Fig. 81) be three radii vec-\\ntores of an orbit, determined in length and position by the pro-\\ncesses already described. If MN and NP are joined, the tri\\nangles MNS and NPS are known in all respects. Then, if\\nMN be produced, so that NK MR NS MS, E is a point\\nof the directrix. Another point, L, is fixed in a similar man-\\nner by producing PN. The directrix being thus determined,\\ndraw perpendiculars to it from S, M, 1ST, and P. The axis ol\\nthe orbit is on KS produced. The ratio, SM MG, is constant\\nfor every point of the curves (Cof. Con. Sec, Pr. II.}", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0186.jp2"}, "185": {"fulltext": "MASSES OF BODIES COMPAKED,\\nFief. 81.\\n173\\nThe distance SK of the focus from the directrix is found\\nthus. Draw MD perpendicular to SK. LNS, the external\\nangle of the triangle NSP being known, subtract MNS from\\nit, and we have LNB, and the including sides LIST, KR, to find\\nthe angle B. This, with the side ME, in the right-angled tri-\\nangle MGE, gives us GM, and the angle GME. Then,\\n180\u00c2\u00b0 (GME EMS) MSD, from which, and MS, we\\ncompute DS and GM DS SK.\\nTc find the perihelion, divide SK, so that SA AK SM\\nMG A is the perihelion.\\nTo find the aphelion, produce KS to B, so as to make SB\\nBK SM MG B is the aphelion.\\nBisect AB in C then SC divided by AC is the eccentricity\\nof the orbit.\\nThe longitude of the perihelion is known from the angle\\nMSA, already obtained for the longitude of SM is given at\\nthe outset.\\n333. Masses of bodies compared by the orbits described\\nabout them. The mass of a body, whether the sun or a planet,\\ncan be compared with that of another, by means of the distance\\nand period of a planet or satellite revolving about each. It\\nhas been proved (Chap. VIII.) that gravity varies directly as\\nthe mass, and inversely as the square of the distance that is,\\nG co y~-. It was shown, also (Chap. VI.), that the centripetal", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0187.jp2"}, "186": {"fulltext": "172 MASSES OF BODIES COMPARED.\\nforce or gravity varies directly as the distance, and inversely\\nas the square of the periodic time that is, G- oo There-\\nM D D 3\\nfore, go M qo or, the united mass of the cen-\\ntral and the revolving body varies directly as the cube of their\\ndistance apart, and inversely as the square of the periodic time.\\nThus, to compare the mass of the sun, about which the earth\\nrevolves, and the mass of the earth, about which the moon\\nrevolves, we have\\n(238,820) 3 (92,381,000) 3 QO AAA\\n127T32F (365.256) J\\nTherefore, the mass of the sun is about 324,000 times that\\nof both earth and moon, or 327,000 times that of the earth alone.\\n334. Examples.\\n1. Were the earth s mass equal to the sun s, in what time\\nwould the moon, at its present distance, revolve about it\\nLetting x stand for the time required, we have 1 327,000\\nX. Ans. lh. 8m. 48s.\\n(27.32/ x l\\n2. How much must the mass of the earth be increased,\\nin order that the moon may revolve about it in the same\\ntime as it now does, when removed to three times its present\\ndistance Ans. It must be 27 times as great.\\n3. The distance of Jupiter from the sun is 481,000,000\\nmiles, and its periodic time is 4332.554 days. The fourth\\nsatellite is 1,162,000 miles from the primary, and revolves\\nin 16d. 16h. 32m. Compare the mass of the sun with that of\\nJupiter. Ana. 1048 1.\\n4. The moon revolves in 27.32 days, at the distance of\\n238,820 miles from the earth Jupiter s second satellite re-\\nvolves in 3.552 days, at the distance of 414,000 miles. What\\nare the relative masses of the earth and Jupiter\\nAns. 1 312.\\n335. Masses of planets which have no satellites. The\\nmethod described in the preceding article can be applied to", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0188.jp2"}, "187": {"fulltext": "PERTURBATIONS OF THE PLANETS. 173\\nthe sun, and all those planets which are attended by satellites.\\nBut Mercury and Venus, which have no satellites, must\\nbe compared in some other way. Each of these planets, by its\\nattraction, sensibly disturbs the motion of the planet nearest to\\nit and the degree of this disturbance, the distance being\\nknown, is a measure of its quantity of matter. Thus, the\\nmasses of Venus and Mars can each be estimated, by observing\\nthe force which they exert on the earth when passing near it.\\nThe mass of Mercury has been determined by its disturbing\\npower exerted on Eneke s comet, as well as on the planet\\nVenus.\\n336. Densities of the planets. The masses of bodies vary\\nas the products of their volumes and densities. Therefore\\ntheir densities vary as the masses divided by the volumes.\\nThe densities, as given in Table IV, may be obtained in this\\nway, and reduced to a scale, in which the earth s density is\\ncalled 1. Or they may be reduced to a scale, in which the\\ndensity of water is 1 in the last form, the numbers are called\\nspecific gravities. These also are given in Table IV\\n337. Perturbations of the planets. The solar system, as\\nwe have seen, consists of many bodies and each one of them\\nattracts every other one, and attracts it more, according as it\\nis nearer and more massive. Hence, no planet can continue\\nto pursue the same elliptic orbit about the sun, as if the sun\\nand planet were the only bodies. Nor can any satellite de-\\nscribe its orbit undisturbed about the primary. The number\\nand variety of these disturbing forces exerted within the system\\nare very great. But many of them are so minute as to be in-\\nsensible. As was shown in Chapter X. respecting the moon,\\nso in regard to every planet and satellite, the disturbing influ-\\nences are of various kinds, some tending to alter the plane of\\nthe orbit, others to change its form, etc. These perturbations,\\nlike those of the moon, are classed into periodical and secular.\\n338. Betrogradation of nodes. If the orbit of a planet is\\noblique to that of another, one component of the disturbing\\nforce tends to move the nodes of the two orbits backward, as", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0189.jp2"}, "188": {"fulltext": "174 PERTURBATIONS OF THE PLANETS.\\nshown in Art. 192. And every satellite, whose orbit is inclined\\nto that of its primary, is acted on by the sun, in the same man-\\nner as the moon is its nodes retrograde on the orbit of the\\nprimary. For the planets, this retrograde motion is excessively\\nslow, generally amounting to only a few minutes in a century.\\n339. Change of inclination. Another disturbance of the\\norbit of a planet has respect to its inclination to the orbit of\\n.another. There are small periodical oscillations in the inclina-\\ntion, at every revolution, which nearly compensate each other,\\nlike those of the moon s orbit (Art. 193). But the compensa-\\ntion not being exact, there is a minute change, which remains\\nunbalanced, and accumulates for many centuries, when the\\nchange is reversed and accumulates in the opposite direction.\\nThese secular oscillations, however, are all within narrow\\nlimits. Thus, the ecliptic, though generally spoken of as a\\nfixed plane, is not truly so, but is subject to a minute change\\nof a few seconds in a century. It is proved that the whole\\nvariation can never amount to 3\u00c2\u00b0, and that within that range\\nit will occupy many thousands of years in making a single sec-\\nular oscillation.\\n340. Advance of apsides. All planets within the orbit oi\\na given planet, conspire, on the whole, to increase its gravity\\ntoward the sun while the general effect of those outside ot\\nthe same orbit is to diminish it. It was shown (Art. 183) that\\nthe sun, being outside of the moon s orbit about the earth,\\nsometimes increases and sometimes diminishes the moon s ten-\\ndency to the earth, but on the whole diminishes it. The same\\nthing is true of every planet outside of the orbit of another.\\nOne consequence of the change in the attraction is, to cause\\nthe line of apsides to advance and to retrograde alternately\\nbut the resultant of the whole action is an advance. The\\nearth s apsides advance 11-J in a year (Art. 147). So the line\\nof apsides of most of the planetary orbits has a slow motion\\nfrom west to east.\\n341. Change of eccentricity.\u00e2\u0080\u0094 A planet tends to increase\\nthe eccentricity of an orbit within its own, when the two", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0190.jp2"}, "189": {"fulltext": "PEKTEEBATIONS OF THE PLANETS. 175\\nplanets are in its line of apsides at conjunction and opposition,\\nand to diminish it when the line from the sun to the outer planet\\nmakes a right angle with the line of apsides; analogous to\\nthe action of the sun on the moon s orbit (Art. 187). These\\ndisturbances are very minute, but they will not balance each\\nther during a svnodical revolution and therefore there is a\\nsmall secular change in the eccentricity of the orbits. For ex\\nample, the eccentricity of the earth s orbit has been diminish\\ning, and for many thousands of years to come it will continue to\\ndiminish, at the rate of 0.00004 per century. The orbit, how-\\never, will never reach the exact form of a circle, but after\\narriving to a minimum of eccentricity, it w T ill begin to return\\nto a more eccentric form, and thus will oscillate about a mean\\nvalue perpetually. And the range of its eccentricity is so\\nlimited, that the ellipse, if correctly represented, can never\\ndiner visibly from a circle.\\nIt is this slow change in the earth s orbit which causes the\\nsecular inequality of the moon s motion (Art. 195).\\n342. Change in the length of the major axis. There are\\nalso minute periodic changes in the length of the major axis oi\\nan orbit that is, in the mean distance of a planet from the\\nsun. But both calculation and observation establish the fact,\\nthat there is no secular inequality, because the periodical\\nchanges exactly compensate each other. And, if the mean dis-\\ntance of each planet from the sun has permanently the same\\nvalue, then, according to Kepler s third law, the periodic time\\nis also constant.\\n343. Long periods. There are in the solar system several\\ncases of inequality, accumulating for centuries, which never-\\ntheless have the character of periodical rather than secular\\ninequalities, and depend on the fact that the periodic times oi\\ntwo planets almost exactly measure a certain length of time.\\nFor example, the earth makes 8 revolutions in very nearly\\nthe same time in which Yenus makes 13. Hence, every fifth\\nconjunction occurs within 1J\u00c2\u00b0 of the same points of their re-\\nspective orbits. At the end of this period of S years, there is\\na minute perturbation, which remains uncompensated, and", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0191.jp2"}, "190": {"fulltext": "176 PERTUKBATIONS OF THE PLANETS.\\nwhich is about doubled at the end of 16 years, and tripled at\\nthe end of 24 years, and so on. This disturbance is very small,\\nnever amounting to more than a few seconds but it requires a\\nperiod of 240 years in order to pass through all its changes.\\nThe long inequality of Jupiter and Saturn is a more remark-\\nable case. Jupiter makes 5 revolutions, and Saturn 2, in\\nnearly the same time. An unbalanced disturbance, which ap-\\npears at the end of this time, goes on accumulating. During\\nthe 17th century, Saturn was constantly retarded, and Jupiter\\naccelerated. But in the 18th, this was reversed, and Saturn is\\nnow accelerated, and Jupiter retarded. This will continue still\\nlonger and the whole period required for this inequality is\\nmore than 900 years. The deviation, at its maximum, is 49\\nfor Saturn and 21 for Jupiter.\\n344. Degree of change in the several elements. Of the sev-\\neral elements named at the beginning of this chapter, we see,\\nfrom what precedes, that the following classification may be\\nmade.\\n1. The 1st and 2d have no secular inequality whatever.\\nTheir value remains constant from age to age. The perma-\\nnency of these two elements secures a constant length of the\\nyear, and a constant amount of heat from the sun on each\\nplanet.\\n2. The 3d and 6th elements have small periodical oscilla-\\ntions, but their secular change is in one direction the nodes\\nperpetually retrograde, the apsides perpetually advance. But\\nthe continual change in the same direction in these two ele-\\nments has no tendency to derange the condition of things on a\\nplanet. As to the well-being of the occupants of a planet, it is\\nof no consequence how the major axis of its orbit is situated,\\nif only the form of the ellipse is preserved. It is also im-\\nmaterial in what direction the line of its nodes may happen\\nto lie.\\n3. The 4th and 5th elements have both periodical and secu-\\nlar inequalities; but they range within very nanow limits,\\nThe smallness of these changes insures all the planets against\\nany considerable change from year to year, in respect to the\\nextremes of heat and cold, and in respect to the seasons.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0192.jp2"}, "191": {"fulltext": "STABILITY OF THE SYSTEM. 177\\n34o. Stability of the system. Several of the secular in-\\nequalities, before their true character had been demonstrated,\\nexcited great interest among astronomers, because they seemed\\nto indicate the ultimate derangement of the order and stability\\nof the system. If the eccentricity of the earth s orbit should\\ncontinue to change in the same direction perpetually, the earth\\nwould at length, though perhaps not in millions of years, be-\\ncome unfit to be the habitation of man, because of the terrible\\nextremes of heat and cold at perihelion and aphelion. So, ii\\nthe inclination of equator and ecliptic should continue its\\nchange perpetually in the same direction as at present, the sea-\\nsons would by and by disappear, and afterward run to an ex-\\ntreme which would produce desolation over the whole surface\\nof the earth. And if the secular inequality of the moon s\\nperiod were always to go on as it has done for centuries past,\\nthe moon would at length be precipitated on the earth.\\nBut La Grange, La Place, and others have demonstrated\\nthat all the perturbations have their limits, and, after in-\\ncreasing with extreme slowness for many ages, must again de-\\ncrease in like manner and, furthermore, that the entire series\\nof changes lies within so narrow bounds, that eo disastrous\\nconsequences can ensue.\\n346. Manner in which the stability is secured The sta-\\nbility of the system is secured by the fulfilment of certain\\nessential conditions in the arrangement of its parts.\\n1. The great mass of matter constituting the solar system is\\nin the central body, the sun being 700 times as great as all the\\nother bodies united. Hence, all movements are principally\\ncontrolled by the sun.\\n2. The planets, and especially the large ones, are at great\\ndistances from each other; and thus the sun s influence over\\neach is but little modified by their mutual attractions.\\n3. The orbits, especially of the largest planets, have but\\nslight eccentricity, and, therefore, always maintain their great\\ndistances from each other.\\n4. The mutual inclinations of the orbits are small. Hence,\\nthere are no large forces operating to change the position of\\norbits, and thus disturb the seasons.\\n12", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0193.jp2"}, "192": {"fulltext": "liO RELATIONS OF ELEMENTS.\\n347. ^Relations of the planetary motions. The planets arc\\nso adjusted to each other, in respect to their velocities, dis-\\ntances from the sun, periodic times, and gravity toward the\\nsun, that if any one of these relations between two planets is\\nknown, all the others become known also.\\nLet r mean distance t periodic time v velocity\\ng gravity. Also, let s (slowness) the reciprocal of ve\\nlocity and I (lightness) the reciprocal of gravity.\\nif\\nv 2 -f oo L (Art. 92)\\nv 2 oo -5-. But by Kepler s third law,\\nt\\nr 2 1\\nf oo r s v 2 oo or v 2 oo\\nr r\\nA 1 1 A 1 l X A\\nAs s v and sr oo and s oo r.\\nv s s 2 s 2 7 1\\nr r 3 a\\nAgain, since voo v z oo But, r 3 oo f v* oo\\nto t\\nor f x oo and s oo\\ns t\\nBy the law of gravity, g oo oo and Z oo r 2\\n7 b T\\nBut s 2 oo s 4 oo r 2 and s 4 go I.\\nBringing together these results, we find four variations,\\ns oo s 1 r oo s 2 oo s 3 I oo s- 4\\nHence, we have the reciprocal of velocity, s the distance,\\nr j the periodic time, t and the reciprocal of gravity, I re-\\nspectively denoted in their ratios by the geometrical series, s\\\\\\ns 2 s s s\\\\ in which the first term and the ratio are equal.