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THE ELEMENTS OF 
 ASTRONOMY 
 
THE 
 
 Elements of Astronomy 
 
 PRINCIPALLY ON THE MECHANICAL SIDE 
 
 INTENDED FOR 
 
 ENGIXEERIXG STUDENTS 
 
 BY fr -■; 
 
 N. F. DUPUIS, M.A., LL.D., F.R.S.C. 
 
 R. UGLOW & COMPANY 
 
 Kingston, Ont. 
 
 1910 
 

 Entered according to Act of the Parliament of Canada, in the year 
 
 nineteen hundred and ten, by R. UGLOW & COMPAXV, 
 
 at the Department of Agriculture. 
 
 Printed and bound at The Jackson Press, Kingston. 
 
PREFACE. 
 
 This book is the outcome of a course of lectures delivered 
 for a number of years to Engineering students in the first 
 year of their course. It deals principally with the mechanical 
 side of astronomy, as that is the side, in the opinion of the 
 author, most cognate to engineering education. As a con- 
 sequence, the hypothetical side of astronomy, embracing 
 theories in regard to stars, nebulae, comets, etc., has not been 
 given the place of prominence, but has been assigned to the 
 latter pages of the work, where it is dealt with as fully as 
 circumstances would permit. 
 
 A limited amount of mathematical work appears in the 
 book, but it is all of the simplest kind, involving only elemen- 
 tary arithmetic, algebra and geometry. 
 
 N. F. D. 
 Kingston, Nov. 1st, 1910. 
 
ERRATA. 
 Page 172, fourth line from top, for "7" read 3>2. 
 Page 187, third line from bottom, for distant read 
 
 distinct. 
 
ASTRONOMY. 
 
 Astronomy ranks arnongst the oldest of the sciences. It is 
 older than any fixed system of Theology, and coeval with 
 religion in its origin. The earliest religious worship was 
 more or less immediately concerned with legends and stories 
 and speculations upon the origin and purpose of the universe, 
 and upon the natures and functions of the sun, moon, and 
 stars. And some echoes of the music of that ancient wor- 
 ship have come down, through all the intervening ages, to the 
 present time. 
 
 The Astronomic field is unbounded, reaching to the utmost 
 limits of vision, and vision enhanced by the most powerful 
 telescopes. Astronomic phenomena are silent and yet grand 
 and impressive. The roseate hue of the morning, the daily 
 rising and setting of the glorious light-giving and life-giving 
 sun, the monthly waxing and waning of the moon, the ever- 
 recurring round of the bountiful and changing year, the 
 nightly pageant of the stars have been things of wonder and 
 admiration in all ages, and the interest in them is not yet and 
 never will be abated. 
 
 The progress of astronomy in modern times has had a 
 most important effect upon ancient notions of things in gen- 
 eral and upon early and mediaeval theological dogma. For 
 this progress has shown that this earth is not a plane, that 
 it is not fixed in space, and that it is not the centre of the 
 universe or even of the solar system, as it was formerly 
 believed to be. And thus the study of astronomy has freed 
 mankind from many a mistaken notion in regard to the na- 
 ture of the universe and the earth's importance in it, as well 
 as from many superstitions and pseudo-theological ideas 
 which, although long held as religious dogmas, were not 
 reasonable, and in some cases not conceivable. 
 
 But the universe is very reticent and reveals little to us 
 spontaneously. A cursory view may give us some ideas, but 
 often these are apt to be more or less false. For in the sub- 
 
2 ASTRONOMY. 
 
 ject of astronomy especially are first appearances deceptive. 
 To arrive at truthful conclusions requires much sifting of evi- 
 dence, together with close observation and logical reasoning. 
 The earth upon which we are compelled to live bulks so 
 large in comparison with every other thing in sight that we 
 are naturally inclined to look upon it as the specially im- 
 IKDrtant object in the universe. In one sense, as our home 
 and the locality where our lives are lived, our work is done, 
 and our observations are made, it is. But to an eye that 
 could look at the whole from a very far-off point of view 
 and see things in their proper perspective, the earth would 
 become a very insignificant body in comparison with my- 
 riads of others which dot the infinite spaces of the universe. 
 
 THE STARS. 
 
 No person with a due sense of beauty can look upward on 
 a clear and moonless night without being ijnpressed with the 
 glory and the beauty of the stars. They appear of all sizes, 
 from those barely visible to the eye to those like Sirius which 
 seem to rejoice in their brilliancy, and their arrangement 
 over the visible heavens appears to be devoid of all system. 
 
 But the stars are to us not only beautiful, they are useful 
 as well. They form the landmarlcs on the celestial vault, the 
 figures on the dial of the universe, and without their presence 
 the study of exact astronomy would scarcely be possible. It 
 is necessary, then, that at the very beginning of the subject 
 we learn something about the stars. 
 
 A very little imagination will enable a person to arrange 
 some of the stars into something like natural groups, and 
 some astronomers of the past, with very active and lively 
 imaginations, so arranged all the stars, naming the groups 
 after animals, or persons, or objects which they were thought 
 to resemble in outline, or people or things which they de- 
 sired to honor, or possibly in some cases from mere fanciful 
 ideas. Thus we have such groups or constellations as Ursa 
 Major (the great bear), Orion (the name of a fabled hunter), 
 Canis Major (the big dog), Aquila (the eagle), Perseus (the 
 
THE STARS. 
 
 name of an ancient hero), Scorpio (the scorpion), etc. Each 
 such group is called a constellation. 
 
 The accompanying figure gives the principal stars and their 
 arrangement in a few of the more prominent of the groups. 
 
 ■ ■ • * 
 
 ■•.'■*. 
 
 ■■ « 
 
 
 urea major 
 
 /Cassiopoeo. 
 
 On on 
 
 - 
 
 * 
 
 • * 
 
 • 
 < 
 
 * • . ' 
 
 
 
 ^, • 
 
 « 
 
 - 
 
 * 
 
 • 
 
 • 
 
 Canis major 
 
 Tau.ru.s 
 
 Leo 
 
 Fig. 1. 
 
 This way of grouping the stars is unscientific, and upon 
 the whole somewhat silly, especially in regard to nomencla- 
 ture. But, originating in very early times, it has been so long 
 in use, and the names of the constellations and even of some 
 of the principal stars, have become so well established in 
 astronomical usage, that it would now appear as a sort of 
 sacrilege to abandon them. Thus Orion and Arc turns, the 
 name of a well-known constellation and the name of a bright 
 star, are mentioned in the book of Job, and the whole lot of 
 them are too intimately woven into the history of astronomy 
 to be now discarded. 
 