\\n348. Mode of using these variations for calculation. If\\nthe velocities of two planets are given, we first take their re-\\nciprocals, and thus have the ratio of s for the two. The terms\\nof this ratio are then raised to the second, third, or fourth\\npower, according as we wish to compare r, or t, or L", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0194.jp2"}, "193": {"fulltext": "RELATIONS OF ELEMENTS. 179\\nBut if the ratio of distances, or times, or gravities is given,\\nthe corresponding root is first extracted, in order to find the\\nratio in respect to s, and then we proceed as before.\\n349. Examples.\\n1 The planetoid Pallas has a period of 4| years how much\\nfurther is it from the sun than the earth is How much less is\\nit attracted How much slower does it move\\nLet t, I be used for the earth, and T, S, R, L for Pallas\\nThen, t T 1 4.667;\\n1* (4.667)* s S\\nS 1 1.67 that is, the earth s ve-\\nlocity is 1.67 times as great as that of Pallas.\\nAgain, r R l 2 (1.67) 2 1 2.7926 or, Pallas is 2.7926\\ntimes as far from the sun as the earth is.\\nAgain, I L l 4 (1.67)* 1 7.7985 therefore, the earth is\\nattracted by the sun about 7.8 times as much as Pallas is.\\n2. What would be the period of a satellite revolving about\\nthe earth close to its surface\\nThe distance of this satellite to that of the moon is as 1 60\\ns 8 1 (60)*; t T 1 (60)* 1 464.66.\\nBut the moon s period is 27.32 days, or 655.68 hours.\\nHence, the period of the satellite is 1.411 h., or lh. 24m. 39s.\\nnearly.\\n3. How much faster must the earth rotate on its axis, in\\norder that bodies on the equator may lose all their weight\\nThis is just the condition of the body in example 2d, whose\\nperiod is 1.411h. But the earth s time of rotation is 24h.,\\nwhich is 17 times 1.411h. Therefore, if the earth were to\\nrotate 17 times more rapidly than at present, all bodies on\\nthe equator would just lose their weight, and revolve inde-\\npendently.\\n4. What would be the periodic time of a body revolving\\nabout the earth, at the distance of 5,000 miles from the\\ncenter? Ans. lh. 59m. 23JS.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0195.jp2"}, "194": {"fulltext": "180 COMETS.\\n5. What must be the moon s distance from the earth, in\\norder to revolve about it once in a year\\nArts. 1,344,000 miles.\\n6. Suppose a planet to be discovered, whose daily velocity is\\n5 times as great as that of Mercury, what is its distance from\\n\u00e2\u0099\u00a6he sun s center? Ans. 1,430,000.\\nCHAPTEE XVIII.\\nCOMETS.\u00e2\u0080\u0094 SHOOTING STARS.\\n350. A comet defined. A comet is a body which consists\\nof nebulous matter, and revolves about the sun in a very eccen-\\ntric orbit. Most comets present a roundish ill-defined appear-\\nance, often having a bright central part called the nucleus.\\nThe fainter part, surrounding the nucleus, is called the coma\\n{hair) and the tail, which distinguishes many comets, is\\nmerely the extension of the coma. It is the streaming ap-\\npearance of the tail, resembling hair, which gave the name\\nu comet to this class of bodies. The nucleus has been some-\\ntimes supposed to be solid but it probably consists always of\\nnebulous matter in a more condensed state than the other\\nparts. The nucleus and coma are called the head of the\\n-comet.\\n351. Number of comets. Many hundreds of comets have\\nJbeen recorded, most of them, of course, visible to the naked\\neye. But lately it is observed that most comets are telescopic\\nobjects. And many which would otherwise be seen, escape\\nobservation by being above the horizon only in the daytime.\\nThe whole number, therefore, belonging to the solar system\\nis undoubtedly to be reckoned by thousands, or tens of thou-\\nsands.\\n352. Eccentricity of orbit. All known cometary orbits are\\n*nore eccentric than any planetary orbit and most of them are", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0196.jp2"}, "195": {"fulltext": "ECCENTRIC ORBITS. 181\\nexceedingly so, their perihelion being as near the sun as Mer-\\ncury and Yen us, or nearer, and their aphelion as far off as the\\nmost distant planets, or even beyond. And some appear to be\\n^ellipses of infinite length that is, parabolas while others ex-\\nhibit the form of hyperbolas. In orbits of these last forms,\\ncomets can, of course, pass the perihelion but once.\\n353. Consequences of great eccentricity.\\n1. One effect of this great eccentricity is, that a comet is too\\nfar from the earth to be seen, except during a small part of its\\nrevolution, while it is near the center of the system.\\n2. Another effect is, that great changes take place in the\\ncondition of the nebulous matter of which the comet is com-\\nposed. As a comet approaches the sun, both the nucleus and\\ncoma grow less in diameter, and enlarge again as it departs\\nBut the tail, if there is one, is rapidly lengthened as the comet\\napproaches, and is diminished in length when it withdraws.\\nSometimes, a comet, whose appearance is spherical when first\\nseen, begins suddenly to exhibit the formation of a tail as it\\ncomes nearer, which at length stretches over a large arc of the\\n-sky; and after the perihelion passage, as it departs from the\\nsun, the tail wholly disappears before the comet becomes in-\\nvisible.\\nIt might be supposed that this diminution of the coma re-\\nsults from the loss of material which is taken away to form the\\ntail, while the comet is approaching the sun and that the sub-\\nsequent enlargement is due to the return of the same material,\\nas the tail is contracted. But this will not fully explain the\\nobserved changes; for the contraction and subsequent expan-\\nsion occur when no tail is formed. Hence, it is supposed that\\nthe heat of the sun reduces the dimensions of the nucleus by\\nexpanding a portion of it into the coma, and also changes the\\nnebulous matter of the coma into a pure, transparent gas, which\\nis afterward condensed into a visible form again, as the comet\\nwithdraws from the sun.\\n354. Form and direction of tails of comets. The forms oi\\ntails belonging to different comets are exceedingly varied. In\\ngeneral, however, the sides diverge from the head, so that the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0197.jp2"}, "196": {"fulltext": "182\\nTAILS OF COMETS.\\nmost distant and faintest part is broadest, as in the comets ot\\n1680 and 1811 (Figs. 82, 83). In some cases, the divergency is\\nvery slight, as in the comet of 1843 (Plate I., at the end).\\nFig. 82.\\nFig. 83\\nCOMET OF 1811.\\nCOMET OP 1680.\\nNot nnfrequently, the principal light of the tail appears to\\nproceed from its edges, presenting somewhat the aspect of two\\ntails diverging from the sides of the coma. In such cases, the\\ncoma and tail seem to have the form of a hollow paraboloid,\\nso that we look through a much greater extent of illuminated\\nmatter on the sides than in the central parts. In the comet of\\n1858, the nucleus was at one time surrounded by a series of\\nparabolical envelopes, which increased in number as the comet\\napproached the sun. (PL II., Fig. 1).\\nIn a few instances, the tail has been known to consist of sev-\\neral luminous rays, diverging from each other, as the comet of\\n1744, in which there were six, the extreme ones making with\\neach other an angle of about 45\u00c2\u00b0.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0198.jp2"}, "197": {"fulltext": "DIMENSIONS OF COMETS. 183\\nThe general direction of the tail is from the sun; so that, as\\na comet approaches the sun, the tail follows it but as it re\\ncedes, the tail is directed forward. The axis of the tail is not,\\nhowever, a straight line, but more or less curved backward, so\\nthat the convex side of the curve is foremost in the motion.\\n355. Cause of the direction and curvature of the tail.\\nModern telescopic observations on some of the most conspicu-\\nous comets, show that the material of which the tail is formed\\nis first projected toward the sun, rather than from it and that\\nsome force emanating from the sun then drives it, with great\\nvelocity, in the opposite direction, causing it to sweep past the\\nnucleus on both sides, and stretch millions of miles into space.\\nThe rate at which it is thus driven from the sun is sometimes\\nenormous. In the case of Halley s comet, in 1835, the nebu-\\nlous matter had a velocity of 2,000,000 miles per day. In Do-\\nnatio (1S5S), it reached the rate of 8,000,000 miles per day.\\nWhat force it is which the sun thus exerts in a direction oppo-\\nsite to its gravity, it is vain to conjecture. It must be supposed\\nthat at least a part of the material driven so violently from the\\ncomets is dissipated and lost and there is indication of this in\\nthe diminished size and brilliancy of those whose returns have\\nbeen noticed. Perhaps the numerous comets which have no\\ntails have been divested of them by this process.\\nThe bending of the tail backward is a necessary consequence\\nof the longer arc which the extreme part of the tail must de-\\nscribe. The material of the tail has the same velocity in the\\norbit as the head, when it is driven from it. This velocity it\\nretains but, having to describe a curve about the sun several\\nmillions of miles outside of the other, it must, of course, fall\\nbehind it.\\n356. Dimensions of comets. The dimensions of comets are\\nvarious, and, on account of their nebulous character, they\\nnever admit of accurate measurement. The nucleus of a large\\ncomet is sometimes 5,000 miles, and the coma 200,000 miles\\nin diameter, wiiile the tail has, in one case, attained the extra-\\nordinary length of 200,000,000 miles.\\nThe apparent length of a comet s tail is often sufficient to", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0199.jp2"}, "198": {"fulltext": "184 DIRECTIONS OF COMETARY MOTIONS.\\nspan an arc of 20\u00c2\u00b0 or 30\u00c2\u00b0 on the sky, and sometimes mucls\\nmore than this. The comet of 1680 extended 97\u00c2\u00b0, and that o^\\n186 1 106\u00c2\u00b0. The fainter part, in all cases, is seen only by in-\\ndirect vision.\\nIt is obvious that the real length can not be inferred from the\\napparent, nntil the distance from us, and the obliquity to\\nour line of vision, are obtained.\\n357. Light of the comets. These bodies, like the planets\\nand satellites, shine by solar light which they reflect to us\u00e2\u0080\u009e\\nBut, unlike all planetary bodies, they are in a condition so-\\nattenuated, that the sun s rays penetrate every part of them\\nwithout obstruction. The brightness of a star is not diminished\\nin the least when seen through the tail or coma of a comet. In.\\na few instances, a star has been seen through the nucleus, and\\neven then was not essentially dimmed.\\nA satisfactory proof that the comets are seen by the sun s\\nlight which they reflect, is, that their brightness diminishes as-\\nthey recede from the sun so that they are at length lost to\\nview, not by being too small to fill an appreciable angle, but\\ntoo faint to be visible. This would not be true of a self-lumi-\\nnous body its brightness would remain the same at all dis-\\ntances from us that is, its light would diminish no faster\\nthan its apparent area. Appendix G.\\n358. Quantity of matter in comets. Though some of the\\nlargest comets surpass all other bodies in the solar system in\\nmagnitude, yet in respect to their mass they are too small to\\nhave produced as yet the slightest perceptible effect. They\\nsometimes come very near planets and their satellites, but are\\nnever known to exert the least influence on them. They do,.,\\nof course, attract the planets, because they are attracted by\\nthem, and suifer great disturbances from them. But until\\nthey themselves produce some effect which is appreciable, their\\nmass must be regarded as infinitely small.\\n359. Directions of cometary motions. The cometary orbits\\nare unlike the planetary, not only in the degree of their eccen-\\ntricity, but in the varied positions of their planes. Instead of", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0200.jp2"}, "199": {"fulltext": "ORBITS OF COMETS. 185\\neing limited to a narrow zone like the zodiac, they make\\n3very variety of angle with the ecliptic, so that a comet is as\\nlikely to pass round the sun from north to south as from west\\nto east. And whether the orbit is much or little inclined, the\\ncomet s motion in it is as often retrograde as direct.\\n360. Means of determining a corners orbit. Since a comet\\ncan be seen only during the time of its describing a short arc\\nnear the perihelion, the astronomer has not the same oppor-\\ntunity for fixing its orbit as he has in the case of a planet,\\nwhich can be observed in all parts of its course.\\nIt is true in theory, that by any three observations on the\\nposition of a body revolving about the sun, its whole orbit can\\nbe determined. But if it is very eccentric, and the observa-\\ntions are confined to a small portion at one extremity, the\\nslightest error may greatly change the distance of the aphelion,\\nand consequently the length of the axis and the periodic time.\\nIt is usual, therefore, to assume the path to be a parabola\\nthat is, an ellipse of infinite length, whose eccentricity is 1.\\nThere are then but four of the seven elements (Art. 325) to be\\ndetermined namely, the 3d, 4th, 6th, and 7th. But instead of\\nthe 2d element in Art. 325, there may be substituted the peri-\\nnelion distance, making in all five elements, as follows\\n2. The perihelion distance.\\n3. The longitude of the ascending node.\\n4. The inclination of its orbit to the ecliptic.\\n6. The longitude of the perihelion.\\n7. The place of the body at a given time.\\nThese five elements may usually be determined without\\nmuch difficulty.\\n361. Process of finding the five elements. The right\\nascension and declination of the comet are observed on every\\nfavorable night with all possible care, and the exact time of\\nevery observation is recorded. Three of these dates are selected,\\nseveral days apart and from the right ascension and declina-\\ntion at each date are deduced the geocentric longitude and\\nlatitude of the comet. The heliocentric places of the earth\\nat the same times are known, since each is 180\u00c2\u00b0 from the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0201.jp2"}, "200": {"fulltext": "186 COMETARY ELEMENTS.\\nsun s apparent place at the same time. If we imagine threti\\nstraight lines to be drawn from the known places of the earth\\nthrough the corresponding positions of the comet, its distance\\nfrom ns in each line must be determined by the following con\\nditions, in accordance with Kepler s laws\\n1. A plane passing through the three positions must also\\npass through the sun.\\n2. The three places must be in a parabola, whose focus is at\\nthe sun.\\n3. The areas included between the radii vectores drawn to\\nthe sun must be proportional to the times.\\nPoints are successively assumed in the given lines, until at\\nlength those are found which will fulfill the above conditions.\\nBy this tentative process the orbit is approximately deter-\\nmined.\\nThree other dates may then be tried in the same manner\\nand if the results nearly agree, the mean may be considered\\nmore accurate than either.\\nThis method is just as applicable for determining, approx-\\nimately, the orbit of a newly discovered planet or planetoid.\\nBut in these cases, the observations can usually be followed\\nup in various parts of the orbit, and thus previous errors cor-\\nrected.\\n362. Determination of the remaining elements. If a comet\\nremains in sight for several months, it is quite probable that\\nlong-continued and careful observations will show that the orbit\\nis not truly a parabola, but an ellipse. In such a case, the 1st\\nand 2d elements (Art. 325) may be computed, and the 5th\\ncorrected. Though there may. be good evidence that the orbit\\nis an ellipse, yet there must be great uncertainty in any deter-\\nmination of periodic time, mean distance, and eccentricity, until\\nthey are settled conclusively by a return of the comet to its\\nperihelion.\\nA comet, on its return to its perihelion, is not to be identified\\nso much by its physical aspect, as by the agreement of its ele-\\nments. If the place of the node, the inclination to the ecliptic,\\nthe place of the perihelion, and the perihelion distance agref\\nvery nearly with those of some comet, which has been prev:", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0202.jp2"}, "201": {"fulltext": "HALLE F S COMET. 