 The number of stars visible to the unaided eye is very 
 deceptive. To the superficial observer this number appears 
 to run far up into the thousands, but an actual count will 
 show that a normal eye cannot see more than from 1,000 to 
 1,500 at any one time. And as we can see only one-half of 
 
ASTRONOMY. 
 
 the whole heavens at once, the total number of stars visible 
 in both hemispheres will vary from 2,000 to 3,000, depending 
 on the quality of the observer's eye. Under even moderate 
 powers of the telescope this number becomes wonderfully 
 increased, and under high powers the celestial vault appears 
 quite crowded with stars. 
 
 By the application of photography things are carried still 
 farther, for it is possible to photograph objects which are 
 quite invisible to the eye, and it has been estimated that up- 
 wards of a hundred million stars may be made to give a 
 record of themselves by means of the highly sensitized photo- 
 graphic plate used in conjunction with the telescope. And 
 most of the important work being done in stellar astronomy 
 at the present time is carried on by means of the telescope, 
 the photographic plate and the spectroscope. 
 
 Fig. 2. 
 
 The stars are variously distributed through the depths of 
 space as well as through its breadth, some of them being 
 
THE STARS. 5 
 
 hundreds, and possibly thousands of times as distant as 
 others ; but to us they all appear to lie upon the surface of a 
 great sphere having the earth as its centre. This apparent 
 sphere is called the sphere of the heavens, or the celestial 
 sphere, as distinguished from the earth itself virhich is called 
 the terrestrial sf)here. 
 
 For all practical purposes the sphere of the heavens may 
 be taken to be infinitely distant, and two lines from any tvi^o 
 points on the earth to the same star are practically parallel. 
 
 One prominent thing in regard to the stars must be noted, 
 that is their relative fixity, on account of which they have 
 received the name of fixed stars. 
 
 However often the stars are observed, whether at intervals 
 of a year, or of ten years, they appear to hold almost abso- 
 lutely the same relative positions in the heavens. In fact, the 
 great constellations are practically the same to us as they 
 were to the ancient Babylonians 5,000 years ago. This does 
 not mean that the stars are in any way attached to one an- 
 other, or that they do not partake of individual and inde- 
 pendent movement. It means merely that the movements of 
 the stars, relatively to one another, are so minute as seen 
 from our distance, that whole ages must pass away before 
 their displacement becomes sensible to a superficial observer. 
 These displacements, however, although small, when consid- 
 ered from year to year, are accumulative and have to be re- 
 corded and accounted for by the professional astronomer. 
 
 Practically then we may say that the stars are fixed in the 
 heavens, or in relation to one another without introducing 
 any serious errors into any results which may appear in this 
 work, and it is with reference to the stars as a whole that 
 direction in the universe is to be fixed. 
 
 THE EARTH. 
 
 The astronomical symbol for the earth is ffi. 
 The first impression formed in looking around over the 
 country is that the earth is an extended plane broken by 
 
6 ASTRONOMY. 
 
 hill and valley. And this was pretty much the view held 
 by all primitive people who had departed from savagery 
 sufficiently far to notice things, for it would not be safe to 
 say what views a savage may hold. 
 
 As there appear to be some primitive people yet, even 
 amongst civilized communities, it may be well to show why 
 the astronomer believes that the earth, broadly speaking, is 
 not a plane either extended or limited, but that it has ap- 
 proximately the form of a sphere. 
 
 (a) If the earth is a plane it cannot be indefinitely ex- 
 tended. For the sun, moon, and stars pass below it in the 
 western and rise from below it in the eastern part of the 
 heavens every twenty- four hours ; and no intelligent person 
 is likely to contend that the sun which sets in the evening is 
 not the same sun as that which rises the next morning, or 
 that the moon and stars are renewed daily. 
 
 And if the plane is limited, travellers going far enough 
 east or west should come to its border or edge, a sort of 
 jumping-off place which forbids any further progress in that 
 direction. On the contrary, such travellers, after a time, 
 invariably return to their starting point, and in a direction 
 which plainly shows that they have gone around the world. 
 
 (b) On an extended plane high mountains such as the 
 Andes or the Rockies should be visible for at least a thousand 
 miles. But such is not the case. The highest mountain in 
 the world. Mount Everest, cannot be seen at a greater dis- 
 tance than about 200 miles, and then it is only the top that 
 appears above the distant scene. 
 
 That the absorptive effects of the atmosphere upon the 
 light coming from distant objects is an argument for the non- 
 appearance of distant mountains, is not tenable. For it fails 
 to explain why the tops only of such mountains are visible 
 while their sides are concealed ; besides, the moon and bright 
 stars are much farther away than any mountain, and yet they 
 can be seen when quite close to the horizon, if clouds do not 
 intervene. 
 
 (c) In the surface of still water we have a something 
 which expresses what may be called the average form of the 
 
FORM OF THE EARTH. 
 
 earth's surface freed from its elevations and depressions and 
 all its irregularities. 
 
 When we stand upon the shore of the ocean, or of some 
 great lake like Ontario, we see at some distance a line where 
 the sky and the water appear to meet. This line is the offing, 
 and it marks the extreme distance at which the surface of 
 the water is visible. 
 
 If a large steamer is going out, we notice that it appears 
 to grow smaller and to rise until the ofHng is reached, after 
 which, while still decreasing in size, it appears to sink behind 
 the intervening water, and we may see the smoke from the 
 funnel for' some time after the vessel has completely disap- 
 peared, just as we may see the smoke from the chimney of 
 a house when the house itself is hidden behind a hill. 
 
 Fig. 3. 
 
 {d) When we are upon the open sea, out of sight of land, 
 the sea-offing extends completely around us so as to form a 
 circle with ourselves at the centre. And as we sail onwards 
 from day to day the offing, although travelling forward's with 
 the ship, remains circular. And this holds true for every 
 ocean in the world. 
 
 But a body which always, and from all points of view, 
 presents a circular outline must be a sphere. And we con- 
 clude that the surface of the ocean is, approximately at least, 
 of a spherical form. 
 
 {e) Some interesting problems in engineering arise out of 
 this curvature of the surface of a body of water, and these 
 problems, in themselves, bear evidence to the earth's rotun- 
 dity. Thus a " level line " as determined by the engineer's 
 
8 ASTRONOMY. 
 
 level is a tangent to the earth's surface at the point of obser- 
 vation, and if the earth were a plane this line would coincide 
 with a water surface for any distance. But if such a line be 
 sighted across a lake several miles in width it is quite appar- 
 ent that the height of the line above the water is greater 
 upon the further side of the lake than it is at the point of 
 observation. 
 
 Again, if the bottom of a canal, several miles long, be made 
 parallel to the engineer's " level line," it is well known that 
 the water in the canal will not be of uniform depth through- 
 out, but will get shallower as we recede from the starting 
 point. And it is found necessary, in order to prevent this, 
 to drop the bottom of the canal eight inches at the end of the 
 first mile, and from this point to adopt a new level line, and 
 to continue this process. 
 
 Fig. 4. 
 
 Thus if A be the starting point and AB be one mile in 
 length and parallel to the level line at A, the water at B will 
 be 8 inches shallower than at ^. It becomes necessary then 
 to drop 8 inches from 5 to & and make b a new starting point 
 for the level line hC, etc. 
 
 Of course, in practice the engineer avoids the abrupt drops 
 of 8 inches at B, C, etc., by distributing them throughout the 
 whole extent of the canal. 
 
 (/) All the heavenly bodies which are sufficiently near to 
 us to have their form certainly determined are spherical or 
 nearly so, as the sun, the moon, and all the visible planets, 
 and from analogy we would infer that the earth also has a 
 spherical form. 
 
 These, and other considerations which will appear from 
 time to time in the sequel, should be sufficient to remove any 
 doubt as to the spherical form of the earth. 
 
GRAVITATION. 9 
 
 1. Gravitation — Up and Down. 
 
 One of the chief difficulties, at least with beginners, is as 
 to how people manage to live upon and cling to different and 
 €ven opposite sides of a body having a spherical form. 
 
 The difficulty arises from want of a clear conception of 
 what is meant, fundamentally, by up and down. These terms 
 do not denote absolute directions, but directions relative to 
 the earth's surface. 
 
 Matter in bulk has a tendancy to draw together, to aggre- 
 gate. If a single material body were placed in space it could 
 have no relations except to itself. But if a second material 
 body be there, the two would exercise an attraction or pull 
 upon each other, and if nothing intervened to prevent it the 
 bodies would in due time come together to form a single 
 body. 
 
 This general form of attraction of matter for matter is 
 known as the attraction of gravitation, or simply gravitation. 
 Its existence is not a matter of theory only, as it has been 
 fully established by a classical laboratory experiment known 
 as Cavendish's experiment. 
 
 This attraction increases directly as the mass or amount 
 of matter in the attracting body, and it is inversely propor- 
 tional to the square of the distance through which the attrac- 
 tion takes place. 
 
 Thus if m denotes the mass of a body, d denotes the dis- 
 tance of a second-body upon which the attraction acts, and a 
 denotes the measure of the attraction, a varies as the quotient 
 of m divided by d^. 
 
 The attraction between two material bodies is mutual ; if 
 A attracts B, so also B attracts A, and the whole attraction 
 between them is the sum of the individual attractions. 
 
 Thus the earth attracts the moon and the moon attracts 
 the earth, but as the earth contains 80 times as much matter 
 as the moon, the pull of the earth on the moon is 80 times 
 as great as the pull of the moon on the earth ; and in coming 
 together, if that were possible, the moon would move 80 
 times as far as the earth. 
 
10 ASTRONOMY. 
 
 Now, the mass of the earth is milHons of times greater 
 than that of any body upon its surface. So we may say that 
 the earth, by virtue of the attraction of gravitation, draws 
 the bodies on its surface towards its centre of attraction just 
 as a magnet, by virtue of magnetic attraction, draws bits of 
 iron and steel toward its polar centre and causes them to 
 cling to its surface. 
 
 Down, then, is the direction of the earth's attraction, and 
 thus upon every part of the earth's surface, down is towards 
 the earth's centre of attraction, and Up is the opposite of 
 down. 
 
 The plumb-line. The ' bob ' or weight at the end of the 
 plumb-line tends to get as near to the centre of attraction of 
 the earth as possible, and hence the plumb-line gives the true 
 directions of up and down. 
 
 Fig. S. 
 
 From the nature of the case, it is readily seen that the 
 plumb-lines at any two places upon the earth's surface can- 
 not be parallel; for even in case of antipodes, or points on 
 the earth exactly opposite, the lines, although parallel, are 
 stretched by their bobs in opposite directions. 
 
 With these conceptions thoroughly mastered there is no 
 difficulty in understanding that all plumb-lines point to the 
 centre of attraction, and that all bodies which stand upright, 
 as trees, columns, spires, human beings, etc., must be ap- 
 proximately parallel to the plumb lines in their vicinity. 
 
 Two plumb-lines 69.1 miles apart make an angle of 1° with 
 one another, and if they are one mile apart the angle between 
 them is about 52". 
 
PLUMB LINE AND LEVEL. 11 
 
 The level depends for its action on the equilibrium of the 
 surface of a liquid, which tends to accommodate itself to the 
 
 Fig. 6. 
 
 rotundity of the earth's surface. It consists of a small glass 
 tube very slightly curved and closed at both ends after being 
 filled with a mobile liquid,, alcohol in preference to water, 
 until there is only a small bubble of air left in the tube. The 
 whole is so mounted as to be readily applied to any plane 
 surface. 
 
 When the surface is ' level ' the bubble stands at the mid- 
 dle position, and any inclination of the plane will cause the 
 bubble to move towards the higher end of the tube. In 
 astronomical instruments the level is a more convenient 
 auxiliary than the plumb-line. And as the level line is per- 
 pendicular to the plumb-line, both instruments serve prac- 
 tically the same purpose. A level plane at any point on the 
 earth has the plumb-line at that point as its normal. And 
 hence we see that level planes at any two points on the earth's 
 surface cannot be parallel, unless the two points are anti- 
 podal. 
 
 Sea level. The word " level " is here used in a somewhat 
 different sense, the whole expression meaning the height or 
 position in elevation of the surface of the sea. 
 
 As all the waters of the oceans are connected and continu- 
 ous, the surface assumes an equilibrium form which ex- 
 presses the mean form of the earth as a whole, and this sur- 
 face is the datum surface to which we refer altitudes and 
 depressions. At an inland point sea-level means the position 
 in altitude which would be reached by the surface of the sea 
 if it could be brought to the point by a subterranean channel. 
 
 We express the height of a mountain by giving its altitude 
 above the surface of the sea, and not above that of the sur- 
 rounding country ; and we express depressions in like manner. 
 
12 ASTRONOMY. 
 
 Many measurements, such as the height of the barometer, 
 the time of oscillation of a pendulum of given length, etc., 
 are affected by altitude, and all such have to be referred to 
 the sea-level, or level of the sea. 
 
 2. Horizon, Zenith, Nadir. 
 
 The word horizon has a popular meaning and also an 
 astronomical one. Popularly it means the line, or rather 
 circle, which limits our view over the earth's surface, and 
 where the sky and land, or the sky and water, seem to meet. 
 
 The astronomical meaning of the word is more definite 
 and exact. 
 
 Tlane o-f visitjl& Tioy/iort. 
 
 8-'a i 
 
 ™ -^ ptoLMe of -fru-e Ko,*f%on. ^ 
 
 Fig. 7. 
 