187\\nously seen, it is fairly presumed to be the same, even though its\\nappearance may essentially differ.\\nWhen a comet is thus identified, its periodic time is, 01\\ncourse, known and from this, its mean distance, and the ec-\\ncentricity of its orbit are readily obtained.\\n363. Comets whose elements have been computed, but not\\nverified. The orbits of more than 300 comets have been com-\\nputed. But a great majority of these appeared to be parabolas,\\nand no prediction of their return could be made. In about 60\\ncases, the movement of the comet seemed to afford evidence\\nthat the orbit was an ellipse, and in 7 others, a hyperbola.\\nFor the elliptic orbits, the returns were, of course, predicted.\\nBut most of the computed periods are long, generally hundreds,\\nand, in several instances, thousands of years so that as yet\\nvery few of them have been verified. The period of a comet\\nseen in 1849 was calculated to be 2,115 years. If the compu-\\ntation be supposed correct, the distance of this comet from the\\nsun at aphelion is about 11 times the distance of Neptune, and\\nits next return will occur in the year 3964. But the results of\\ncalculation, in such cases, are exceedingly uncertain. The cir-\\ncle NE (Fig. 84) represents the orbit of Neptune S, the sun\\nana SC, the orbit of the comet of 1849. The focus is very close\\nto the vertex of the ellipse, as represented by the dot\\nFig. 84.\\nf S ^SZZZ\\n364. Halley s comet This is the only comet of long period,\\nthe elements of whose orbit are all known. It is a comet oi\\nconsiderable splendor, and describes its orbit in 75 or 76 years.\\nHalley observed it in 1682; and finding, by computation, that\\nits path was nearly identical with those of the comets of 1607\\nand 1531, he conjectured that the three were one and the same\\ncomet, and predicted that i A would return early in 1759. It\\ndid return March 12th of that year, and again on the 16 th of", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0203.jp2"}, "202": {"fulltext": "188 COMETS OF SHOET PERIODS.\\nNovember, 1835. On its last return, it reached the perihelion\\nwithin two days of the calculated time. What renders such\\nagreement remarkable is not merely the great length of the\\nperiodic time, but the great allowance to be made for the dis-\\nturbing influence of the principal planets. On its last return\\nbut one, the period of this comet had been increased nearly\\ntwo years by the attractions of Jupiter and Saturn. The aphe-\\nlion is nearly 600,000,000 miles beyond the orbit of Neptune.\\nFigure 85 presents the form of the orbit of Halley s comet, and\\nits magnitude in comparison with the larger planetary orbits.\\nThe eccentricity is nearly 0.97 hence the distance of the focus\\nfrom the vertex is only .03 of the semi-major axis. The dot at\\nthe left hand correctly represents the place of the focus occu-\\npied by the sun.\\nFig. 85.\\n365. Comets of short period, whose orbits are known.\\nThe eight comets in the following table are known by the\\nnames of the persons who either discovered them, or first pre-\\ndicted their returns.\\nCOMET.\\nPeriod\\nin years.\\nPerihelion Distance.\\nAphelion Distance.\\nEncke s\\n3|\\nH\\nH\\nH\\n7i\\n13|\\n32,000,000\\n110,000,000\\n70,000,000\\n64,000,000\\n82,000,000\\n108,000,000\\n192,000,000\\n387,000,000\\n475,000,000\\n510,000,000\\n537,000,000\\n585,000,000\\n530,000,000\\n603,000,000\\nDe Yico s\\nWinnecke s\\nBrorsen s\\nBiela s\\nD Arrest s\\nFave s\\nMechain s", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0204.jp2"}, "203": {"fulltext": "biela s comet. 189\\nIt will be perceived by the table, that these comets consider-\\nably resemble each other in period and distance. They are\\nalso alike in being telescopic, and nearly or entirely destitute\\nof tails, and in moving from west to east, excepting the last, at\\ninclinations to the ecliptic not larger than 15\u00c2\u00b0 or 20\u00c2\u00b0.\\n366. A resisting medium. Two of the above comets,\\nEncke s and Faye s, have given decided indications of acceler-\\nation in their orbits. This shows that they meet with some\\nobstruction, which diminishes their projectile force, in conse-\\nquence of which the centripetal force draws them into a smaller\\norbit, which is, of course, described in less time.\\nSome suggest that as the received theory of light requires the\\nexistence of a medium throughout space, a substance of so little\\ndensity as a comet may possibly be obstructed by it sufficiently\\nto render the diminution of period perceptible.\\nAccording to others, the obstruction may arise from collision\\nwith innumerable small bodies which revolve about the sun.\\nThe earth is meeting with such bodies incessantly, as is proved\\nby the numerous shooting stars which are continually striking\\ninto the atmosphere. It is reasonable to suppose that other\\nbodies, as well as the earth, also meet them and that the\\nthinnest and lightest bodies, such as the comets, should show\\nthe effect of such collisions.\\nIf Encke s and Faye s comets, in either of these -ways, are\\ngradually diminishing their periodic times, then every other\\ncomet must by and by exhibit the same change and the time\\nwill come eventually when all this class of bodies will, at their\\nrespective perihelia, approach so near as to fall upon the sun,\\nand be combined with its substance.\\n367. Division of Biela s comet. One of the most remark-\\nable facts which has occurred in the history of comets was the\\ndivision of Biela s comet into two distinct comets. This ap-\\npearance was first noticed at its return, in 1846. The two\\ncomets were unequal in size, and the larger had a short tail\\nthe other was only a little elongated whereas, before the di-\\nvision, the comet was spherical, without any appearance of\\ntail. Since the division took place, the two bodies have moved", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0205.jp2"}, "204": {"fulltext": "190 BEMAKKA.BLE COMETS.\\nm separate and independent orbits. Their distance apart in\\n1852 was about 1J millions of miles. Appendix H.\\n368. Other remarhMe comets. A few other comets are\\nhere mentioned, which, on account of their splendor, or foi\\nsome other reason, are regarded as objects of special interest.\\n369. The comet of 1680.\u00e2\u0080\u0094 (Fig. S3). This was a comet ol\\nunusual brilliancy, and appears to have been the first whose\\nelements were calculated by Newton. At perihelion, its center\\nwas only 130.000 miles from the surface of the sun; so that, if\\nits diameter was as large as that of many comets, it must have\\ncome in contact with it. Its velocity at perihelion was suffi-\\ncient to have carried it round the sun at that distance in less\\nthan three hours.\\n370. The comet of 1744. This was the most splendid\\ncomet of the 18th century. The remarkable features of it\\nwere, its great brightness, and the number of its tails. Its\\nlight was nearly equal to that of Yenus, and it was distinctly\\nseen in the daytime, even by the naked eye. After passing\\nthe perihelion, its tail was spread into six distinct branches,\\nnear 40\u00c2\u00b0 in length, and the extreme ones diverging about as\\nmany degrees from each other.\\n371. The comet of 1770. The great interest which at\\ntaches to this comet arises from the fact that it has twice suf-\\nfered a great change of orbit, in consequence of the disturbing\\naction of Jupiter. It first appeared in 1770, shining with con-\\nsiderable splendor. In 1776, it again passed the perihelion,\\nand has never been seen since. Computations made by La\\nPlace and others showed that, before its first appearance, it had\\nrevolved in a large orbit, beyond our vision, and had a period\\nof 48 years. In 1767, it came near Jupiter, and lost so much\\nof its velocity, that it was drawn into a small orbit, whose\\nperihelion was far within the orbit of the earth. As two of its\\nrevolutions were about equal to one of Jupiter, it was predicted\\nthat it would be again subjected to a great disturbance at its\\naphelion. This actually took place in 1779, so that it has", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0206.jp2"}, "205": {"fulltext": "REMARKABLE COMETS.\\n191\\nnever returned to our view. Its present period is calculated to\\nbe about 20 years. AB (Fig. 86) is a part of Jupiter s orbit\\nE is the earth s orbit CD is the path\\nof the comet before 1767. Near D.\\nit was so retarded by Jupiter, that the\\nsun drew it into the small orbit DFH, B\\nwhich it described twice, when, uear\\nD, it was again powerfully affected\\nby Jupiter, and received a great accel-\\neration, which caused it to pass out\\nonce more into a large orbit, DK.\\n37 2. The comet of 1843.\u00e2\u0080\u0094 The\\nbrightness of tiiis comet was so great,\\nthat it was seen during the day.\\nIts perihelion distance was less than\\n550,000 miles, and its exterior parts\\nwere probably in actual contact with\\nthe sun. ~No other comet has been\\nknown to approach so near. The tail spanned 70\u00c2\u00b0 of the\\nsky, and was unusually straight and slender, as exhibited in\\nPL I.\\n373. The comet of 1858. This is also called Donati s\\ncomet, having been discovered by Donati, of Florence. It was\\nremarkable for the series of envelopes formed successively\\nabout the -nucleus, as it approached the perihelion. The ap-\\npearance of the head is shown in PL II., Fig. 1, and the entire\\ncomet in Fig. 2. Its period is computed to be about two\\nthousand years.\\n374. The comet of 1861. This comet came so near the\\nearth, that it is believed a part of the tail swept across it. But\\nit is not certain that any visible effect was produced. The\\napparent length of its tail, at one time, was 106\u00c2\u00b0. Fig. 87\\nshows its form at that time.\\n37 5. Effects of collision between a planet and a comet.\\nWhether a direct collision between the earth and the nucleus", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0207.jp2"}, "206": {"fulltext": "192\\nSHOOTING STARS.\\nFig. 87.\\nJ f V%f Ijlfft\\n\u00e2\u0080\u00a2IS:\\nof a coinet would produce serious ef-\\nfects, it is impossible to know, because i\\nso little is understood respecting the\\ndensity of the nucleus. But the coma\\nand tail consist of matter thousands of I\\ntimes more rarefied than the earth s\\natmosphere, and would probably fail I\\nto penetrate it at all. The earth is\\nthought to have passed through a\\ncomet s tail, at least in one instance,\\nbut without producing any perceptible\\neffect.\\n376. Shooting stars. This is the\\npopular name given to those bodies\\nwhich, appear like stars or planets mov-\\ning across some part of the sky, and\\nthen vanishing. They are equally well\\nknown by the name of meteors. They\\nmay be seen in any clear night, by\\nwatching an hour or two, especially if\\nthe moon is not shining.\\n377. Height a?id velocity. By means\\nof concerted observations, made at sta-\\ntions quite distant from each other, the\\nangle can be measured, which is in-\\ncluded by lines drawn from a meteor to the stations, both at\\nthe beginning and end of its motion, and thus its distance\\nand velocity can be measured. The heights of meteors are\\nthus found to be generally about 50 miles, and their velocities\\n20 or 30 miles per second. Coming into the air with such\\ngreat velocity, they are almost instantly set on fire, and their\\nsubstance becomes incorporated with the atmosphere.\\n378. Gaseous meteors. If the ordinary meteors were more\\ndense than a gas, they would hardly lose all their motion, as\\nthey do, before reaching the earth. The most interesting facts\\nrelating to this class of bodies are the following", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0208.jp2"}, "207": {"fulltext": "SHOOTING STARS. 193\\n1. They often occur in showers that is, thousands and hun-\\ndreds of thousands of them are seen in a single night.\\n2. These showers have periodical returns.\\n3. The meteors of a shower come into the atmosphere in a\\ngiven direction, or, in other words, in parallel lines. The op-\\ntical effect is, that they appear to describe arcs of great circles,\\nhaving a common place of intersection.\\n379. Dates of meteoric showers. The most remarkable\\nmeteoric shower of the present century was November 12-13,\\n1833. Not less than 200,000 meteors were seen during the\\nnight at any one station. Like showers occurred at the same\\ntime in 1799 and 1866. And generally, there are more meteors\\nabout the 12th of November than at any other time of the year.\\nOther dates at which meteors are unusually abundant are\\nApril 21st, August 10th, and December 7th.\\n380. Origin of the gaseous meteors. The known motion of\\nthe earth, and the observed velocity and direction of this class\\nof bodies, lead to a knowledge of their heliocentric motions.\\nIt is found in this way that they describe ellipses about the\\nsun, and are therefore to be regarded as minute cometary\\nbodies. Those which come in showers seem to belong to ex-\\ntensive groups, which revolve about the sun in zones or rings.\\nThere appear to be three or four of these zones, whose planes\\nare situated at different obliquities to the ecliptic, and across\\nwhich the earth passes once a year. When the earth traverses\\na more crowded portion of such a ring of meteors, the phenom-\\nenon of a meteoric shower occurs. Appendix I.\\n381. Solid meteors. There is another class of meteoric\\nbodies, which afford indubitable evidence of being solid. Like\\nthe gaseous meteors, they plunge into the atmosphere with\\ngreat velocity, and are inflamed by the violent attrition. Be-\\nfore reaching the earth they usually explode, and scatter their\\nfragments. Some of them, however, appear to lose only small\\nportions of their mass by explosion, and pass on in their orbits\\naround the sun greatly disturbed, of course, by the earth s at-\\ntraction.\\n13", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0209.jp2"}, "208": {"fulltext": "194: THE STELLAR UNI TERSE.\\n382. Aerolites. This is the name usually given to the frag\\nments thrown down by solid meteors though in rare instances,\\nan aerolite obviously constitutes the entire meteor itself. Aer-\\nolites consist of iron, silex, and a few other materials, which\\nare all known among terrestrial substances. But they are\\nalways distinguishable from terrestrial bodies by their peculiar\\nstructure. Since the great velocities of meteors, solid as well\\nas gaseous, have become known, the former theories as to the\\norigin of meteoric stones, or aerolites, have been abandoned.\\nSuch velocities, if they could be generated at all on the earth,\\ncould never exist in horizontal or downward directions. Both\\nsolid and gaseous meteors are therefore considered as describ-\\ning orbits about the sun. The interplanetary spaces, which\\nhave been generally reckoned as vacant, may perhaps be to a\\ngreat extent occupied by innumerable bodies, of a grade far\\nbelow that of comets and planetoids.\\nCHAPTEK XIX.\\nTHE FIXED STARS. THEIR CLASSIFICATIONS. THEIR DIS-\\nTANCES AND MOTIONS. DOUBLE STARS, CLUSTERS, AND\\nNEBULiE. THE NEBULAR HYPOTHESIS.\\n383. The stellar universe. The bodies described in the\\nforegoing chapters all belong to the solar system. If our inves-\\ntigations are extended outside of this system, we find that there\\nare other systems, greater or less than this, unlimited in num-\\nber, and separated from the solar system and from each other\\nby solitudes so vast, that each system is only a point in com-\\nparison with the distances between them. The central sun in\\neach of these countless systems is a fixed star.\\nThe word universe is employed to express the sum total\\nof all these systems, the number of which, and the extent of\\nspace occupied by them, are utterly beyond the reach of human\\ncomprehension.\\n384 The fixed stars* and their magnitudes. The fixed", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0210.jp2"}, "209": {"fulltext": "MAGNITUDES OF STARS. 10\\nstars are so called, because, to common observation, they always\\nmaintain the same situations with respect to each other. AH\\nthe thousands of bright points ordinarily seen in the sky by\\nnight are fixed stars, with the exception of two or three, possi-\\nbly four, which are planets.\\nThe fixed stars are classified according to magnitudes, thongb\\nthe word, when thus used, signifies only degrees of bright?} ess.