 Let a plane touching the earth's hypothetical surface, and 
 perpendicular to the plumb-line at A, be indefinitely ex- 
 tended. And let another plane, passing through the earth's 
 centre and parallel to the first plane, be similarly extended. 
 Since parallel planes meet at infinity, these two planes prac- 
 tically meet and form one great circle about the heavens 
 where these two planes meet the celestial sphere. 
 
 This great circle is the astronomical horizon of the point 
 A, as also of the antipodal point A'. 
 
 As it is convenient at times to refer to these planes, the 
 first will be called the plane of the visible horizon, or simply 
 the visible horizon, and the other the plane of the true 
 horizon. 
 
 The angular distance between these two planes, as seen 
 from A, decreases as the distance from the earth increases. 
 Thus, at the distance of the moon this angle, MAM', is about 
 57', and at the distance of the sun it is only 8". 8, while at the 
 distance of the nearest fixed star it is altogether inappre- 
 ciable, being less than the forty-thousandth part of one 
 second. 
 
HORIZON AND ZENITH. 13 
 
 We may state the same idea otherwise as follows : When 
 the moon is on the true horizon it is 57' below the visible 
 horizon ; when the sun is on the true horizon it is 8". 8 below 
 the visible horizon; and when a fixed star is on the true 
 horizon it is also on the visible horizon. 
 
 The zenith of a place on the earth i.s that point in the celes- 
 tial sphere to which the plumb-line at the place is directed 
 upwards, that is, it is the point in the heavens directly over- 
 head. And the nadir is the point in the celestial sphere to 
 which the plumb-line, at the place, is directed downwards. 
 The zenith and the nadir are opposite points in the celestial 
 sphere. Evidently no two places can have the same zenith, 
 and they can have the same true horizon only when antipodal. 
 
 The figure (8) represents a plane section through the cen- 
 tre of the earth, and through the two places A and B on its 
 surface, and A is supposed to be directly north from B. 
 
 Fig. 8. 
 
 Then EF is a section of the earth's surface; HH', the tan- 
 gent line at A to the circle EF, is a section of A's horizon; 
 and similarly hh' is a section of B's horizon. 
 
 Also A A' represents the plumb-line at A, and BB' the 
 plumb-line at B. Then AA' points to A's zenith, and BB' to 
 B's zenith. 
 
 A can see the star at S but not at T, as S is above A's hori- 
 zon, and T is below it. And for similar reasons B can see 
 the star at T but not the one at 5". 
 
 If A passes southward to B, his horizon gradually rises 
 above S and sinks below T ; or as it appears to A, during the 
 journey, T rises above the southern line of his horizon, while 
 5" sinks below the northern line. And here we have a full 
 
14 
 
 ASTRONOMY. 
 
 explanation why old and familiar stars gradually sink down 
 and disappear and new ones come into view in the opposite 
 part of the heavens v\»hen an observer travels from North to 
 South, or South to North. The changes here described as 
 taking place constitute another proof that the earth is ap- 
 proximately spherical. 
 
 The Horizon is divided into four equal parts by the four 
 cardinal points of the compass, North, E ast, Sou th and West. 
 Each of these parts is 
 again divided into 8 
 equal parts, giving in all 
 the 32 points of the 
 mariner's compass. The 
 names of these points, 
 starting from the north, 
 are : — North, north by 
 east, north north-east, 
 northeast by north, north- 
 east, northeast by east, 
 east northeast, east by 
 north, east, east by south, 
 east southeast, southeast 
 by east, southeast, south- Fig. 9. 
 
 east by south, south southeast, south by east, south, south by 
 west, south southw'est, southwest by south, southwest, south- 
 west, by west, west southwest, west by south, west, west by 
 north, west northwest, northwest by west, northwest, north- 
 west by north, north northwest, north by west, north. 
 
 The mariner then divdies each of these 32 points into four 
 equal parts called quarter points, thus making 128 quarter 
 points in the circle of 360°, so that the value of a quarter 
 point is 2° 48' 45". 
 
 A better way of expressing direction on the earth's surface 
 is the one followed by the surveyor and the astronomer, in 
 which all directions are referred at once to one of the car- 
 dinal points. Thus, north northeast is expressed as north 
 22° 3(7 east or N. 22° 30' E., or E. 67° 30' N. ; and S. 27 10' 
 
ALTITUDE AND AZIMUTH. 
 
 15 
 
 W. means a direction which makes the angle 27° 10' west of 
 the south meridian. 
 
 Equator and Poles of the Sphere. The section of a sphere 
 by a plane which passes through its centre is called a great 
 circle of the sphere. On the surface of the sphere there are 
 two points which are equidistant from all points on this 
 circle. These points are called the poles of the great circle, 
 and the circle itself is called the equator to these poles or 
 points. This use of the terms poles and equator is a generic 
 one, and is not to be confounded with the particular mean- 
 ings when applied to the earth. 
 
 It is evident that the line joining two points as poles is 
 perpendicular to the- plane of their equator. 
 
 The zenith and nadir are the two poles of the horizon, and 
 the horizon is the equator to the zenith and nadir considered 
 as poles. 
 
 3. Altitude and Azimuth, Vertical Circles, Etc. 
 
 In the accompanying figure Z is the zenith, NESW is the 
 celestial horizon, and the earth is at the centre 0. N, W, E, 
 and 6" are the cardinal points of the compass. 
 
 /-^.. 
 
 r>>\ 
 
 "r " ' *'/ 
 
 ' ^v "~"iy 
 
 / — iV *■/ 
 
 
 i 1/ i.r 
 
 
 srU^^^^^ . . 1 h\:, 
 
 
 rtarth anA Sau.tli lir 
 
 Fig. 10. 
 
 Circles such as EZW, PZQ, etc., which pass through Z 
 and meet the horizon in opposite points are called ' Vertical 
 Circles, being great circles which rise vertically from the 
 
16 ASTRONOMY. 
 
 horizon to the zenith. As P and Q may be any pair of oppo- 
 site points on the horizon, the number of vertical circles is 
 unlimited, but certain ones have special names. Thus the 
 vertical circle passing through the east and west points of the 
 horizon, E and W, is called the prime vertical ; and the one 
 passing through the north and south points of the horizon, 
 A'' and S, is the meridian of the place having Z as its zenith. 
 
 The projection of this upon the earth, that is, the line run- 
 ning north and south upon the earth's surface, is spoken of 
 as the meridian line, or north and south line. 
 
 If a long suspended plumb-Hne be viewed from a little dis- 
 tance, its projection upon the sky represents part of a ver- 
 tical circle.' 
 
 And this method of getting the projection of the pole star 
 upon the horizon, or in fact of any other star of not very 
 high altitude, is sometimes practically employed. 
 
 The small circle, UMV, parallel to the horizon, is a circle 
 cf altitude or an almucantur. 
 