\\nThe stars which can be seen by the naked eye, in the most\\nfavorable circumstances, are divided into six magnitudes.\\nThose which can be seen only by the aid of the telescope,\\ncalled telescopic stars, are arranged into several more so that\\nall the magnitudes are 16 or 18.\\nStars of the same magnitude are not equally bright for\\nthere is a continual gradation in respect to brightness so that,\\nif the intensity were accurately measured, probably the light\\nof but very few would be found exactly equal.\\nStars of the first magnitude are fewest in number, and, gen-\\nerally, the smaller the magnitude, the larger the number of\\nstars included under it. The limits of the successive magni-\\ntudes differ somewhat, according to different astronomers but\\nthe following round numbers do not vary widely from any of\\nthem.\\n1st magnitude\\n20\\n4th magnitude\\n300\\n2d\\n40\\n5th\\n950\\n3d\\n140\\n6th\\n4450\\n*n all, near 6,000, visible to the naked eye. The numbers of\\nthe telescopic stars increase at so rapid a rate, that they have\\nto be reckoned by millions.\\n385. Cause of unequal brightness. We might suppose\\neither that the stars are themselves unequal in respect to the\\nquantity of light which they emit, or that they appear un-\\nequally bright on account of their different distances. It is\\nundoubtedly true that there is some diversity in the bodies\\nthemselves and yet, the rapid increase of numbers as the mag-\\nnitudes are less, indicates that difference of distance is the chief\\ncause of inequality in brightness. If there is any approach to", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0211.jp2"}, "210": {"fulltext": "196\\nCONSTELLATIONS.\\na uniform distribution of the stars in space, those which are\\nnearest should be fewest in number, and should, in general\\nappear brightest.\\n386. Constellations. The fixed stars are also classed topo-\\ngraphically in constellations. This division is very ancient;\\nand some of the constellations are mentioned by the earliest\\nwriters. The names given to them are those of the animals,\\nheroes, and other objects of pagan mythology.\\nConstellations of the zodiac.\\nAries.\\nLibra.\\nTaurus.\\nGemini\\nScorpio.\\nSagittarius.\\nCancer.\\nCapricornus\\nLeo.\\nYirgo.\\nAquarius.\\nPisces.\\nConstellations north of the zodiac.\\nUrsa Major.\\nUrsa Minor.\\nDraco.\\nAuriga.\\nLeo Minor.\\nCanes Yenatici.\\nCygnus.\\nYulpecula.\\nAquila.\\nCepheus.\\nComa Berenices.\\nAntinous.\\nCassiopeia.\\nCamelopardalus.\\nAndromeda.\\nPerseus.\\nBootes.\\nCorona Borealis.\\nHercules.\\nLyra.\\nDelphinus.\\nPegasus.\\nOphiuchus,\\nConstellai\\nions south of the zodiac.\\nCetus.\\nMonoceros.\\nHydra.\\nOrion.\\nCanis Major.\\nCrater.\\nLepus.\\nCanis Minor.\\nCorvus.\\nCentaurus.\\nCrux.\\nEridanus.\\nLupus.\\nArgo Navis.\\nThe foregoing are the principal constellations but several\\nmore, mostly small ones, may be found on globes and charts.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0212.jp2"}, "211": {"fulltext": "ANNUAL PARALLAX. 191\\nWithin each constellation, the brightest stars are designated\\nby the letters of the Greek alphabet in the order of brightness.\\nTims, a Lyrse, is the brightest star in Lyra /3 Scorpionis, the\\nbrightest but one in Scorpio, etc. After the Greek letters are\\nall used, Roman letters, and then numerals, are employed. In\\nsome cases, the order of brightness does not accord with the\\norder of the alphabet. This may result from a change of\\nbrightness, which has taken place since the stars were first\\nnamed. When a capital letter follows a number, there is ref-\\nerence to the catalogue of some astronomer. Thus, 84H is the\\nstar 84 of a certain constellation in Herschel s catalogue.\\nA few conspicuous stars are still known by individual names\\ngiven to them in ancient times as Arctnrus, Antares, Sirius,\\nYega, etc.\\nThe first catalogue of stars was made by Hipparchus, before\\nthe time of Christ, and contained 1,022 of the most conspicuous\\nstars. Catalogues of the present day contain hundreds of thou-\\nsands of stars, whose right ascensions and declinations are given\\nfor a certain date.\\n387. Effect of telescopic power on fixed stars. One indica-\\ntion of the vast distance of the fixed stars is, that no power\\nof a telescope sensibly magnifies them. Even under a power\\nwhich increases the diameter of a body 5,000 times, they appear\\nno larger than to the naked eye. It is inferred that they fill an\\nangle so small, that 5,000 times that angle is still too minute to\\nbe perceived. Any appearance of disk which a star presents,\\neither with a telescope or without, is the effect of the light\\nupon the retina of the eye. It is called a spurious disk, since\\nan increase of magnifying power causes no increase of its di-\\nameter.\\n388. Annual parallax. Another proof that the fixed stars\\n\u00e2\u0080\u00a2are at an immense distance from us, is the fact that while we\\nshift our position every six months from one side of the earth s\\norbit to the opposite, a distance of 185,000,000 miles, there is\\nno perceptible change in the relation of the stars to each other.\\nIt is only after long-continued and most accurate observation,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0213.jp2"}, "212": {"fulltext": "198 ANNUAL PAKALLAX.\\nthat a few stars have been discovered to suffer an annual\\nchange of position, which is clearly of the nature of paral-\\nlax.\\nThe annual parallax of a star is the angle, at the star, sub-\\ntended by the radius of the earth s orbit. As this angle is in\\nalmost all cases too small to be detected, it shows that the\\nearth s orbit, seen from the distance of the stars, appears as a\\nmere point.\\n389. The parallactic path of a star. If the annual paral-\\nlax of a star is in any case perceptible, its apparent movement\\nduring the year depends entirely on its situation in relation to\\nthe ecliptic.\\nA star in the plane of the ecliptic will appear to oscillate\\nback and forth in a straight line once in a year. It will appeal\\nstationary at the two opposite seasons, when the earth is going\\ntoward it, and from it and if we imagine a diameter of the\\nearth s orbit joining these two positions, the star will seem to\\ndescribe a straight line parallel to that diameter, its motion\\nduring each half-year being opposite to the general direction of\\nthe earth s motion.\\nBut if a star at the pole of the ecliptic should exhibit any\\nparallax, its apparent motion would be in an orbit parallel to\\nthe earth s orbit, and similar to it it may be regarded, there-\\nfore, as a circle described about the point in which the star\\nwould be seen from the sun. Moreover, the star s apparent\\nplace, and the earth s real place in their respective orbits would\\nbe diametrically opposite.\\nAt a point between the plane of the ecliptic and its pole,\\nthe parallactic orbit would be an ellipse, the ratio of whose\\naxes would depend on the latitude of the star.\\n390. Discovery of annual parallax. It is justly reckoned\\namong the greatest achievements in practical astronomy, that\\nthe annual parallax has, in a few cases, not only been clearly\\ndetected as existing, but has been satisfactorily measured y\\nthough it is never so great as 1\\nThe parallax of a Centauri is .\u00c2\u00a71 that of 61 Cygni, Q .o5;\\nof a Lyras, 0 .26 of Sirius, V .23. A few others have been", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0214.jp2"}, "213": {"fulltext": "DISTANCES OF STARS. 199\\nobtained, which are still smaller, and therefore less relia\\nble.\\nThe parallax of a star is most satisfactorily determined, wher\\nit is in the same telescopic field with other stars. For then\\nthe distances between the stars may be measured with greal\\nprecision by a micrometer, and all errors arising from aberra-\\ntion, refraction, and instrumental disturbance are wholly\\navoided, because all the stars in the same field are affected\\nalike by these causes of displacement. Parallax is the only cir-\\ncumstance which can produce an annual change in their rela-\\ntive positions. The star 61 Cygni is, in this respect, very\\nfavorably situated, and its parallax is thought to be quite\\naccurately determined.\\n391. Distances of those stars whose parallax is known.\\nIf a triangle is formed by the lines joining the sun, earth, and\\nstar, and the angle at the sun be a right angle, we have the\\nproportion\\nSin an. par. rad 92,381,000 miles dist. of the star.\\nThis gives the distance of a Centauri, the nearest star,\\n21,000,000,000,000 miles, nearly. Light, moving at the rate\\nof 185,000 miles per second, would require about 3.6 years to\\ncome from that star to us 9.3 years from 61 Cygni 12.6\\nyears from a Lyras and 14.2 years from Sirius. And if we\\nreckon the parallax of the pole-star at 0 .07, as it has been com-\\nputed to be, it requires 47 years for its light to reach us.\\nIn order to compare these amazing distances with the dimen-\\nsions of the solar system, we may use with advantage the dia-\\ngram described in the note, Art. 263. The distance from the\\nsun to Neptune being represented by 30 feet, the distance of\\nthe nearest star, Centauri, must be represented by 40 miles,\\nand that of 61 Cygni by 110 miles, etc. Thus isolated are the\\nsystems of the universe from each other.\\nAs to all other stars besides those above named, it is only\\nknown that they are still more distant. There is no improb-\\nability that, from the remotest telescopic stars yet seen, light\\nmay occupy thousands of years in coming to us. Therefore,\\nwe see all the stars as they were years ago perhaps not aa\\nthey are now. And if at any time a change has been detected", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0215.jp2"}, "214": {"fulltext": "200 STARS ARE SUNS.\\nin the aspect or place of a star, that change occurred, not when,\\nit was seen, but 10, 100, or 1,000 years before, according to its\\ndistance.\\n392. Nature of the fixed stars. The stars are situated at\\nsuch vast distances from the solar system, that if they merely\\nreflected the light of the sun, they would be invisible. In\\norder to exhibit such brightness as they do, they must not only\\nshed light, but a very intense light of their own. They can.\\nnot be compared with any one of the bodies in the solar sys-\\ntem, except the sun itself. All the fixed stars, therefore, are to\\nbe considered as suns, and probably the centers of systems re-\\nsembling the solar system. It is ascertained, respecting some,\\nof those stars whose distance is known, that they shed more\\nlight than the sun. For example, a Centauri has been found\\nto shed near four times as much light as the sun. For the\\nlight of the sun at the earth is about 500,000 times as great as\\nthe light of the full moon. And the light of the full moon was\\nfound by Sir John Herschel s observations to equal 27,000\\ntimes that of a, Centauri. Therefore, the light of the sun at\\nthe earth is (500,000 x 27,000) 13,500,000,000 times that of\\na Centauri at the earth. But that star is 230,000 times as far\\noff as the sun. And since the quantity of light received from\\na luminous body varies inversely as the square of the distance,\\nif a Centauri were brought as near to us as the sun, its light\\nwould be 52,900,000,000 230,000) 2 times as great as it is at\\npresent, or nearly four times as great as the light of the sun.\\nIn a similar manner, Sirius, the brightest, but not the,\\nnearest fixed star, is found to shed 100 times as much light as\\nthe sun.\\nOn the other hand, if the sun were removed from us to the\\nnearest fixed star, its apparent diameter would be only T and,\\ntherefore, would be a star having no sensible magnitude, and\\nhaving only J of the brightness of Sirius. Appendix J.\\n393. Proper motion of the stars. There is increasing evi-\\ndence that there is among the stars a parallactic motion of a.\\nhigher order than the annual parallax already noticed. The\\nentire solar system appears to be moving toward a certain.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0216.jp2"}, "215": {"fulltext": "DOUBLE STARS. 201\\npoint in the constellation Hercules, whose right ascension is\\n260\u00c2\u00b0, and its declination 35\u00c2\u00b0 north. This motion of the system\\nis inferred from what is termed the proper motion of the stars.\\nSince the time of Hipparchns (130 B. C), Sirius, Arcturus,\\nand Aldebaran have changed their position southward more\\nthan half a degree. The star 61 Cygni moves 5 each year,\\n\\\\i Cassiopeiae 4 and s Indi 8 and a large number of other\\nstars have a small progressive motion. The general effect of a\\nmotion of our own system would be to cause a minute ap-\\nparent separation of the stars in the region toward which we\\nare moving, and a crowding together of the stars in the region\\nfrom which we move. From a comparison of the proper mo-\\ntions of several hundreds of stars, a motion of the solar system\\nin the direction named above has been deduced. And the rate\\nof that motion has been estimated to be about 154,000,000\\nmiles per year, which is only one-fourth the earth s velocity in\\nits orbit.\\nIf the motion is really perceptible, it is probable that a\\nchange of direction will, after a few centuries, manifest itself,\\nfrom which something may be inferred as to the position and\\nmagnitude of the orbit which the sun describes.\\nSome of the stars have a proper motion, which can not be ex-\\nplained by the supposed motion of the solar system. In those\\ncases, it must be concluded that they are themselves describing\\nvast system-orbits about some distant center. Appendix K.\\n394. Double stars. It is discovered in a great number of\\ninstances that a fixed star, when examined by the telescope,\\nreally consists of two stars, very close to each other. If the\\ndistance between them does not exceed 32 such stars are\\ncalled double stars. Their distance apart is often less than 1\\nand some are so close, that the highest power of the telescope\\nand the most acute vision are requisite to separate them.\\nHence, certain double stars are habitually used as tests of the\\nexcellence of an instrument.\\nWhen Sir William Herschel first began his observations on\\nthis class of objects, in 1780, he knew of only four but he ex-\\ntended the list to 500 himself, and the number now known ex-\\nceeds 6.000.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0217.jp2"}, "216": {"fulltext": "202 DOUBLE STAKS.\\n395. Relative intensity and color. In comparatively fe^\\ninstances are the two stars equally bright. They sometimes\\ndiffer so little as to fall within the limits of the same magni-\\ntude; but geuerally they are of different magnitudes. Thus,\\nthe component stars of y Leonis are of the 2d and 4th magni-\\ntudes of 7] Lyrse, 4th and 8th and of the pole-star, 2d and\\n9th. Figures 1, 2, 3, and 4, in PL III., present the telescopic\\nappearance of the double stars there named. In 4, they are so\\nclose as to appear like a single star, of tapering form.\\nA fact of great interest, in relation to double stars is, that\\nthey often differ in color. Sometimes these colors are com/pie-\\nmentary that is, they are such as would compose white light,\\nif mingled together. In such cases, if the stars differ much in\\nmagnitude, the appearance of color in the fainter star may be\\nonly an illusion. But this can not be true when the colors are\\nnot complementary. The components of y Andromedee are\\norange and green of Bootis, white and violet of a Herculis,\\nyellow and blue and of (3 Scorpionis, white and blue.\\nSingle stars are frequently of a deep red color but a decided\\ncase of green or blue is never met with, except in a component\\nof a double star.\\n396. Two ways in which stars might appear double. The\\ntwo stars which compose a double star may be supposed either\\nto be really near each other, or only to appear near together,\\nbecause they fall almost into the same line of vision, while one\\nis actually at an immense distance beyond the other. In the\\nlatter case, the stars are said to be optically double. When Sir\\nWilliam Herschel commenced examining double stars, he very\\nnaturally supposed that, in the very few cases known, one star\\nhappened thus to be nearly in the same visual line with the\\nother; and he began the work of observing them, with the ex-\\npectation of detecting annual parallax in objects so favorably\\nsituated. For, if the nearer star is perceptibly affected by par-\\nallax, it would exhibit an annual motion relatively to the more\\ndistant star, in a manner not to be mistaken.