 If M be a heavenly body, as a star, the angle ZOM is the 
 zenith distance of the star, and the angle POM is the altitude 
 of the star. And we see that the altitude of a heavenly body 
 is the complement of its zenith distance ; so that if these 
 angles are denoted by a and s, respectively, we have 
 0+^=90°. 
 
 The angle SOP, between the plane of SZO and the plane 
 of PZO, is the azimuth of M. In this case the azimuth is 
 reckoned from the south, but it may equally well be reckoned 
 from any one of the cardinal points. As the sun rises daily 
 at the eastern horizon and sets at the western one, the sun's 
 altitude is continually changing during his apparent diurnal 
 motion, and the measuring of the sun's altitude at some par- 
 ticular time in the day is one of the commonest observation 
 problems in navigation. In like manner the sun's azimuth 
 changes continually throughout the day. 
 4. The Altazimuth. 
 
 We speak of the horizon, of the meridian, of a vertical 
 circle, etc., as if they were real lines drawn upon the surface 
 of the heavens, whereas such lines have existence only in 
 
ALTITUDE AND AZIMUTH. 
 
 17 
 
 theory. It is doubtful, however, if real lines, even if they 
 did exist, would not be more objectionable than useful, for 
 we can, by means of proper instruments, place upon the sur- 
 face of the heavens any of these lines, whenever and wher- 
 ever we please. How this is done we proceed to explain. 
 
 But, being interested in geometric principles which underlie 
 the action of instruments rather than in their manufacture 
 and sale, we shall use diagrammatic illustrations instead of 
 realistic ones. 
 
 v?.^- 
 
 Fig. 11. 
 
 T is a telescope whose Hne of sight is fixed at right angles 
 to a horizontal axis H, about which it can be rotated. This 
 axis rests upon two supports P, P which are firmly con- 
 nected to the vertical axis V, around which the whole can be 
 rotated. 
 
 Thus the line of sight of the telescope is perpendicular to 
 the horizontal axis, and the horizontal axis is perpendicular 
 to the vertical one. And it is easily seen that by rotation 
 about these two axes the telescope may be directed to any 
 point in the visible heavens. 
 
18 ASTRONOMY. 
 
 If the telescope be pointed to the zenith it will be in line 
 with, or parallel to, the vertical axis, and will continue to 
 point to the zenith while being rotated about the vertical 
 axis. If the telescope be placed at right angles to the vertical 
 axis and the whole be rotated about the vertical axis, the line 
 of sight will trace out the horizon. 
 
 If the telescope be directed to an object M in the heavens 
 and be then rotated on the vertical axis, the line of sight will 
 trace out the circle of altitude or almucantur MM' on which 
 the object M lies. And finally if the telescope be turned 
 about the horizontal axis only, its line of sight will trace out 
 a vertical circle. 
 
 The field of view of the telescope appears as a circle 
 crossed by two spider lines, technically called threads or wires, 
 at right angles, one being vertical and the other horizontal, 
 and the line of sight passes through their point of intersec- 
 tion. So when a star is brought to this intersection the two 
 lines, projected upon the sphere of the heavens, give small 
 portions of the vertical circle passing through the star, and 
 a tangent to the circle of altitude at that point upon it where 
 the star is situated. 
 
 This instrument is called an altazimuth, because it gives 
 the means of measuring at once the altitude and the azimuth 
 of any heavenly body, or of any elevated point or object 
 required. 
 
 5. Earth's Axial Rotation. 
 
 As the earth is a spherical body posited in space, it is alto- 
 gether probable that it is in motion, and the following ob- 
 servations and considerations strengthen this probability. 
 
 As has been already pointed out, the relative positions of 
 the stars are the same from year to year, so that if the stars 
 move materially they must move as a whole, and not indi- 
 vidually. 
 
 Upon any starlit night, preferably when the moon is absent, 
 let one take up a position in which he can command a fairly 
 unobstructed view of the horizon, and let him direct his 
 view, at first, to the northern sky. We will suppose that he 
 is at latitude 45° north. 
 
EARTH'S AXIAL ROTATION. 19 
 
 He will observe about half-way between the north point 
 of the horizon and the zenith, a fairly bright star which 
 stands pretty much alone, having no equally bright stars 
 within some distance of it, and in line with the two stars, in 
 Ursa Major, known as the pointers. This is Polaris, or the 
 north star or the pole star. 
 
 Our observer, by continuing his observations for several 
 hours, will notice that all the stars of the northern sky ap- 
 pear to move in circles having Polaris near the centre, the 
 direction of motion being opposite to that of the hands of 
 his watch. 
 
 Those stars at the proper distance from the pole, in this 
 case 45°, as represented by the circle A, will graze the north- 
 ern horizon at A'' at their lowest point, and will pass through 
 the zenith, Z, at their highest. 
 
 Fig. 12. 
 
 Stars represented by the circle B, more distant than A is, 
 dip below the horizon in the lower part of their course, pass 
 south of the zenith in the upper part, and like the sun and 
 moon regularly rise and set. 
 
 But stars at less than 45° from the pole, as represented by 
 the circle C, never reach the horizon and therefore never set, 
 
20 
 
 ASTRONOMY. 
 
 and can be seen, by means of a telescope, at any time when 
 the northern sky is unclouded. Hence the circle A is called 
 the Circle of Perpetual Apparition. 
 
 Of the stars which rise and set, those which rise near the 
 east point of the horizon remain about 12 hours above the 
 horizon and set near its west point; those which rise south 
 of east remain less than 12 hours above the horizon and set 
 south of west. And the farther south a star rises, the farther 
 south it sets and the shorter time it remains above the hori- 
 son. And these observations are for 45° north latitude, or 
 for an observer situated half-way between the earth's equator 
 and its north pole. 
 
 Fig. 13. 
 
 If the observer goes southward the pole star descends to- 
 wards the north point of the horizon, and the circle of per- 
 petual apparition gets smaller, no longer reaching to the 
 zenith ; and if he goes northward the opposite change takes 
 place, that is, the pole star rises and the circle of perpetual 
 apparition grows larger and includes a greater number of 
 stars. Altogether similar phenomena would be observed by 
 a person living south of the equator. 
 
 To an observer on the equator, E, the pole star is on the 
 horizon, and there is no circle of perpetual apparition, or in 
 
EARTH'S AXIAL ROTATION. 21 
 
 other words, this circle is reduced to the pole itself, and all 
 the stars regularly rise and set. 
 
 And to an observer at the north pole of the earth, N, the 
 pole is at the zenith, and the circle of perpetual apparition 
 takes in the whole of the visible heavens, and the stars neither 
 rise nor set but travel around in circles parallel to the 
 horizon. 
 
 We see from this that the character of the apparent mo- 
 tions of the stars is to some extent dependent upon the 
 position of the observer. 
 
 In order to explain these apparent motions, the ancient 
 astronomers supposed that the stars were equally distant 
 from the earth, which was the centre of the universe, and 
 that they were fixed upon some kind of a transparent crystal- 
 line shell which daily rotated about an axis pointing to the 
 north pole of the heavens, for, as we shall see hereafter, the 
 present pole star was not the po)e star in their days. 
 
 But it then became necessary to have other shells or hollow 
 spheres to carry the sun, the moon, and each individual 
 planet, for these all have their own distinct apparent mo- 
 tions. The motion of these shells on their several axes was 
 supposed to grind out a sort of inaudible but philosophic 
 .sound known as the music of the spheres. 
 
 Such a cumbrous explanation for such simple phenomena 
 is, of course, illogical, and as the stars are not all at the same 
 distance and cannot all be carried on even a thousand re- 
 volving shells, the explanation is absurd. Besides, the simple 
 hypothesis that the earth rotates every 24 hours about a 
 central axis which points to the north pole of the heavens 
 explains fully not only all the phenomena described, but also 
 much more that has not as yet been referred to. 
 
 These considerations compel us to adopt the hypothesis 
 that the apparent daily revolution of the sun, the moon, and 
 the stars is due to a real rotation of the earth about its own 
 axis. Northwards this axis is directed to a point in the 
 heavens only a little more than one degree from the star 
 Polaris. The miller's objection, that if the earth turns 
 
22 ASTRONOMY. 
 
 around the water would be spilt out of his mill-pond, is left 
 to be answered by the reader. 
 
 When one pole. A'', is elevated above the horizon, the 
 
 Fig. 14. 
 
 opposite pole, 5", is depressed to an equal distance below the 
 horizon. 
 
 " One pole rides high, one sunk beneath the main 
 Seeks the dark night and Pluto's dusky reign." 
 So that corresponding to the circle of perpetual apparition, 
 in which the stars never set, there is an opposite circle of 
 equal dimensions in which the stars never rise. This is called 
 the Circle of Perpetual Occidtation. 
 
 Only those living on the equator are in a position to see 
 all the stars from pole to pole. 
 
 We have a number of direct proofs of the rotation of the 
 earth about its axis, but we shall at present content ourselves 
 with explaining a very important one known as Foucault's 
 Pendulum Proof. It is a well-established principle in Phy- 
 sics that when a heavy ball suspended by a cord or wire is 
 set to oscillate in any given plane, it will continue to oscillate 
 in that plane until turned out of it by some extraneous force. 
 But if the weight is suspended by a uniform cord or wire, 
 
EARTH'S AXIAL ROTATION. 
 
 23 
 
 and is well protected from air currents, there is no extra- 
 neons force to act upon it. 
 
 For the sake of easy explanation, let us suppose that the 
 pendulum CW is suspended from C, a point directly above 
 the north pole,iV, of the earth, and that XY is a small portion 
 •=* of the earth's surface 
 
 about the pole. Let the 
 pendulum be started to 
 swing along a line ANB 
 drawn on the surface 
 XY. After some little 
 time, an hour say, it will 
 be seen that the plane of 
 oscillation has apparent- 
 ly shifted from the line 
 Fig. IS. ANB to a new line aNb, 
 
 the angle BA^b being about 15°. This may be accounted for 
 by supposing that the plane of oscillation has shifted through 
 15° in the direction of the movement of the hands of a 
 watch, or by supposing that the surface XY has shifted 
 15° in the opposite direction. But as the plane of oscillation 
 is invariable, the surface XY, and therefore the earth itself, 
 must rotate in a direction opposite that of the hands of a 
 watch, as indicated by the arrows. 
 
 Theory tells us that on the equator there is no apparent 
 rotation of the plane of oscillation ; at places north of the 
 equator the apparent rotation is right-hand, and at places 
 south of the equator it is left-hand, and also that the rate of 
 rotation increases as you pass from the equator towards 
 either pole. And the theory has been verified wherever and 
 whenever the experiment has been conducted. And thus we 
 have a most convincing visible proof of the earth's rotation 
 on its axis. 
 
 Other experimental or mechanical proofs are furnished by 
 (a) dropping a ball from the top of a tall tower, when the 
 ball invariably deviates to the east of the vertical; (b) 
 the creeping of the rails upon a railway running north and 
 
24 
 
 ASTRONOMY. 
 
 south; (c) the almost invariable direction of the trade winds, 
 which direction is due to the northerly or southerly course of 
 the wind compounded with the easterly rotational movement 
 of the earth's surface. 
 6. Terrestrial and Celestial corresponding points and lines. 
 
 The distinctive points upon the earth are the north terres- 
 trial pole and the south terrestrial pole, these being the points 
 where the axis meets the surface. 
 
 The distinctive circles are: The equator, which lies half- 
 way between the poles ; the meridians, which are great circles 
 passing through the poles and crossing the equator at right 
 angles ; and the circles of latitude, or parallels of latitude as 
 they are commonly called, which are small circles parallel to 
 the equator. 
 
 Fig. 16. 
 
 Now, from 0, the centre of the earth, let the foregoing 
 points and lines be projected Uf>on the sphere of the heavens. 
 The projection gives us the following: (1) The poles of the 
 earth, p, p' become the celestial poles, or poles of the heavens. 
 
EQUATOR AND MERIDIANS. 25 
 
 P, P' ; (2) the terrestrial equator, ee', becomes the celestial 
 equator EE' ; (3) a meridian, pqp', becomes the celestial 
 meridian, PQP' ; and (4) the circle of latitude, cc', becomes 
 the circle of declination CC. And thus the points and circles 
 on the celestial sphere are projections, and therefore enlarged 
 copies of those upon the earth. 
 
 But as the terrestrial and celestial meridians are supposed 
 to be fixed, each on their own sphere, and as the earth rotates 
 within the sphere of the heavens, it follows that no one meri- 
 dian on the earth can be said to correspond to any particular 
 meridian in the heavens. In fact, any one terrestrial meri- 
 dian passes under all the celestial meridians in a trifle less 
 than 24 hours. 
 
 Also, if the earth should by any means shift the direction 
 of its axis, the whole enumerated set of celestial points and 
 circles would be correspondingly shifted amongst the stars. 
 We shall see hereafter that such a shifting is going on, al- 
 though ver)r slowly. 
 
 7. Local Meridian. 
 
 The celestial meridian which passes through the zenith of 
 a place passes also through the north and south points of the 
 horizon, and is called the meridian of the place, or the local 
 meridian. As this meridian is fixed in regard to the earth, it 
 rotates with the earth and passes every star in one revolution 
 of the earth, the apparent phenomena being, however, that 
 the stars, in their diurnal rotation, pass this meridian. 
 
 When any celestial body is on the local meridian it is said 
 to culminate, and the culmination of sun, moon, and stars 
 are matters of daily observation in every astronomical ob- 
 servatory. 
 