\\n397. Binary stars. It soon became evident, however, that\\ndouble stars are too numerous to allow the supposition that", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0218.jp2"}, "217": {"fulltext": "ORBITS OF BINARY STARS. 203\\ntheir apparent proximity is only casual. It was calculated\\nthat the chance, that of all the stars visible to the naked eye,\\ntwo would accidentally appear within 4 of each other, was\\nonly 1 in 9,000 whereas one hundred such cases were already\\nknown.\\nBut another most interesting discovery was presently made\\nnamely, that some of the double stars exhibit motions which\\nindicate a revolution of one around the other or, rather, of the\\ntwo around a common center, and in periods of various lengths,\\nhaving no connection whatever with the earth s annual motion.\\nSuch motion can not be parallactic it must be real and such\\nstars are not optically, but physically double. They are called\\nbinary stars, and are to be regarded as the centers of double\\nstellar systems.\\n398. Gravitation outside of the solar system. The binary\\nstars afford evidence that the same law of attraction which pre-\\nvails within the boundary of the solar system prevails also at\\nimmeasurable distances beyond it. In the case of every binary\\nstar which has yet completed the whole, or any considerable\\npart of its revolution, since its discovery, it is found that the\\npath of one component star is an ellipse, while the other occu-\\npies one of the foci within it. Hence, the law of attraction is,\\ngravity varies inversely as the square of the distance, just as\\nwithin, the solar system. Though the relative motion may be\\nrepresented by considering either star as occupying the focus,\\nand the other star as revolving about it, yet the true focus is\\nthe center of gravity between them, while each describes its\\norbit about that center.\\n399. The real and the apparent orbit. It is not to be as\\nsumecl that the plane of a stellar orbit is perpendicular to oui\\nline of vision. But if it is oblique, although it is always pro-\\njected on the sky as an ellipse, yet the apparent eccentricity\\nmay differ in any degree from the real eccentricity, and the\\ncentral star will probably appear out of the focus of the ap-\\nparent orbit. The true orbit, however, can be readily deduced\\nfrom the apparent one, by means of the position of the central\\nstar. If the plane of revolution of a binary star were coinoi-", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0219.jp2"}, "218": {"fulltext": "204\\nPERIODS OF BINARY STARS.\\nFig. 88.\\ndent with oar line of vision, one star would appear to oscillate\\nin a straight line across the other.\\nThe ellipse, BCD (Fig. 88), represents the apparent orbit of\\nUrsse Hajoris, the central star\\nbeing at A. The real orbit, of\\nwhich A is the focus, is BDF.\\nThe apparent orbit of a Centauri\\nis still more eccentric (Fig. 89),\\ncompared with the real one, be-\\ncause more oblique to the Hue of\\nvision. It has not yet described\\nquite half its orbit, since it began\\nto be observed.\\nAt the bottom of PI. III. are\\nshown the relative positions and\\ndistances of y Yirginis from 1837\\nto 1860, and the form of the apparent orbit. The real orbit\\nis even more eccentric, the major axis being somewhat fore\\nshortened by obliquity.\\nFig. 89.\\n400. Periods of Unary stars. The shortest period knows\\nis that of Herculis, about 31 years. The period of n Coronse\\nis 43 years that of I Ursas Majoris (Fig. 88) is 58 years.\\nThese, and a few others of short period, have completed their", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0220.jp2"}, "219": {"fulltext": "PERIODS OF BINARY STARS. 205\\nrevolutions once or twice since they were discovered. The\\norbits of such are quite accurately determined. One revo-\\nlution of a Centauri (Fig. 89) has not yet been made since its\\ndiscovery its period is calculated to be 77 years. A large\\nnumber of binary stars, whose periods are computed to be some\\nhundreds or thousands of years, have been observed as yet only\\nthrough a short arc hence their periodic times, and the forms\\nof their orbits, are quite uncertain.\\n401. Dimensions of stellar orbits. There are two binary\\nstars whose parallax has been so satisfactorily measured, that\\ntheir distances from us may be considered as well known\\nthese are a Centauri and 61 Cygni. Hence, by the angular\\nlength of the semi-major axes of their orbits, we may find the\\nmean radius vector of each. The major axis of the orbit or\\na Centauri is about 30 and its distance from the earth is\\n21,000,000,000,000 miles.\\nrad sin 15 21,000,000,000,000 1,464,000,000 miles\\nwhich is equal to about 16 times the earth s distance from the\\nsun. The distance between the components of 61 Cygni is\\nabout 4,012,000,000 miles.\\n402. Masses of the binary stars. For those binary stars\\nwhose periods and distances apart are known, the mass of the\\nJ33\\nsystem can be computed. For M oo hence, for a Centauri\\n(the earth s distance from the sun, and its period being called 1),\\n16 3\\nM 0.69. That is, the mass of the two components of\\na Centauri is about 0.7 of the mass of the sun and earth. So,\\nfor 61 Cygni, whose period is computed to be 540 years, and\\nthe distance of the two components 44 times the radius of the\\nearth s orbit, the mass of the double star is 0.3 of the mass of\\nthe sun and earth.\\n403. Triple and quadruple stars, There are a few in-\\nstances of three or four stars, which are known to be physically\\nconnected, and to constitute a system. Figs. 5, 6, PL III.,\\npresent the appearance of 11 Monocerotis and C Cancri. In", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0221.jp2"}, "220": {"fulltext": "206 PEKIODIC STARS.\\nthe latter, the two close components revolve in 59 years, and\\nthe distant one more slowly. The faint star e Lyrae is quadru-\\nple, consisting of two very close double stars. They give evi-\\ndence of belonging to one system, but their revolutions are ex-\\nceedingly slow.\\n404. Periodic and temporary stars. There are among the\\nfixed stars several instances in which there appear to be revolu-\\ntions of another sort, the nature of which is not understood.\\nStars which exhibit these changes are called periodic stars. A\\nremarkable example occurs in the star o Ceti. It passes\\nthrough its changes of brightness in about 11 months. When\\nbrightest, it is of the 2d magnitude, and remains so for twc\\nweeks. It then diminishes during 3 months to the 10th mag-\\nnitude, remains thus 5 months, and increases again during 3\\nmonths to its maximum of brightness.\\nAlgol (/3 Fersei) has a very short period, occupying only 2d.\\n20h. 48m. Its changes succeed each other with great regular\\nity, thus\\nDuring 2d. 14h. Om. it remains of the 2d magnitude.\\nOd. 3h. 24m. diminishes from 2d to 4th.\\nOd. 3h. 24m. increases from 4th to 2d.\\n2d. 20h. 48m. whole period.\\nSome of this class of stars have periods of only a few days,\\nwhile in others the changes go on very slowly, and appear to\\nrequire several years. The periods of some are quite uniform,\\nand of others irregular. As accurate observations are mul-\\ntiplied, the number of known periodic stars is constantly in-\\ncreasing.\\nTo this class probably belong those stars which are called\\ntemporary stars. That of 1 572 is celebrated. It appeared so\\nsuddenly, and of such brilliancy, as to attract the attention of\\ncommon people, and rapidly increased, till in a few weeks it\\nsurpassed Jupiter in brightness. It then faded slowly, and\\nafter about 1^ years entirely disappeared. Several other cases\\nless marked than this are on record. And the earlier cata-\\nlogues contain numerous stars which are not to be found at the\\npresent day. Undoubtedly some of these records are mistakes,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0222.jp2"}, "221": {"fulltext": "NEBULA. 207\\n\u00c2\u00a311 two or three instances, it is known that the bodies were\\nplanets, not fixed stars. But in the course of coming centuries,\\nsome of the temporary stars may again become visible, and\\nthenceforward be recognized as periodic stars.\\n405. Cause of periodicity. The conclusion can not be\\navoided, that the variable magnitudes of stars, at least when\\nthey recur regularly, are the result of some sort of revolution\\nMore than this is mere conjecture. In some cases, the star\\nmay be partially dark on one side, and produce the changes\\nby rotation on its axis. In others, there may be opaque bodies,\\neither single or existing in groups or zones, revolving about\\nthe central star.\\nNewton suggested that the sudden appearance of a tem-\\nporary star might be the result of a comet falling upon the\\ncentral body, which was before invisible, and causing confla-\\ngration.\\n406. Clusters of stars. The fixed stars are frequently\\ngrouped together in clusters, such as the Pleiades, in Taurus\\nPresepe, in Cancer and Coma Berenices. If a telescope of\\nlow power is used, the number of stars appears greatly in-\\ncreased. Figure 1 in PL IV. gives a telescopic view of the\\nPleiades.\\nThere are others which to the naked eye appear nebulous,\\nbut by the use of the telescope are plainly seen to be clusters\\nand in some of them the stars are so numerous as not to be\\neasily counted. The clusters in Perseus and Hercules are fine\\nexamples. For the latter, see PI. IY., Fig. 3 a is its appear-\\nance with a low power b is the central part of it with a high\\npower.\\n407. Nebula. These are faint patches of light, having gen\\nerally an ill-defined edge, and in ordinary telescopes presenting\\nthe same nebulous aspect which the closer clusters do to the\\nnaked eye. As the powers of the telescope are increased,\\nmany nebulae are resolved into clusters of stars, while many\\nothers retain their nebulous appearance under every power yet\\nemployed. The number of nebulae now known exceeds 5,400,", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0223.jp2"}, "222": {"fulltext": "208 FORMS OF NEBULA.\\nTheir forms are exceedingly various and in some cases they\\nseem in this respect to be greatly changed as the telescope is\\nimproved in its magnifying and defining powers.\\nSince every advance which is made in the Construction oi\\ninstruments resolves some nebulas into clusters of stars, many\\nastronomers have been led to suppose that all nebulas are clus-\\nters, only too remote to be resolved by means hitherto em-\\nployed. Some facts, however, connected with this class oi\\nbodies seem to indicate that there are, in some regions of space,\\nimmense tracts occupied with nebulous matter not yet formed\\ninto stars.\\n408. Varieties of for in among nebula.\\n1 Globular. A large number, especially of the smaller neb-\\nulas, present a circular outline, and grow brighter gradually\\nfrom the circumference toward the center, thus suggesting the\\nidea of a spherical form. The nebulous stars, so called, differ\\nfrom them in that the nebulosity continues nearly uniform up\\nto a central star. The planetary nebulae have a well-defined\\nedge, and no bright center, and therefore bear some resem-\\nblance to a planet.\\n2. Elliptical. Several nebulas present the appearance of an\\noblate spheroid seen edgewise. The most remarkable example\\nis the great nebula of Andromeda. Its length is 1^\u00c2\u00b0, and it is\\neasily seen by the naked eye (PL IV., Fig. 2). The dumb-\\nbell nebula, between Cygnus and Aquila, appears in the best\\ntelescopes to have an elliptical shape. The brightest part of\\nit has a form slightly resembling a dumb-bell, or an hour-glass.\\n(PI. II., Fig. 4).\\n3. Spiral. This description of nebulas is becoming rather nu-\\nmerous since the latest improvements in telescopes. Some\\nnebulas of very irregular shape, as formerly described, exhibit,\\nin the best instruments of this day, delicate appendages having\\na spiral arrangement. The whirlpool nebula, near the tail of\\nUrsa Major, is the most remarkable instance of this form (PL\\nIV., Fig. 5). The crab nebula, in Taurus, may yet be found to\\nDelong to this class (PL IT., Fig. 4).\\n4. Annular. A few nebulas have an outline nearly circular\\nor elliptical but appear more luminous on the edges than in", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0224.jp2"}, "223": {"fulltext": "MAGNITUDES OF NEBULAE. 209\\nthe central part. Such are called annular nebulae. The ap-\\npearance is that of a hollow sphere or spheroid in which case\\nwe look through the greatest depth near the edges. An inte-\\nresting example is situated in Lyra, midway between (3 and y\\n(PL IL, Fig. 3).\\n5. Irregular. Besides the foregoing forms, which are all in-\\ndicative of a central force, and of revolution, there are various\\nshapes of great irregularity. None is so celebrated as the great\\nnebula of Orion, which has been a subject of observation\\nand record for more than two centuries. It becomes more ex-\\ntended and more complex with every new improvement in tel-\\nescopes.\\n409. Magnitude of clusters and nebulce. Every cluster of\\nstars, whether a complex system of suns or not, must occupy\\nan immense space. They are at least as far distant as the\\nnearest star, and how much further we can not know, and yet\\nthey fill a sensible angle, and some of them a large one. It is\\neasy, therefore, to assign the lowest limit for their dimensions.\\nThe length of the nebula in Andromeda is 1|\u00c2\u00b0. Supposing it\\nas near as a Centauri, its absolute length must be 6,000 times\\nthe distance from the earth to the sun. And if it be many\\ntimes further from us than the nearest star, which is far more\\nprobable, then its dimensions must be just so many times\\ngreater.\\n410. Changes in the nebulce. In repeated instances it has\\nbeen thought that the forms of certain nebulas had essentially\\naltered since their discovery. But this is not certain for it is\\nfound that the same nebula assumes a new aspect as the tele-\\nscope is improved, because some of the more delicate features,\\nwhich were not before noticed, are brought to view. It may\\nbe, therefore, that all apparent changes of form hitherto noticed\\nare to be explained in this way.\\nBut there are a few faint nebulas, which are known to have\\ngrown more dim within a short time for they can not now be\\nseen by the same instruments which only a few years ago\\nbrought them distinctly into view. In one or two in-\\nstances, a nebula has entirely ceased to be visible. Such\\n14", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0225.jp2"}, "224": {"fulltext": "210 THE GALAXY.\\nbodies may, perhaps, have regular changes, like the periodic\\nstars. Appendix L.\\n41 1. The galaxy. This is a belt or zone, of nebulous ap-\\npearance, which encircles the heavens, nearly coincident with\\na great circle, and cuts the plane of the equator at an angle of\\n63\u00c2\u00b0. It is usually called the milky-way. 2s~ear the constella-\\ntion Cygnus, it divides into two parts, which continue separate\\nnearly a semicircle (150\u00c2\u00b0), and then reunite. Its edges are\\ngenerally ill-defined, and also quite crooked and irregular T\\nhaving many projections and indentations.\\nThe telescope shows that the whiteness of the galaxy is due\\nto unnumbered stars, too faint to be seen individually. Their\\ndistribution is quite unequal the stars, in some parts, being\\ncrowded very closely together, while here and there spaces oc-\\ncur which contain but few. These inequalities are most marked\\nin the southern hemisphere. A small portion of the southern\\ngalaxy is shown in PI. III. In the most luminous parts, Sir\\nWilliam Herschel estimated that, within an area less than z \u00c2\u00b1q\\npart of the hemisphere, there passed the field of his telescope\\n50,000 stars, large enough to be distinctly seen. The whole\\nnumber of stars in the milky-way is to be reckoned by millions.\\nIt appears, therefore, that by far the largest part of the stars\\nwhich are within the reach of our vision lie in a thin stratum\\nor ring, in the plane of which the sun is situated. As we our-\\nselves, being near the sun, are in this plane, we see the stars\\nmostly crowded into the zone or belt which is called the\\ngalaxy, while over the other parts of the sky they are more\\nsparsely distributed.\\n412. The nebular hypothesis What it proposes. The hy-\\npothesis which is known by the name of the nebular hypothesis\\nproposes to explain in what manner the bodies composing the\\nsolar system may have arrived at their present state, as to mo-\\ntion, condition, and mutual relations, through the operation oi\\nknown laws, which the Creator has employed during the\\nalmost countless ages since the material was at first formed.