 Culmination is usually observed by means of an instru- 
 ment called a transit, which is an altazimuth having no ver- 
 tical axis, and accurately adjusted to trace out the meridian 
 only, by rotation on its horizontal axis. 
 
 The culmination of a body is also spoken of as its meridian 
 transit. 
 
26 
 
 ASTRONOMY. 
 
 8. Latitude and Declination. 
 
 The angular distance of any place on the earth from the 
 terrestrial equator is the latitude of the place, and is said to 
 be north or south (N. or S.) according as the place is north 
 or south of the equator. Thus the latitude of Kingston is 
 44° 13' N. 
 
 Similarly the angular distance of a heavenly body from 
 the celestial equator is called the declination of the body, and 
 it is north or south according as the body is north or south 
 of the equator. And thus declination in the heavens cor- 
 responds to latitude upon the earth. Astronomical latitude 
 has a different meaning, and has no real correspondent in 
 terrestrial relations. 
 
 If we were at the equator, the north pole of the heavens 
 would be at the horizon at its north point N. As we went 
 northward the pole would rise; and if we could get to the 
 north pole of the earth our latitude would be 90°N., and the 
 north pole of the heavens would be at our zenith. So that 
 the altitude of the celestial north pole above our horizon 
 measures our latitude north. 
 
 Similarly the altitude of the south pole of the heavens 
 gives the latitude of the place south. 
 
 In the figure E is the earth, Z the zenith of an observer, 
 SZA^ is the local meridian, SEN a section of the horizon, P 
 the north pole of the heavens, and Eq the position of the 
 celestial equator where it crosses the local meridian. 
 
LATITUDE AND DECLINATION. 
 
 27 
 
 Then, as EZ is perpendicular to EN, and EEq is perpen- 
 dicular to EP, it follows that the angle A/'£P = the angle 
 ZEEq, and the angle Z£P=the angle SEEq. 
 
 But NEP is the altitude of the pole and ZEEq is the 
 zenith distance of the equator. Hence the latitude of any 
 place on the earth is the same as the altitude of the pole, or 
 the zenith distance of the equator, as measured at the place. 
 
 And the co-latitude of a place is the same as the zenith 
 distance of the pole, or the altitude of the equator as observed 
 at the place. 
 
 Again, if © denotes the sun when on the local meridian, 
 the angle oEEq is the sun's declination, and if we denote 
 the angle O ES, which is the sun's altitude when on the meri- 
 dian, by a, we readily see that a—y-\-S=90° — <^-|-8. 
 
 Whence <j,—90°+S—a 
 where ^ is the latitude, S is the sun's declination, and a is the 
 sun's meridian altitude. 
 
 Thus we can find our latitude upon the earth, by finding 
 the altitude of the pole, or of the sun on the meridian, if we 
 
 -1 ,^,_^ 
 
 ^ 
 
 Fig. 18. 
 
 know the sun's declination, and this is given in the Nautical 
 Almanac for every day in the year. 
 
 The following experimental observation may be carried 
 out by the beginner : 
 
 T is a table which is placed with its longer edge as nearly 
 north and south as can be arranged, and is then carefully 
 
28 
 
 ASTRONOMY. 
 
 leveled. 5 is a box, with right-angled corners, so placed 
 upon the table that its horizontal edges are parallel with 
 those of the table. By placing one's eye, E, in the proper 
 position the edges of the table and the box may be brought in 
 line with Polaris, P, by moving the box on the table. 
 
 Then, carefully measuring the lengths a and b, we have 
 a/b=the tangent of the altitude of Polaris; and this angle, 
 taken from a table of natural tangents, is the altitude of 
 Polaris and approximately the latitude. 
 
 Thus if a=12 in. and b=l5 in., tangent of altitude of 
 Polaris=0.8, the altitude itself is 38° 40'; and this is ap- 
 proximately the latitude. 
 
 As Polaris is not at the pole but about 1 ° 20' away, it re- 
 volves around the pole and has the same 
 altitude as the pole, as at A and A', twice in 
 each revolution. But at these times the star 
 is changing its altitude most rapidly, and a 
 failure to get the observation at the right 
 B' time would produce the maximum of error. 
 
 Fig. 19. At B and B', on the other hand, the star is 
 
 directly above or below the pole and has its altitude practi- 
 cally constant for a short time, so that an error in the time 
 of observation would give a minimum error in the result. 
 At B the distance of Polaris from the pole must be sub- 
 tracted from the observed altitude of Polaris to give the 
 latitude, and at B', it must be added. 
 
 The accompanying table gives approximately the times 
 when Polaris will have the position B above the pole. The 
 position B' below the pole is 12 hours earlier or later oii the 
 same date. 
 
 Hour Date 
 
 Hour Date 
 
 Hour Date 
 
 Hour Date 
 
 Noon, Apr. 10 
 
 1 p.m. Mar. 25 
 
 2 p.m. Mar. 10 
 
 3 p.m. Feb. 25 
 
 4 p.m. Feb. 10 
 
 5 p.m. Jan. 25 
 
 6 p.m. Jan. 10 
 
 7 p.m. Dec. 25 
 
 8 p.m. Dec. 10 
 
 9 p.m. Nov. 25 
 
 10 p.m. Nov. 10 
 
 11 p.m. Oct. 25 
 Midn't, Oct. 10 
 
 1 a.m. Sept. 25 
 
 2 a.m. Sept. 10 
 
 3 a.m. Aug. 25 
 
 4 a.m. Aug. 10 
 
 5 a.m. July 25 
 
 6 a.m. July 10 
 
 7 a.m. June 25 
 
 8 a.m. June 10 
 
 9 a.m. May 25 
 
 10 a.m. May 10 
 
 11 a.m. Apr. 25 
 Noon Apr. 10 
 
LONGITUDE AND RIGHT ASCENSION. 29 
 
 The latitude may also be found from the sun's altitude 
 when on the meridian. In figure 18, if S be the length of the 
 shadow cast by the box B, a/S is the tangent of the angle of 
 the sun's altitude. Thence we have 
 
 Latitude^90°+ sun's declination — sun's altitude. 
 The declination is positive when the sun is north of the 
 equator, that is, from March 20th to Sept. 23rd, and it is 
 negative during the other half of the year. 
 
 9. Longitude and Right Ascension. 
 
 A meridian is counted as extending only from pole to pole, 
 instead of completely around the earth, and thus every place 
 has its own meridian, that is, the meridian passing through it. 
 
 The angle between the plane of this meridian and the plane 
 of some other meridian, taken as a first meridian, is the lon- 
 gitiide of the place. 
 
 For geographical purposes longitude is frequently meas- 
 ured east and west from the first meridian up to 180°, but 
 it is better and more in accordance with astronomical usage 
 to express it in time instead of in angle. 
 