\\n413. Argument from analogy. The organized bodies on", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0226.jp2"}, "225": {"fulltext": "THE NEBULAE HYPOTHESIS. 211\\nthe earth, whether animal or vegetable, are not created in their\\nmature and perfect state, performing at once all the functions\\nfor which they were designed; but they grow to this condition\\nby a series of changes, which extend generally through a num-\\nber of years.\\nSo the soils of the earth were not first formed in their present\\ncondition, fitted to sustain the vegetation which clothes them\\nbut are the result of slow disintegration of the rocky mountain\\ntops, through the action of water and changes of temperature.\\nIt is more in accordance with the Creator s plan of operation,\\nso far as we can discover it, that the sun, planets, and satellites\\nshould have been brought into their present condition through\\na long-continued course of change, than that they should have\\nbeen created and set in motion as we now see them.\\n414. Facts in the solar system which form the oasis of the\\nhypothesis.\\n1. The sun, the planets, and the satellites, so far as they are\\nknown to rotate at all on their axes, rotate nearly in the same\\ndirection, from west to east. And the revolutions of all planets\\nabout the sun, and of all satellites about their primaries, with\\nbut few and trifling exceptions, are in the same general direc-\\ntion, from west to east.\\n2. The sun, which contains nearly the whole material of the\\nsystem, is a sphere in a condition of intense heat. The interior\\nof the earth is in a red-hot melted state, as is proved by the\\nvolcanoes on its surface. The moon is covered with volcanic\\ncraters, which show that it is, or has been, in the same condi-\\ntion, internally, as the earth now is.\\n415. The nebular hypothesis stated. It assumes that the\\nwhole space occupied by the solar system, and extending far\\nbeyond its present limits, was filled with nebulous matter, in an\\nexceedingly rare and intensely heated condition and that this\\nentire mass was put into a state of rotation in the direction\\nwhich we now call from west to east.\\nThis assumption being made, the following consequences\\nwould ensue, during the lapse of immense periods of time, in\\naccordance with the we 1-known laws of the material creation.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0227.jp2"}, "226": {"fulltext": "212 THE NEBULAE HYPOTHESIS.\\nBy gravity and the centrifugal force, the vast nebula takes a\\nspheroidal shape.\\nHeat is radiated from its exterior into the boundless space\\naround it and by this loss, the nebula contracts in diameter.\\nBut as it contracts, the given velocity of rotation at the surface\\ncauses a quicker rate of revolution, until, at length, the cen-\\ntrifugal force of the equatorial part equals the attraction toward\\nthe center of the entire mass. As soon as these two forces are\\nequal, the equatorial part rotates independently of the interior,\\nwhile the latter contracts still further, and leaves the superfi-\\ncial part revolving as a nebulous ring.\\nAfter the central portion has left the ring, it goes on con-\\ntracting as before, till it leaves a second ring. Thus, an indefi-\\nnite number of concentric nebulous rings may be left, each\\nrevolving from west to east, and at a swifter rate according as\\nit is nearer the center. The central mass, which thus succes-\\nsively deposits its rings, is the sun of the system.\\n416. While the material composing each ring goes on cool\\ning and contracting, unless the quantity is exactly equal on\\nevery side, which is improbable, the whole of it, at length, is\\ndrawn toward the heaviest side, until it is gathered into a\\nspheroid, revolving once on its own axis, while it revolves once\\naround the central mass. These spheroids ire the planets, re-\\nvolving around the sun.\\nBut as the planetary spheroid continues to contract by cool-\\ning, its rate of rotation is quickened, untr it leaves its equa-\\ntorial part revolving in a ring about it, in the same manner as\\nthe central nebula has done and this it may do in repeated\\nnstances.\\nThese subordinate rings are likely also to collect into so\\nmany spheroids, revolving about the larger ones, and on their\\nown axes. These are satellites. In case the parts of a ring are\\nvery exactly balanced, they may preserve their condition of a\\nring, instead of gathering into a satellite. Ax. example is seen\\nin the ring of Saturn.\\nIt is conceivable that a multitude of u*all rings, instead ol\\none large one, may be detached from the central mass when\\nthe separation occurs. This seems to have been the c^se in", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0228.jp2"}, "227": {"fulltext": "THE NEBULAR HYPOTHESIS. 213\\nthe formation of those rings from which the planetoids were\\nformed.\\n417. After the planets and satellites have cooled sufficiently,\\nthey become non-luminous bodies, and are gradually changed\\nfrom nebulous into a liquid or solid condition. And, in a\\ngiven case, the exterior may be solid, while the interior re-\\nmains in a liquid and highly heated condition. This is the\\npresent state of the earth, and the present or recent condition\\nof the moon.\\nThat the planes of motion throughout the system are not co-\\nincident, is to be ascribed to disturbing influences which the\\nseveral bodies have been exerting on each other during the\\nvast periods of time that have elapsed since they were detached\\nfrom the solar mass.\\n418. Application to other systems. Every fixed star which\\nis single may be the condensed nucleus resulting from an op-\\noration similar to that which has been described; and the\\ndouble and triple stars may be considered as cases in which\\neither the nebula became divided into two or three parts, be-\\nfore the contraction had proceeded far, or else the nebulous\\nmass, being very oblate, a large part of it was detached at\\nonce, and collected into a body, nearly equal to the central\\npart.\\nThe nebulae of regular form, not capable of being resolved\\ninto separate stars, may still be in the condition of the solar\\nsystem before its rings began to be separated from the original\\nbodv.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0229.jp2"}, "228": {"fulltext": "APPENDIX\\nA.\u00e2\u0080\u0094 Art. 107.\\nThe exact period of the sun s rotation is not easily deter-\\nmined, because of the independent motions of the spots them-\\nselves. That they do have such motions is apparent from the\\nfact that they differ from each other somewhat in their east-\\nward velocity, and also that some of them move a little north-\\nward or southward wmile crossing the disk. Among the various\\nresults obtained by different observers, the lowest is about\\n25 days, and the highest about 25 days and 12 hours.\\nB.\u00e2\u0080\u0094 Art. 111.\\nThe perspective effect described in Art. Ill, may perhaps\\nbe better understood by the aid of Fig. I., which represents a\\nsection of the sun through a spot. Let ah be the breadth of\\nthe opening in the outer stratum, cd that of the narrower one\\nin the inner stratum. When this spot is seen near the middle", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0230.jp2"}, "229": {"fulltext": "APPENDIX.\\n215\\nof the disk, we look into it almost at right angles to the sur-\\nface, along the lines marked p, p, and can see ef of the denser\\npart of the sun (which is the macula), and also some of the\\ninner stratum on all sides of cd and this is the umbra. But\\nwhen the spot is very near the edge, we look along the lines\\nrr through ab, and can see only that part of the inner stratum\\nwhich is beyond cd; in other words, only that part of the um-\\nbra is seen which lies nearest to s, the edge of the disk.\\nC.\u00e2\u0080\u0094 Art. 112.\\nThe bright points and streaks which are generally visible\\nover most of the sun s disk, giving it a mottled appearance,\\nare called f amice (little torches), and the dark specks among\\nthem are often called pores. The faculse are described by some\\nobservers, as having the appearance of willow leaves crossing\\neach other in all directions, and by others, as resembling rice\\nKg. II\\ngrains, or bits of straw. They are most conspicuous at the\\nedges of spots, and at places where spots are forming or closing\\nup. Irregular bands of faculse are frequently seen projecting\\nthemselves with great velocity over the area occupied by a\\nspot, and even forming bridges entirely across it. Fig. II.\\nimperfectly represents these appearances.\\nD.\u00e2\u0080\u0094 Art. 115, and 228.\\nThe combination of the spectroscope with the telescope has\\nenabled astronomers to gain considerable additional knowledge", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0231.jp2"}, "230": {"fulltext": "216 APPENDIX.\\nrespecting the nature and condition of the sun s exterior. See\\nNat. Phil., Art. 398-400.\\nThe dark lines of the solar spectrum show that the photo-\\nsphere consists of the following substances in the gaseous\\nstate: sodium, calcium, magnesium, chromium, iron, copper,\\nzinc, barium, nickel, hydrogen, etc. The intense light of the\\nliquid parts below, shining through these gases, causes their\\nspectrum lines, which would otherwise be bright colored lines,,\\nto become dark ones.\\nThe same instrument has more recently proved the existence\\nof a less luminous envelope outside of the photosphere. The\\nappearance of irregular projecting masses of faint red light\\nfrom behind the moon during a total solar eclipse, had pre-\\nviously led to the suspicion of such an atmosphere. See\\nArt. 228, 3. By the use of modern instruments, not only can\\nthese protuberances, or prominences of reddish light be viewed\\nat any time, but also the envelope itself can be traced entirely\\naround the disk of the photosphere. This outer covering is.\\ncalled the chromosphere, because its spectrum exhibits colored\\ninstead of dark lines. This covering of red-hot gas consists\\nlargely of hydrogen, having an average depth of several hun-\\ndred miles but, being generally in a state of extreme commo-\\ntion, its more elevated parts are from 50,000 to 100,000 miles,\\nhigh. The parts thus thrown upward by the terrific forces in\\noperation there, are sometimes completely detached from the\\nrest. The prominences of the chromosphere often resemble\\nmountains, trees, flames, or clouds but more frequently they\\nassume fantastic forms wholly indescribable. These forms\\nchange very rapidly, indicating a motion of several thousands\\nof miles in a single hour. In some cases there is evidence of\\nrotary motion parallel to the surface of the sun that is, there\\nare vast whirlwinds of fire. In others, jets of red-hot hydro-\\ngen are spouted upward to the height of 50 or 60,000 miles.\\nFig. III. will convey some idea of the variety and singularity\\nof the forms of the prominences of the chromosphere. The\\nphotosphere, or bright surface of the sun, is represented in each\\npart of the figure by the curve ah.\\nThe corona, which is white, and surrounds the chromosphere,\\nextends considerably beyond its highest prominences. It is", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0232.jp2"}, "231": {"fulltext": "APPENDIX.\\n217\\ndistinctly seen on-\\nly during the to-\\ntality of a solar\\neclipse, and its\\nboundary is not at\\na uniform height\\non all sides, but\\nvaries irregularly\\nfrom 100,000 to\\n200,000 miles in\\nheight from the\\nphotosphere.\\nA still fainter\\nwhite light is seen\\nduring the time of\\na total solar eclipse,\\nextending outward\\nbeyond the coro\\nna this is called\\nthe halo. It was for\\na time suspected\\nto be an effect pro-\\nduced by our own\\natmosphere. But\\nthere is increasing\\nevidence furnished\\nby recent eclipses,\\nthat it truly sur-\\nrounds the sun.\\nIts extent is very\\nunequal on differ-\\nent sides, having\\nin some places\\ndeep gaps reach-\\ning down to the co-\\nrona, and in other\\nparts extending\\nupward to nearly\\ntwice the diameter\\nof the sun.\\nFig. III.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0233.jp2"}, "232": {"fulltext": "218 APPENDIX.\\nE.\u00e2\u0080\u0094 Art. 116.\\nThere is an interesting connection between the periodicity\\nof the solar spots, and that of magnetic disturbances on the\\nearth. By a careful comparison of these phenomena, as ob-\\nserved and recorded through a period of nearly a hundred\\nyears, it is found that with the periodic increase and decrease\\nof the amount of spot-surface on the sun s disk, there is a cor-\\nresponding increase and decrease of terrestrial magnetic storms,\\nindicated by the agitations of the needle and the occurrence\\nof the aurora borealis. In each case, the maximum occurs at\\nabout the same time once in ten or eleven years, and the mini-\\nmum at nearly corresponding times between. In general,\\nthere are frequent auroras and frequent disturbances of the\\nneedle in those years in which the sun exhibits the greatest\\nspot-area and when the solar spots are few and small, auroras\\nare infrequent, and the needle is but little disturbed. What-\\never may be the cause of spots on the sun, it is in the highest\\ndegree probable that the same cause produces these alternations\\nin terrestrial magnetism.\\nF._ Art. 256.\\nThere appears to be increasing evidence that there is at\\nleast one planet revolving within the orbit of Mercury. A\\nround, dark spot has been repeatedly seen crossing the sun s\\ndisk and a comparison of the dates of such observations leads\\nto the belief that an inferior planet exists, w T hose periodic time\\nis about 39 days. The name Yulcan, has been already given\\nto the supposed planet, The existence of such a body, or else\\nof a group of smaller bodies, has been for some time suspected,\\nbecause of an unexplained morion of the perihelion of Mer-\\ncury s orbit.\\nG.\u00e2\u0080\u0094 Art. 357.\\nIt does not necessarily follow from the reasoning in Art. 357,\\nthat all the light received from a comet is reflected. What is\\nthere stated would be true if a part is reflected, and another\\npart originates in the comet itself. And the spectra of some", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0234.jp2"}, "233": {"fulltext": "APPENDIX. 219\\ncomets examined within a few years, furnish quite satisfactory\\nevidence, that while they reflect the sun s light, they also\\nradiate the light of some incandescent substances, either gas-\\neous, or in the state of a comminuted solid.\\nH.\u00e2\u0080\u0094 Art. 367.\\nBiela s comet, which separated into two parts in 1846 while\\nin sight from the earth, and which reappeared as two comets\\nin 1852, has since then, it is believed, been partially or wholly\\ndivided into innumerable cometary fragments. For it has\\nfailed to appear at the times of its expected return since 1852,\\nand in its stead there has been an unusual number of shooting\\nstars coming into the earth s atmosphere at times and in direc-\\ntions corresponding to such a supposition. The path of the\\nearth and that of Biela s comet so nearly intersected each other,\\nthat if the latter body has suffered the catastrophe supposed,\\nit was to be expected that some of its fragments would meet\\nthe earth, and appear in its atmosphere as shooting stars.\\nI.\u00e2\u0080\u0094 Art. 380.\\nThe dissolution of a comet into a group or ring of meteors\\nhas taken place in other instances besides that mentioned in\\nAppendix H. The annual meteoric shower of August 10th,\\ncomes from a ring which coincides with the orbit of Comet III.,\\n1862. A small arc of this orbit is represented in Fig. IT.,\\nintersecting the earth s orbit at A, through which point the\\nearth passes on the 10th of August. The planes of the two\\norbits intersect in the line AB, and their inclination, the angle\\nESM, is 64\u00c2\u00b0 3 The perihelion of the meteoric orbit is P\\nand PC drawn through the sun S, and produced, is the axis,\\nwhich meets the aphelion at the distance of about 10,000,000,000\\nmiles from the sun, or more than three times the distance of\\nNeptune. The cometary fragments seem to be distributed\\naround the whole circuit of the orbit, though unequally so\\nthat the earth, when it passes across their path, always meets\\na few, and sometimes large numbers of them. The small\\ncomet, III., 1862, was probably the mere remainder of a large", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0235.jp2"}, "234": {"fulltext": "220\\nAPPENDIX.\\ncornet, which has for ages been scattering its particles along its\\npath for the August shower has been known for a long time.\\nFig. IV.\\nAnother example of identity between a comet and a me-\\nteoric shower, is that of comet I., 1866, or Tempers comet,\\nand the shower of November 13th. The orbits have the same\\nelements, and their periodic time is 33 years. In this case,\\nthe fragments of the comet, instead of occupying the whole\\ncircumference, are gathered into a group, of such length, how-\\never, that the earth strikes into it on three successive returns\\nto the same place in its own orbit. Among the most brilliant\\ndisplays of meteors from this group are those of 1799, 1833,\\nand 1867. Fig. V. shows a short arc of this orbit, along which\\nthe meteors are moving in the direction of the arrows, in a\\ngroup of varying thickness. It intersects the earth s orbit\\nat A, the planes of the two being inclined at an angle of", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0236.jp2"}, "235": {"fulltext": "APPENDIX.\\n221\\n17\u00c2\u00b0 4:4: represented by ES1I. The aphelion is about as far\\nfrom the sun as the orbit of Uranus. The meteors in both of\\nMar. V.\\nthe foregoing orbits have a retrograde motion, as the arrows\\nshow. Hence, the earth meets them, moving partly in a direc-\\ntion opposite to its own motion.\\nJ.\u00e2\u0080\u0094 Art. 392.\\nSpectroscopic observations made upon the brighter stars\\nreveal the interesting fact, that, like the sun, they have a\\ngaseous photosphere containing substances of the same nature\\nas some of those existing on the earth. For example, a Taori\\nhas hydrogen, sodium, magnesium, iron, mercury, and several\\nother known elements in its gaseous exterior. Likewise,\\na Orionis, by the dark lines of its spectrum, is proved to have\\na constitution much like that of a Tauri. Hundreds of stars\\nof the larger magnitudes have in like manner furnished some\\nindications of the elements which compose them. But even\\nthe brightest stars shed so little light at our immense distance\\nfrom them, that only the most conspicuous lines due to a given\\nsubstance are visible. Yet the very exact coincidence of the\\nfew lines which can be seen, with those of the corresponding\\nterrestrial elements, is considered as conclusive proof that\\nthese elements enter into the composition of such stars. It is", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0237.jp2"}, "236": {"fulltext": "222 APPENDIX.\\nbelieved, therefore, that at least the brightest stars have a\\nphysical constitution similar to that of the sun of our own sys-\\ntem. Their light, emanating from the denser central parts,\\npasses through a luminous gaseous envelope, and by the dark\\nlines thus exhibited, reveals the nature of the envelope.\\nThere is no reason to suppose that the fainter stars, as a\\nclass, differ in their constitution from the brighter ones. They\\nare too far off, however, to afford us sufficient light for ascer-\\ntaining their true character by any means which have as yet\\nbeen devised.\\nK\u00e2\u0080\u0094 Art. 393.\\nOne of the most remarkable discoveries made by the use of\\nthe spectroscope is that of the motion of certain stars either\\ntoward, or from the solar system. A certain wave-length of\\nlight belongs to each point through the length of the spectrum.\\nThe waves of the red extremity are longest, and those of the\\nviolet extremity are shortest and there is a regular gradation\\nfrom one to the other. Nat. Phil., Art. 436. Hence, every\\nline of the spectrum, since it has a fixed place, indicates pre-\\ncisely a certain wave-length corresponding to its location.\\nNow, suppose that in the spectrum of a star, some of the\\nstronger lines of a substance, hydrogen, for example, are dis-\\ncovered and known by their prominence and general locations,\\nto be hydrogen lines and suppose again, that when carefully\\nexamined under a high power, and compared with hydrogen\\nartificially heated, that they are slightly displaced toward the\\nviolet end of the spectrum. This shows that the waves are a\\nlittle shorter than those of hydrogen at rest. Such a displace-\\nment proves, therefore, that either the star is coming toward\\nus, or we are approaching it and the degree of displacement\\nindicates the velocity of approach. A star, on the other hand,\\nwhich shows a displacement of a set of lines from their true\\nplaces toward the red extremity of the spectrum, is thereby\\nknown to be increasing its distance from the solar system.\\nThus, the star Sirius is discovered to be moving from the sun\\nat the rate of nearly 30 miles per second.\\nThe star may indeed be moving in a direction oblique to the", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0238.jp2"}, "237": {"fulltext": "APPENDIX. 223\\nline joining it and the sun but the spectroscopic displacement\\nindicates only that component of the motion which is in the\\nvisual direction. The other component, if it exists, is what\\nhas been long recognized as the proper motion of the star\\nthat is, its angular change of place, which cannot, however, be\\nreckoned as a linear quantity, till the distance of the star from\\nthe solar system is ascertained.\\nL.\u00e2\u0080\u0094 Art. 410.\\nSo long as successive improvements in telescopes led occa-\\nsionally to the resolving of a nebula into a cluster of stars, it\\nremained uncertain whether all nebulae consist of separate\\nstars or not, until a new mode of investigation was discovered.\\nNotwithstanding the great difficulties in the way of examining\\nsuch faint objects with the spectroscope, the general question\\nseems to be satisfactorily answered. All nebulse, which have\\nbeen hitherto resolved, exhibit a spectrum, apparently con-\\ntinuous, though dark lines too delicate to be discerned may\\nexist. The bodies composing such nebula?, therefore, consist\\nof solid or liquid matter, which may or may not be surrounded\\nby a gaseous envelope. Also, several of the nebulas not yet\\nresolved, show the same kind of spectrum which indicates\\nthat these, too, are solid or liquid, but so remote as not to yield\\nto the power of any telescope yet applied to them.\\nOn the other hand, the larger part of irresolvable nebulas,\\nbright enough to be examined, form a spectrum which consists\\nonly of one, two, or three bright lines and these generally\\ncoincide with those of some known gas. Thus, the ring\\nnebula of Lyra gives a spectrum of one line, and that the\\nbrightest nitrogen line and the great nebula of Orion, a spec-\\ntrum of three lines, one nitrogen, one hydrogen, and the third\\nunknown.\\nM.\u00e2\u0080\u0094 Aet. 264.\\nTo identify any Planet, When the observer has not the use\\nof an Ephemeris he can find the approximate, place of any of the\\nprimary planets by the following process", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0239.jp2"}, "238": {"fulltext": "APPENDIX.\\n224\\nDiscarding the elliptical orbit, assume that the planet moves\\nuniformly in a circular orbit. Multiply the mean daily motion\\nboth of the planet and the earth, as given in column VI, Table\\nII, page 228, by the number of days that have elapsed since\\nthe beginning of the century, being careful to include the leap-\\ndays to the product add the corresponding numbers in column\\nVII. Divide by 360, so as to reject all the completed revolu-\\ntions, and the remainders will be the mean heliocentric longi-\\ntudes of the planet and of the earth.\\nIn Fig. VI, let S be the sun E, the earth V, the vernal\\nequinox as seen from the earth V, the same, as seen from the\\nsun and P the planet, the ecliptic being in the plane of the\\ndiagram. V SP will be the heliocen-\\ntric longitude of the planet V SE the\\nheliocentric longitude of the earth\\nPSE the difference between them,\\nand VEP the geocentric longitude of\\nthe planet.\\nIn the triangle SEP, knowing SP\\nand SE, either in astronomical units\\nor in miles, and the angle ESP, we\\ncan compute the angle SEP by plane\\ntrigonometry. As SV and EV are\\nparallel, SEV is the supplement of\\nV SE. By subtracting SEV from\\nSEP, we have VEP, the required East\\ngeocentric longitude of the planet.\\nIf the diagram be held in the plane of the ecliptic, and the\\nline EV pointed toward the vernal equinox, EP will point\\nnearly in the direction of the planet. The inclination and\\neccentricity of the orbits of Mercury and the moon are so great\\nthat this method cannot be applied satisfactorily to finding\\ntheir places.\\nWest", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0240.jp2"}, "239": {"fulltext": "SPECTROSCOPE.\\n(Fauth Co., Manufacturers, Washington, D. C.)", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0241.jp2"}, "240": {"fulltext": "TABLE L\u00e2\u0080\u0094 THE CALENDAR,\\nA Tajl* to r Nd the Day of the Week of ajsty given date, fkom tee Yeab 5000\\nTO THE YEAB 2700 OF THE CHBI3TIAN Era.\\nCkmtueibs before Christ.\\nCenturies after Christ\\n4SO0\\n4100\\n3400\\n2700\\n2000\\n1300\\n600\\n4700\\n4000\\n3300\\n2600\\n1900\\n1200\\n500\\n4600\\n3900\\n3200\\n2500\\n1800\\n1100\\n400\\n4500\\n3800\\n3100\\n2400\\n1700\\n1000\\n300\\n4400\\n3700\\n3000\\n2300\\n1600\\n900\\n200\\n5000\\n4300\\n3600\\n2900\\n2200\\n1500\\n800\\n100\\n4900\\n4200\\n8500\\n2S00\\n2100\\n1400\\n700\\nNew j\\nStyle 1\\nOld J\\nStyle\\nI\\n1700\\n2100\\n0-\\n700-\\n1400-\\n2100-\\nC\\nB\\n1800\\n2200\\n200-\\n900\u00c2\u00ab\\n1600\\n2300-\\n300-\\n1000-\\n1700-\\n2400*\\nF\\n1500\\n1900\\n2300\\n400*\\n1100*\\n1800\u00c2\u00ab\\n2500*\\n~G~\\n1600.\\n2000\\n2400*\\n500\u00c2\u00bb\\n1200\u00c2\u00ab\\n1900*\\n2600*\\n600\u00c2\u00ab\\n1300\u00c2\u00ab\\n2000*\\n2700\\n~b\\nA\\ng\\nF\\nd\\nC\\nB\\n100\u00c2\u00ab\\n800*\\n1500-\\n2200*\\nC\\nD\\nF\\nG\\nA\\nB\\nD\\nE\\nF\\nG\\nB\\nC\\nD\\nE\\nF\\nG\\nB\\nG\\nA\\nB\\nc\\n\u00e2\u0080\u00a21\\n28-\\n56-\\n\u00e2\u0080\u00a257\\n84-\\nD\\nE\\nA\\nG\\nF\\nE\\nC\\nE\\nF\\nA\\nB\\n\u00e2\u0080\u00a229\\n\u00e2\u0080\u00a285\\n86\\nC\\nD\\nE\\nD\\nC\\nA\\nF\\nG\\nA\\nB\\nA\\nC\\nD\\nE\\nE\\n2\\n30\\n58\\nA\\nG\\nB\\nA\\nC\\nE\\nB\\nC\\nD\\nF\\n3\\n4*\\n31\\n59\\n87\\nB\\nD\\nC\\nD\\nD\\nE\\nE\\nF\\nG\\n32-\\n\u00e2\u0080\u00a233\\n60-\\n\u00e2\u0080\u00a261\\n88-\\nE\\nF\\nE\\nG\\nB\\nA\\nC\\nF\\nG\\nA\\n\u00e2\u0080\u00a25\\n6\\n7\\n\u00e2\u0080\u00a289\\nD\\nF\\nE\\nG\\nB\\nA\\nE\\nF\\nG\\nF\\nG\\nA\\nB\\nB\\nC\\n34\\n62\\n90\\nC\\nD\\nF\\nG\\nG\\nA\\nC\\nD\\n35\\n63\\n91\\nB\\nC\\nD\\nB\\nE\\nF\\nG\\nE\\nD\\nC\\nA\\nF\\nA\\nB\\nB\\nC\\nD\\nE\\nE\\n8-\\n36-\\n64-\\n92-\\nG\\nA\\nC\\nD\\nC\\nA\\nC\\nC\\nD\\nF\\nA\\n\u00e2\u0080\u00a29\\n\u00e2\u0080\u00a237\\n38\\n39\\n\u00e2\u0080\u00a265\\n\u00e2\u0080\u00a293\\nF\\nE\\nG\\nA\\nB\\nA\\nE\\nD~\\nC\\nA\\nG\\nF\\nE\\nC\\nB\\nD\\nE\\nF\\nG\\n10\\n11\\n66\\n94\\nF\\nG\\nB\\nD\\nE\\nF\\nG\\nA\\nB\\nD\\nA\\nB\\n67\\n95\\n96-\\nD\\nE\\nC\\nF\\nD\\nG\\nA\\nB\\nG\\nD\\nE\\nF\\nF\\nG\\nB\\nC\\n12-\\n40-\\n68-\\nB\\nE\\nF\\nE\\nD\\nE\\nG\\nA\\nC\\nC D\\n\u00e2\u0080\u00a213\\n\u00e2\u0080\u00a241\\n\u00e2\u0080\u00a269\\n\u00e2\u0080\u00a297\\n98\\nA\\nB\\nA\\nG\\nE\\nC\\nD\\nF\\nG\\nA\\nB\\nB\\nE\\nF\\nG\\nA\\n14\\n42\\n70\\nG\\nB\\nC\\nE\\nA\\nC\\nD\\nE\\nF\\nE\\nF\\nF\\nG\\nA\\n15\\n43\\n71\\n99\\nF\\nD\\nA\\nB\\nC\\nB\\nB\\nC\\nD\\n16-\\n44-\\n72-\\n\u00e2\u0080\u00a273\\nF\\nG\\nA\\nG\\nC\\nD\\nE\\nG\\nG\\nB\\nD\\n\u00e2\u0080\u00a217\\n18\\n19\\n\u00e2\u0080\u00a245\\nC\\nD\\nE\\nF\\nA\\nE\\nF\\nA\\nB\\nB\\nC\\nC\\n46\\n74\\nB\\nA\\nC\\nD\\nE\\nD\\nF\\nG\\nA\\nG\\nF\\nG\\nA\\nA\\nE\\nE\\nF\\n47\\n75\\n76-\\nB\\nC\\nE\\nF\\nG\\nB\\nC\\nD\\n20-\\n48-\\nF\\nG\\nA\\nG\\nB\\nC\\nD\\nC\\nE\\nD\\nA\\nB\\nd\\nE\\nF\\nG\\nB\\nC\\nE\\nD\\nF\\nE\\nF\\nA\\nG\\nB\\nC\\nD\\n\u00e2\u0080\u00a221\\n\u00e2\u0080\u00a249\\n\u00e2\u0080\u00a277\\n78\\n79\\nE\\nF\\nA\\nB\\nC\\nD\\nE\\nF\\nA\\nB\\nG\\nA\\n22\\n23\\n24-\\n50\\n51\\n52-\\n\u00e2\u0080\u00a253\\nD\\nC\\nA\\nE\\nD\\nF\\nE\\nC\\nB\\nA\\nG\\nG\\nA\\nB\\nG\\nB\\nG\\nF\\nE\\nI)\\nF\\nG\\nG\\nA\\nB\\nF\\nG\\nA\\nF\\nE\\nD\\nC\\nB\\nC\\n80-\\n\u00e2\u0080\u00a281\\nB\\nA\\nG\\nF\\nD\\nC\\nB\\nA\\nE\\nA\\nB\\nD\\nC\\nD\\nE\\nG\\n\u00e2\u0080\u00a225\\n26\\nG\\nD\\nC\\nE\\nF\\n54\\n82\\nF\\nC\\nB\\nC\\nD\\nE\\nF\\nQ\\nA\\n27\\n55\\n83\\nE", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0242.jp2"}, "241": {"fulltext": "TABLE I. THE CALEKDAK.\\n227\\nh\\nH\\nQ\\no\\nffl\\n3 J 1 fc*\\nrd\\nEh\\n1 93\\n1\\nGO\\nIS\\nEh\\nrd\\nS\\no3\\nGO\\n1 3\\nrd\\nEh\\n03\\nGO\\nd\\ngo\\no\\nEh\\nE 1 1\\no\\n3\\na|*\\n03 1 S3\\nGO 1 GO\\nO\\nEh\\nr0\\nEh\\no3\\nGO\\no\\n3\\nH\\nrd 1\\nEh 1 Eh\\no 1 o rd 1 C\\nS 1 Eh J i Eh J fe\\no3\\nGO\\nSeptember.\\nDecember.\\nCO\\ni ill\\nio 1 eo 1 t- 1 go 1 os\\n1 C\u00c2\u00bb 1 1 M 1\\nO\\nCO\\ni\\nGO 1 OS O 1 H 1 OJ\\nCO\\nCM\\nO\\nS S\\nco 1 io\\nCD\\nCO\\ntf iO\\nco\\nGO\\nOS\\n1\\nr-l\\ncm\\nFeb., L.Y.\\nAugust.\\no*\\nGO\\nO*\\nOS\\nCM\\nO TM\\nCO 1 CO\\no\\nO*\\ntH I O*\\nCM 1 cm\\nCO 1 o\\nco\\nCM\\nCO\\n1\u00e2\u0080\u00941\\ntH I IO\\nTH 1 tH\\nCD 1 J 1 GO\\nOS\\nc\u00c2\u00a9\\ni 1 GO\\n\u00c2\u00b0I2IS\\nCM\\ntH\\nH i CO\\ntH\\nm\\n1\\n\u00e2\u0096\u00ba-a\\nW 1 1 1 00 1 O\\n1 1 1 CQ 1\\no\\nCO\\n00\\ntH~\\nT-l\\nOS 1 O 1 tH I CM\\nH 1 1 1\\nCO\\ncm\\n^+1\\ncm\\n1 W 1 1 o\\nCD\\ni\\nW 1 \u00c2\u00abD 1 b\u00c2\u00bb\\nGO\\nos\\no\\ntH\\n1\\nTH\\nCM\\nCO\\nsi\\ngo\\nOi\\nOS\\nCM\\nO 1 TH\\nCO 1 CO\\nC3\\nCM 1 CO 1 Tt IO\\n1 w 1 1 w\\nCO\\nCM\\nCM\\ntH\\n3 1 S 1 1 s\\nOS\\no\\nCM\\n00 1 1 S 1 s\\nCM\\nCO\\nth (N CO\\ntH\\niO\\nco\\nJanuary, L. Y.\\nApril.\\nJuly.\\n0~l tH I\\nCO i CO 1\\nCO\\n05\\n1 o\\nCM 1 CM\\no\\ncm\\nCM\\nGO\\ncm\\no\\nCM\\nco\\ni 1 CO\\nT-t 1 T-t\\nOS\\ntH\\no\\nCM\\ncm\\nCM\\nCM\\nOS\\nO j H\\nCM\\nCO\\nTj\\nIO\\n05\\nCO\\nIO\\nCO\\ni\\nGO\\n1 TH\\nFebruary.\\nMarch.\\nNovember.\\n35\\nCM\\nGO\\nOS\\no\\nCO\\nS3 i\\nOS\\nO\\nCQ\\nCM\\nCM j CO 1 1 IO\\n03\\nCO\\ntH\\ntH\\n\u00c2\u00bbo\\nCD 1 I- 1 GO\\nH I H I H\\nIffl\\nto\\nt\\nCO\\nOS 1 O 1 T-l\\n1 rl 1 H\\ntH\\nCM CO\\nJanuary.\\nOctober.\\nOS\\no\\nCO\\nCO\\n1 1\\nCM\\nCM\\nCO\\nCM\\nCM\\ncm\\nO 1 i 1 oo\\n1 1\\n1\u00e2\u0080\u00941\\nco\\nT-l\\nGO\\nOS 1 1 T-l\\nH I W 1\\nGO\\nOS\\nO\\nI\u00e2\u0080\u0094I\\nN 1 CO tJI\\ncm\\nCO\\nia co t\\n1 B? rf\\nC5\\nP\\n1\\nCD\\nC3\\nCM\\nm\\nH\\nO\\ni\\nPh\\no\\nPQ\\nEh\\nW\\nW\\nEh\\nO\\nH\\nW\\nEh\\nfe\\nO\\nO\\n1\\n!?5\\nj\\nh4\\nPh\\nM\\nH\\nI\\nfa/3 isD\\nr3\\nH\\na\\n^3\\nS3\\nrd\\na\\nA\\n4)\\n-1-3\\ntj\\nh\\nS\\nCO\\n3\\nf\\nCO\\no\\nO\\nq\\nq\\n1 1\\n.3 S3\\na s\\nS Td\\nd rd\\ng\\n.a s\\no\\nI\\nrd\\no o\\n,3\\n.a 1\\nd\\nf\\nto\\n.2\\nd\\nrd\\nII\\na\\no\\nrd H3\\n21\\nEh\\nffi\\nO\\nrd\\nd\\nd\\nrd\\nrd\\nr=-\\ntH\\no3\\ne3\\nrd\\n+3\\nr^\\nc3\\n0-\\nr/)\\n-M\\no3\\nS3\\n03\\n1\u00e2\u0080\u00941\\nCD\\nd\\nd\\n.3\\nH\\n\u00e2\u0096\u00a0fi.\\nbD .03\\n8\\nd 5?\\nO rd\\nej\\nK\\nS o\\nA rS\\nEh\\n5\\nq\u00c2\u00b0\\n-d\\nd\\nd\\n0Q", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0243.jp2"}, "242": {"fulltext": "228\\nELEMENTS OF THE PLANETS.\\nTable II. Elements of the Planets.\\nI.\\nIT.\\nin.\\nIV.\\nV.\\nVI.\\nvn.\\nvin.\\nNAME.\\ng\\nRelative\\nSidereal\\nRevolution\\nSynodical\\nRevolut n\\nMean daily\\nHeliocen-\\ntric Long.\\nHeliocen-\\ntric Long.\\nMercury.\\n3\\nin days.\\nin days.\\nJan.1,1801.\\nJan.1,1885.\\n0.387098\\n87.969\\n115.877\\n4 5\\n11\\n32.6\\n213 20\\n82 24\\nVenus\\n9\\n0.723332\\n224.701\\n583.921\\n1 36\\n7.8\\n11 33\\n206 54\\nEarth\\n6\\n1.000000\\n365.256\\n59\\n8.3\\n100 39\\n100 18\\nMars\\n3\\n1.523691\\n686.980\\n779.936\\n31\\n26.7\\n64 23\\n296 45\\nJupiter.\\nn\\n5.202800\\n4332.554\\n398.884\\n4\\n59.3\\n112 15\\n147 00\\nSaturn\\nh\\n9.538800\\n10,759.106\\n378.092\\n2\\n0.6\\n135 20\\n81 28\\nUranus.\\nV\\n19.183380\\n30,686.246\\n369.656\\n42.4\\n177 48\\n179 52\\nNeptune.\\n5!\\n30.054370\\n60,228.072\\n367.485\\n21.7\\n227 18\\n52 13\\nMoon*\\nc\\n0.000259\\n27.321\\n29.530\\n13 10\\n36.6\\n118 17\\n105 13\\nIX.\\nX.\\nXI.\\nXH.\\nxni.\\nXTV.\\nXV.\\nXVI.\\nxvn.\\na\\n02\\nInclinat n\\nof Orbit.\\nJan.1,1801.\\nVaria-\\ntion in\\n100 yrs.\\nEccentri-\\ncity of\\nOrbit,\\nJan.1,1801.\\nVariation\\nin 100 yrs.\\nLong, of\\nA. Node\\nJan. 1,\\n1801.\\nMotion\\nwest.in\\n100 yrs.\\nLong, of\\nPerihel.\\nJan. 1,\\n1801.\\nMotion\\neast, in\\n100 yrs.\\nRotat n\\nin\\nhours.\\n11\\nR.V.\\n3\\n7 9\\n18\\n.205 515\\n.000 004\\n45 57\\n13 4\\n74 21\\n9 43\\n24.09?\\n3 23 28\\n\u00e2\u0080\u00945\\n.006 811\\n-.000 063\\n74 51\\n32 24\\n128 43\\n5 12\\n23.35?\\n8\\n.016 792\\n-.000 042\\n99 31\\n19 10\\n23.93\\nft\\n1 51 6\\n-0.2\\n.093 307\\n.000 090\\n48\\n41 26\\n332 23\\n26 13\\n24.62\\nu\\n1 18 51\\n-23\\n.048 162\\n.000 159\\n98 26\\n26 19\\n11 8\\n11 5\\n9.92\\nh\\n2 29 36\\n-15\\n.056 151\\n-.000 312\\n111 56\\n32 23\\n89 9\\n32 11\\n10.24\\nV\\n46 28\\n3\\n.046 611\\n-.000 025\\n72 59\\n59 55\\n169\\n3 56\\n9.50?\\n1\\n1 46 59\\n.008 719\\n130 6\\n46\\n5 8 40\\n.054 908\\n13 53\\n1934\u00c2\u00b0\\n266 10\\n4069\u00c2\u00b0\\n708.73\\nSun\\n608.\\nxvm.\\nXIX.\\nXX.\\nXXI.\\nxxn.\\nXXIH.\\nXXIV.\\nXXV.\\n.a\\nB\\nMean Di-\\nameter in\\nmiles.\\nMean\\nangular\\nDiam.\\nRelative\\nVolume.\\nRelative\\nMass.\\nRePtive\\nD nsity.\\nRel tive\\nGr vity.\\nSolar\\nLight\\nHeat.\\nVelocity\\nin Orbit\\nin miles\\nper sec.\\n11\\n2\\n2,992\\n7\\n0.054\\n0.065\\n1.21\\n0.46\\n6.67\\n29.55\\n7,660\\n17\\n0.880\\n0.769\\n0.85\\n0.82\\n1.91\\n21.61\\n5\\n7,918\\n1.000\\n1.000\\n1.00\\n1.00\\n1.00\\n18.38\\n4,211\\n9\\n0.248\\n0.111\\n0.73\\n0.39\\n.43\\n14.99\\nn\\n86,000\\n37\\n1350.\\n311.953\\n0.24\\n2.64\\n.037\\n8.06\\nh\\n70,500\\n16\\n689.\\n93.329\\n0.13\\n1.18\\n.011\\n5.95\\nw\\n31,700\\n4\\n75.\\n14.460\\n0.22\\n0.90\\n.003\\n4.20\\nf\\n34,500\\n3\\n102.\\n16.862\\n0.20\\n0.89\\n.001\\n3.36\\n2,161\\n1866\\n0.020\\n0.012\\n0.60\\n0.16\\n1.000\\n0.63\\nSun\\n860,000\\n1924\\n1295000.\\n326800.\\n0.25\\n27.71\\nMean geocentric values.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0244.jp2"}, "243": {"fulltext": "ELEMENTS OF THE SATELLITES.\\nfc^ J\\nTable III. Elements of the Satellites.\\nTHE MOON.\\nMean distance from the earth, (miles)\\nMean sidereal revolution, (days)\\nMean synodical revolution, (days)\\nMean revolution of nodes, (days)\\nMean revolution of apsides (days)\\nMean inclination of orbit to ecliptic.\\nEccentricity of orbit\\nMean diameter of moon, (miles)\\nDiameter, (earth s 1)\\nSurface, (earth s 1)\\nVolume, (earth s 1)\\nDensity, (earth s 1)\\nMass, (earth s 1)\\nGravity, (earth s 1)\\n238.820\\n27.32166\\n29.53058\\n6793.39108\\n3232.57534\\n5\u00c2\u00b0 8 44\\n0.054908\\n2161\\n0.2730\\n\u00e2\u0096\u00a0f 3 or 0.0745\\nis or 0.0203\\nor 0.6052\\ni-:* or 0.0123\\nor 0.165\\nSatellites\\nof\\nJupiter.\\nSidereal\\nRevolutions.\\nh. m. s.\\n18 27 34\\n14 36\\n42 33\\n13\\n3\\n16 16 31 50\\nDistance in\\nequatorial ra-\\ndii of Planet.\\n6.04853\\n9.62347\\n15.35024\\n26.99835\\nDistance\\nin\\nmiles.\\n260000\\n414000\\n661000\\n1162000\\nDiameter\\nin\\nmiles.\\n2365\\n2123\\n3471\\n2966\\nSatellites\\nof\\nSaturn.\\n22 37 23\\n8 53 7\\n21 18 26\\n17 41 9\\n12 25 11\\n15 22 41\\n21\\n79\\n25\\n7 41\\n53 40\\n3.3607\\n4.3125\\n5.3396\\n6.8398\\n9.5528\\n22.1450\\n26.7834\\n64.3590\\n122000\\n157000\\n194000\\n248000\\n347000\\n804000\\n973000\\n2338000\\n1163\\n2908\\n1745\\nSatellites\\nof\\nUranus.\\n2 12 29 21\\n4 3 28 8\\n8 16 56 31\\n13 11 7 13\\n7.40\\n10.31\\n16.92\\n22.56\\n123000\\n172000\\n282000\\n376000\\nSatellite of\\nNeptune.\\n5 21 2 43\\n12.\\n222000", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0245.jp2"}, "244": {"fulltext": "230\\nMEAN PLACES OF PRINCIPAL STAES.\\nTable IV*. Mean Places of Principal Stars 1885, Jan. 0.\\nNo.\\nSTAR S NAME.\\nMag.\\n9\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n21\\n25\\n2G\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n4(3\\n47\\n48\\na Andromedae (Alplierat),\\n7 Pegasi (Algenib)\\nRight Ascen-\\nsion.\\n2,0\\n2.7\\nNebula in Andromeda.\\nj3 Ceti\\nS3 Andromedae\\na Ursa? Minoris (Polaris).\\na Eridani (Acliernar).\\na Arietis\\nCluster in Perseus.\\no Ceti (Mira)\\na Ceti\\n(3 Persei (Algol)\\na Persei\\n7] Tauri (Pleiades)\\ny Tauri (Hyades)\\na Tauri (Aldebaran)\\na Auriga? (Capella)\\n(3 Orionis (Rigel)\\n6 Orionis\\nNebula in Orion\\na Orionis\\na Argus (Canopus)\\na Canis Maj. (Sirius).\\na Geminorum (Castor).\\na Canis Min. (Procyon).\\n;3 Geminorum (Pollux)\\nCluster, Prsesepe\\na Hydra?\\na Leonis (Pegulus)\\n7] Argus (variable)\\na Ursa? Maj oris (Dublie)\\na Crucis\\na Virginis (Spica)\\na Bootis (Arcturus)\\ni3 Ursa? Minoris\\na Corona? Borealis\\na Scorpii (Antares)\\na Ophiuclii\\na Lyra? (Vega)\\nAnnular Nebula, Lyra\\na Aquila? (Altai r)\\nDumb-bell Nebula\\na Delphini\\na Cvgni\\n12 tear Catalogue, 1879.\\n61 Cygni\\na Piscis Aus.(Fomalhaut)\\na Pegasi (Markab)\\n2,\\n2.3\\n2.\\n1.\\n2,\\nVar.\\n2.3\\nVar.\\n2.\\n3*.\\n4.\\n1.\\n1.\\n1.\\nVar.\\nVar.\\n1.\\n1.\\n1.7\\n1.\\n1.3\\n2.\\n13\\n1-6\\n2.\\n1.\\n1.\\n1.\\n2.\\n2.\\n1.3\\n2.\\n1.\\nl.3\\n3.7\\n1.7\\n6.\\n5.\\n1.3\\n2.\\nH. II. S.\\n2 26\\n7 18\\n35\\n37 49\\n1 3 17\\n16 37\\n33 25\\n41\\n10\\n13\\n56 16\\n41\\n3 16 7\\n3 40 38\\n4 13 15\\n29 19\\n8 11\\n9\\n26 8\\n29\\n48 56\\n21 24\\n6 40 4\\n7 27 15\\n7 33 16\\n7 38 16\\n8 20\\n9 21 56\\n10 2 14\\n10 40 36\\n10 56 37\\n12 20 11\\n13 19 8\\n14 10 25\\n14 51 3\\n15 29 49\\n16 22 21\\n17 29 36\\n18 33 3\\n18 49\\n19 45 10\\n19 54\\n20 34 18\\n20 37 31\\n20 52 46\\n21 1 45\\n22 51 17\\n22 59 2\\nAnnual\\nVar.\\n3.09\\n3.08\\n3.01\\n3.34\\nf 22.46\\n2.23\\n3.37\\nNorth Polar\\nDistance.\\n3.12\\n3.88\\n4.25\\n3.55\\n3.40\\n3.43\\n4.42\\n2.88\\n3.06\\n3.24\\n1.33\\n2.64\\n3.84\\n3.14\\n3.67\\n2.94\\n3.20\\n2.31\\n3.75\\n3.27\\n3.15\\n2.73\\n\u00e2\u0080\u00940.23\\n2.54\\n3.67\\n2.78\\n2.03\\n2.92\\n2.79\\n2.04\\n-2.53\\n2.68\\n3.32\\n2.98\\n61 32 40\\n75 27 21\\n49 23\\n108 37 5\\n64 59 22\\n1 18 16\\n147 49 16\\n67 4 55\\n33\\n93 32\\n86 21 43\\n49 29 18\\n40 32 57\\n66 15 6\\n74 39 3\\n73 43 22\\n44 7 14\\n98 20\\n90 23\\n95 29\\n82 36\\n142 37\\n106 33 33\\n57 51 37\\n84 28 52\\n61 41 50\\n69 50\\n98 9 38\\n77 28 16\\n149 4 48\\n27 37 42\\n152 27 42\\n100 33 38\\n70 13 7\\n15 22 28\\n62 53 52\\n116 10 32\\n77 21 20\\n51 19 22\\n57 7\\n81 26 5\\n67 36\\n74 29 36\\n45 7 49\\n9 52 47\\n51 48 56\\n120 13 53\\n75 24 48\\nAnnual\\nVar.\\n-19.89\\n-20.02\\n-19.80\\n-19.17\\n-18.94\\n-18.36\\n-17.18\\n-14.32\\n-14.13\\n13.11\\n-11.40\\n-8.98\\n-7.53\\n-4.06\\n-4.42\\n-2.94\\n-6.97\\n1.88\\n4.69\\n7.53\\n8.97\\n8.40\\n15.44\\n17.46\\n18.86\\n19.35\\n20.01\\n18.91\\n18.89\\n14.72\\n12.32\\n8.32\\n2.89\\n-3.15\\n9.25\\n-12.50\\n-12.71\\n-13.70\\n-17.52\\n-18.99\\n-19.30", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0246.jp2"}, "245": {"fulltext": "PLANETOIDS.\\n231\\nTable V. The Planetoids.\\nNo.\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\nNAME.\\nCeres\\nPallas\\nJuno\\nVesta\\nAstrsea\\nHebe\\nIris\\nFlora\\nMetis\\nHygeia\\nParthenope.\\nVictoria\\nEgeria\\nIrene\\nEunomia\\nPsyche\\nThetis\\nMelpomene.\\nFortuna\\nMassalia\\nLutetia\\nCalliope\\nThalia\\nThemis\\nPhocea\\nProserpina\\nEuterpe\\nBellona\\nAmphitrite..\\nUrania\\nEuphrosyne\\nPomona\\nPolyhymnia..\\nCirce\\nLeucothea\\nAtalanta\\nFides\\nLeda\\nLaetitia\\nHarmonia\\nDaphne\\nIsis\\nAriadne\\nNysa\\nEugenia\\nHestia\\nAglaia\\nDoris\\nPales\\nVirginia\\nMean daily\\nmotion\\nmean\\ndist nce\\n770.8332\\n769.7324\\n812.9059\\n976.7787\\n857.9269\\n939.3696\\n962.5806\\n1086.3309\\n962.3390\\n637.1610\\n923.6604i\\n994.8347J\\n857.9451!\\n852.4385;\\n825.4550\\n710.9629J\\n911.3975!\\n1020.1198\\n9296590;\\n949.0444\\n933.5544\\n715.6529!\\n833.0737\\n640.1662\\n954.6367\\n819.6847:\\n9866944\\n766.0691\\n869.0352\\n975.1642\\n635.1686\\n852.5880;\\n732.0291\\n806.1634\\n685.1834\\n780.0110\\n826.0660\\n782.5641\\n769.9967\\n1039.3353\\n770.1514\\n930.9057\\n1084.1384\\n941.3988\\n789.0034\\n883.9660\\n725.9827\\n646.1069\\n653.3922\\n822.4986\\n.442031\\n.442444\\n.426644\\n.373474\\n.411037\\n.384780\\n.377713\\n.342696\\n.377786\\n.497171\\n.389663\\n.368139\\n.411031\\n.412896\\n.422209\\n.465440\\n.393532\\n.360903\\n.387788\\n.381813\\n.386578\\n.463536\\n.419548\\n,495809\\n380112\\n424240\\n,370549\\n,443825\\n.402312\\n,373952\\n498079\\n412845\\n,456985\\n,429055\\n476133\\n438604\\n,421994\\n437657\\n.442345\\n,355500\\n.442287\\n.387401\\n.343281\\n384155\\n.435285\\n.402381\\n.493134\\n,423247\\nNo.\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n61\\n62\\n63\\n64\\n65\\n66\\n67\\n70\\n71\\n2\\n73\\n74\\n75\\n76\\n77\\n78\\n79\\n80\\n81\\n82\\n83\\n84\\n85\\n86\\n87\\n88\\n89\\n90\\n91\\n92\\n93\\n94\\n95\\n96\\n97\\n98\\n99\\n100\\nNAME.\\nNemausa\\nEuropa\\nCalypso\\nAlexandra.\\nPandora\\nMelete\\nMnemosyne.\\nConcordia\\nElpis\\nEcho\\nDanae\\nErato\\nAusonia.\\nAngelina.\\nCybele\\nMaia\\nAsia\\nLeto\\nHesperia\\nPanopea.\\nNiobe\\nFeronia\\nClytia\\nGalatea\\nEurydice\\nFreia\\nFrigga\\nDiana.\\nEurynome.\\nSappho\\nTerpsichore.\\nAlcmene.\\nBeatrice\\nClio\\nIo\\nSemele\\nSylvia\\nThisbe\\nJulia\\nAntiope\\niEgina\\nUndina\\nMinerva\\nAurora\\nArethusa.\\nMgle\\nClotho\\nIanthe\\nDice\\nHecate\\nMean daily-\\nmotion\\n975.6485\\n651.2204\\n837.8551\\n794.1220\\n774.3196\\n847.7131\\n635.2707\\n799.5964\\n793.9788\\n958.1112\\n687 6656\\n642.5658\\n956.1364\\n806.8077\\n558.3014\\n824.7087\\n941.5410\\n765.2766\\n689.8760\\n839.0994\\n774.6491\\n1040.1026\\n815.4003\\n765.7921\\n813.0315\\n5609129\\n814.1350\\n836.5607\\n928.8736\\n1020 0052\\n736.1744\\n772.7477\\n936.6007\\n977.8108\\n821. 4080\\n649.2352\\n543.7017!\\n770.2917J\\n870.8412\\n636.1509J\\n851.2296 1\\n622.3687J\\n775.6388\\n630.8636^\\n659.2278\\n666.2189\\n813.1887\\n805.3700\\n758.6620\\n652.0664\\nLog. of\\nmean\\ndist nce.\\n.373809\\n.490852\\n.417891\\n.433412\\n.440724\\n.414505\\n.498032\\n.431423\\n.433465\\n.379060\\n.475086\\n.494726\\n.379658\\n.428824\\n.535425\\n.422471\\n.384111\\n.444125\\n.474157\\n.417462\\n.440601\\n.355287\\n.425757\\n.443930\\n.426599\\n.534074\\n.426206\\n.418339\\n.388033\\n.360936\\n.455350\\n.441312\\n.385635\\n.373167\\n.423632\\n.491736\\n.543097\\n.442234\\n.406712\\n.497631\\n.413306\\n.503972\\n.440231\\n.500047\\n.487314\\n.484260\\n.426543\\n.429341\\n.446640\\n.490476", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0247.jp2"}, "246": {"fulltext": "232\\nPLANETOIDS.\\nTable V. (continued). The Planetoids.\\nNo.\\nNAME.\\n101\\n102\\n103\\n104\\n105 I\\n106!\\n107\\n108!\\n109\\n110 J\\n1111\\n112 j\\n113 j\\n114 i\\n115\\n116\\n117\\n118 1\\n119 i\\n120\\n121\\n122!\\n123 1\\n124 I\\n125 I\\n126 I\\n127\\n128\\n129!\\n130!\\n131 i\\n132 i\\n133 I\\n134 i\\n135 i\\n136 1\\n137 1\\n138\\n139,\\n140!\\n141\\n142\\n143\\n144\\n145\\n146\\n147\\n148\\n149\\n150\\nHelena\\nMiriam\\nHera\\nClymene\\nArtemis\\nDione\\nCamilla\\nHecuba\\nFelicitas.\\nLydia\\nAte\\nlpkigenia..\\nAmalthea.\\nCassandra\\nThyra\\nSirona\\nLomia\\nPeith\\nAlthea\\nLachesis\\nHermone.\\nGerda\\nBrunhild\\nAlcestis\\nLiberatrix.\\nVelleda\\nJohanna\\nNemesis\\nAntigone\\nElectra\\nVala\\n^Ithra\\nCyrene\\nSophvosyne.\\nHertha\\nAustria\\nMelibcea\\nTolosa\\nJuewa\\nSiwa\\nLumen\\nPolana\\nAdria\\nVibilia\\nAdeona\\nLucina\\nProtogeneia.\\nGallia\\nMedusa.\\nNuwa\\nMean daily\\nmotion\\n853.6127\\n816.7370\\n799.0675\\n634.4466\\n971.0795\\n629.5650\\n545.4463\\n616.3698\\n802.0510\\n785.1449\\n849.9278\\n934.4391\\n968.1836\\n810.8275\\n965.9609\\n771.4040\\n686.0326\\n931.6917\\n855.5046\\n644.3548\\n551.5624\\n615.5690\\n801.8499\\n832.0020\\n780.7231\\n930.9792\\n775.3364\\n777.4964\\n727.2294\\n642.9388\\n942.2999\\n846.3646\\n663.5850\\n8645740\\n638.1149\\n1026.3921\\n641.8566\\n926.0192\\n765.7567\\n789.1234\\n814.5161\\n942.8756\\n773.0080\\n821.2984 1\\n815.4470!\\n789.8850\\n638.6654!\\n769.5145\\n1139.1950\\n689.3407,\\nLog. of\\nmean No.\\ndist nce.\\n412497\\n.425283\\n.431615\\n.498408\\n.375168\\n.500644\\n.542170\\n.506777\\n.430555\\n.436704\\n.413749\\n.386304\\n.376032\\n.427385\\n.376698\\n.441816\\n.475775\\n.387156\\n.411856\\n.493921\\n.538941\\n.507153\\n.430609\\n.419921\\n.438339\\n.387377!\\n.440344\\n.439538!\\n458890\\n.494558;\\n.3838781\\n.414966\\n.485406\\n.408803\\n.385167\\n.359129\\n.495046\\n.388924 i\\n.443944!\\n.436343\\n.426071\\n.383701!\\n.441216\\n.423670\\n.425740\\n.434962\\n.496488\\n.442526\\n.328939\\n.474381\\n151\\n152\\n153\\n154\\n155\\n156\\n157\\n158\\n159\\n160\\n161\\n162\\n163\\n164\\n165\\n166\\n167\\n168\\n169\\n170\\n171\\n172\\n173\\n174\\n175\\n176\\n177\\n178\\n179\\n180\\n181\\n182\\n183\\n184\\n185\\n186\\n187\\n188\\n189\\n190\\n191\\n192\\n193\\n194\\n195\\n196\\n197\\n198\\n199\\n200\\nNAME.\\nAbundantia.\\nAtala\\nHilda\\nBertha\\nScylla\\nXantippe.\\nDejanira\\nCoronis\\niEmilia\\nUna\\nAthor\\nLaurentia\\nErigone\\nEva\\nLoreley\\nRhodope\\nUrda\\nSibylla\\nZelia\\nMyrrha\\nOphelia\\nBaucis\\nmo\\nPhsedra\\nAndromache.\\nIdunna\\nIrma\\nBelisaria\\nClytemnestra.\\nGarumna.\\nEucharis\\nElsbeth\\nIstria\\nDeipeia\\nEunike\\nCeluta\\nLamberta.\\nMenippe\\nPhthia\\nIsmene\\nKolga\\nNausika\\nAmbrosia\\nProene\\nEurycleia\\nPhilomela.\\nArete\\nAmpella\\nByblis\\nDynamene.\\nMean daily\\nmotion\\nLog. of\\nmean\\ndistance.\\n850.7264\\n639.0187\\n451.5802\\n622.3629\\n713.7875 1\\n670.2300\\n854.8040\\n730.5502\\n647.7291!\\n787.1915\\n970.0005\\n673.1350\\n981.1480!\\n829.6880\\n642.0938J\\n803.0021\\n614.4750.\\n570.0346\\n978.5025\\n868.8279\\n635.5487\\n966.3982\\n780.2369\\n732.1255\\n541.0099\\n622.6360\\n774.6923\\n920.0970\\n692,2257\\n787.4120\\n644.0102\\n944.0487\\n756.3767\\n623.2669\\n7830772!\\n977. 1085\\n782.3914:\\n748.8250\\n924.9882\\n454.0674\\n722.4983\\n952.5933\\n858.2960^\\n836.9383\\n728.9100\\n653.8370!\\n780.9746\\n922.9325\\n618.17301\\n783.26091\\n.413478\\n.496329\\n.596847\\n.503975\\n.464292\\n.482522\\n.412092\\n.457571\\n.492411\\n.435951\\n.375489\\n.481270\\n.372181\\n.420728\\n.494938\\n.430193\\n!.507668\\n.529402\\n.372963\\n.407382\\n.497905\\n.376567\\n.438520\\n.456947\\n.544534\\n.503848\\n.440585\\n.390782\\n.473172\\n.435870\\n.494075\\n.383341\\n.447526\\n.503555\\n.437468\\n.373376\\n.437722\\n.450417\\n.389247\\n.595257\\n.460780\\n.380673\\n.410913\\n.418209\\n.458222\\n.489692\\n.438246\\n.389894\\n.505931\\n.437400", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0248.jp2"}, "247": {"fulltext": "PLANETOIDS.\\n233\\nTable V. (continued). The Planetoids.\\nNo.\\nNAME.\\n201\\n202\\n203\\n204\\n205\\n206\\n207\\n208\\n209\\n210\\n211\\n212\\n213\\n214\\n215\\n216\\n217\\nPenelope\\nChryseis.\\nPompeia.\\nCallisto\\nMartha\\nHersilia\\nHedda.\\nLacrimosa.\\nDido\\nIsabella...\\nIsolda\\nMedea.\\nLilaea\\nAschera.\\n(Enone\\nCleopatra.\\nEudora\\nMean daily\\nmotion\\n809.9320\\n655.0080\\n782.7813\\n812.0185\\n766.6919\\n1027.3643\\n729.1020\\n637.0860\\n780.0227\\n667.2952\\n644.9370\\n779.8090\\n840.9460\\n770.4950\\n759.6820\\n665.7647\\nLog. of\\nmean\\ndist nce.\\n.427706\\n.489173\\n.437577\\n.426960\\n.443590\\n,358855\\n.458146\\n497206\\n,438599\\n,483792\\n,493660\\n438679\\n416826\\n,442158\\n446250\\n,484457\\nNo.\\n218\\n219\\n220\\n221\\n222\\n223\\n224\\n225\\n226\\n227\\n228\\n229\\n330\\n231\\n232\\n233\\nNAME.\\nBianca\\nThusnelda.\\n(Mar. 19, 1881\\n(Jan. 18, 1882\\nPhilosophia.\\nAthamantis.\\n(Sept, 10, 1882\\nRussia\\n(May 11, 1883\\nMean daily\\nmotion\\n817.2760\\n982.3480\\n974.5910\\n678.2950\\n645.2880\\n650.1600\\n826.1800\\n568.9810\\n792.4160\\n626.1270\\n1084.5100\\n567.8920\\n963.8230\\n701.3150\\n870.2300\\nLog. of\\nmean\\ndist nce.\\n.425090\\n.371828\\n.374123\\n.479058\\n.493502\\n.491324\\n.421954\\n.529939\\n.434036\\n.502229\\n,343182\\n.530494\\n,37734a\\n406915", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0249.jp2"}, "248": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0250.jp2"}, "249": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0251.jp2"}, "250": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0252.jp2"}, "251": {"fulltext": "PLATE II\\nCOMET OF 1858,-NKBULi:.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0255.jp2"}, "252": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0256.jp2"}, "253": {"fulltext": "PLATE 111.\\nPART OF GALAXY.-DOUBLE STARS\\nI. Castor. 2. y Leonis.\\n3. 39 Drac.\\n4. A Oph. 5. 11 Monoc.\\n6. Cancri\\nHIB\\nS\\nB\\nH\\nRevolutions of y Virginia.\\n1837. 1838. 1839. 1840. 1845. 1850. 1860. Orbit", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0259.jp2"}, "254": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0260.jp2"}, "255": {"fulltext": "PLATE IV\\nCLUSTERS.-NEBULH.", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0263.jp2"}, "256": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0264.jp2"}, "257": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0265.jp2"}, "258": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0266.jp2"}, "259": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0267.jp2"}, "260": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0268.jp2"}, "261": {"fulltext": "", "height": "4401", "width": "2546", "jp2-path": "introductiont00olms_0269.jp2"}, "262": {"fulltext": "", "height": "4496", "width": "2664", "jp2-path": "introductiont00olms_0270.jp2"}}