 As the earth rotates through 360° in 24 hrs. we have 15° is 
 equivalent to 1 hr., IS' to 1 m., and IS" to Is. 
 
 Hence the following rule for changing angle into time : 
 
 hr, 
 Divide the | ' | by IS; call the quotients 
 
 Multiply the remainder from the division of 
 
 call the products 
 
 Add results. 
 
 mm. 
 sec. 
 I by 4, and 
 
 mm. 
 
 sec. 
 
 Example. To change 76° IS! 52" to time : 
 
 Dividing by 15, 5h. Im. 3s. 
 With remainders 1 13 7 
 
 Multiply by 4 4m. 52s. ^VeoS. or 0.47 nearly. 
 
 Sum— S» 5" 5S».47. 
 
 To change time into angle, multiply h. m. s. each by 15 and 
 call the products ° ' ", and reduce. 
 
30 ASTRONOMY. 
 
 Example. To express 5* S™ 55».47 in angle : 
 
 Multiplying by IS, 75° 75' 832".05, 
 
 And reducing gives 76° 28' 52".05. 
 The advantage of expressing the longitude of a place in time 
 instead of in angle is apparent from the fact that the longi- 
 tude expressed in time tells us at once how much the local 
 time of the place is behind that of the first meridian. 
 
 Thus, if the longitude of a place be 8* 20™, then the time 
 at the place is 8'' 20'" slower than at the first meridian; so 
 that if the time at the first meridian is 10'' 50™ a.m., the time 
 at the given place is 2* 30" a.m. 
 
 Taking the meridian of Greenwich as the first meridian, 
 the longitude of Kingston is S* 5"* 55«.5, which is equivalent 
 to saying that the local time at Kingston is 5* 5*" 55*. 5 behind 
 the local time at Greenwich. 
 
 In the ephemeris the times for the occurrence of many 
 phenomena are given for the first meridian only, and from 
 these the times of occurrence at any given meridian are to be 
 found by correcting for the longitude of that meridian. 
 
 Just as every place on the earth has its own terrestrial 
 meridian, so every celestial body, as the moon, or a star, has 
 its own meridian in the heavens, and the angle between the 
 plane of this meridian and the plane of some other meridian, 
 taken as a first meridian, is called the Right Ascension of the 
 heavenly body. 
 
 Right ascension is always expressed in time, unless under 
 particular circumstances, and is measured from west to east 
 around the circuit of the heavens, or from hrs. to 24 hrs. 
 
 We have then the correspondences : 
 
 Terrestrial. Celestial. 
 
 Latitude Declination 
 
 Longitude Right Ascension. 
 
 10. First Meridian. 
 
 The equator is a natural line or circle from which to mea- 
 sure latitudes, but there is nothing of that kind amongst 
 terrestrial meridians, so that the choice of a first meridian 
 must be more or less arbitrary. 
 
FIRST MERIDIAN. 31 
 
 As a matter of convenience it is easily seen that the first 
 meridian should pass through some large and old-established 
 astronomical observatory. As a consequence, nearly every 
 nation that possesses a national observatory is to some extent 
 jealous of its honor, and wishes to take the meridian of that 
 observatory as the first meridian. 
 
 All British subjects adopt the meridian of Greenwich, near 
 London, while the French prefer that of their observatory at 
 Paris, and the Russians that of St. Petersburg. The Ameri- 
 cans very commonly follow the usage of Great Britain, al- 
 though using also the meridian of the Naval Observatory at 
 Washington. 
 
 The matter is somewhat confusing, and the giving of the 
 longitude of a place has no meaning until the position of 
 the adopted first meridian is known. 
 
 In this work the meridian of Greenwich is taken as the 
 first meridian and the origin of time and longitude. 
 
 There is no such difficulty in fixing upon a first meridian 
 in the heavens, as national jealousy does not reach that far, 
 and there are four quite distinctive meridians. 
 
 The one adopted as the first celestial meridian cuts the 
 equator where the sun crosses it when coming north in the 
 spring. This point on the celestial equator is called, sym- 
 bolically, the first point of Aries, because it is the point and 
 time at which the sun, in its apparent annual journey, enters 
 the Constellation Aries. It is also called the ascending node 
 (nodus, a knot), because it is the place where the sun ap- 
 pears to pass from the south side of the equator to the north 
 side. And as astronomy originated, as far as we know, in 
 the northern hemisphere, it is natural to call that hemisphere 
 the upper one. 
 
 This point is also called the vernal equinox, as spring be- 
 gins when the sun reaches this point, and the days and nights 
 are equal in length. 
 
 The sun is at the vernal equinox about March 20th. 
 
 11. Registration. 
 
 A place on the earth's surface is registered by giving its 
 longitude and its latitude, for these being given the position 
 
32 ASTRONOMY. 
 
 of the place is known, as no two places can have the same 
 longitude and the same latitude. 
 
 In a similar manner a heavenly body is registered by giving 
 its right ascension and its declination. 
 
 Star catalogues are catalogues giving these elements for 
 large numbers of stars, sometimes rising into the thousands. 
 In the British ephemeris, as in some other astronomical al- 
 manacs, the right ascensions and declinations of the sun and 
 the planets are given for every day in the year at noon, and 
 for the moon they are given for every hour. And in this 
 way we keep account of the positions and motions of these 
 bodies. 
 
 12. Wanderings of the Pole. 
 
 With the very accurate means of measurement possessed 
 by present-day astronomers, it has been lately discovered that 
 the latitude of a place, contrary to all previous expectations, 
 is not an absolutely fixed quantity, but undergoes some varia- 
 tion, which, although very small, appears to be continuous 
 and very irregular. And two places, like Berlin and Hono- 
 lulu, which are both in north latitude and about 12 hours 
 apart, possess the correlative property that when the latitude 
 of the one increases, that of the other decreases by the same 
 amount. 
 
 As latitude is measured from the equator, it follows that 
 the equator and therefore the poles must shift in regard to 
 the body of the earth. As far as is known, however, the 
 greatest movement of the pole is not more than about 60 feet 
 from the mean position, and this is about one-half second of 
 angle as seen from the earth's centre. 
 
 The cause of this wandering of the pole is not certainly 
 known. But the inequality of precipitation of rain and snow 
 upon different parts of the earth, as also the irregular rising 
 and falling of different sea coasts might well be cause 
 enough. 
 
 13. The Equatorial 
 
 Just as the altazimuth by motions about its two axes traces 
 out vertical circles and circles of altitude, so the equatorial 
 
DIMENSIONS AND FORM OF EARTH. 35 
 
 by motions around its two axes traces out meridians and cir- 
 cles of declination. The construction of the two instruments 
 is much alike, with variations for convenience, but the axis 
 which in the altazimuth is vertical and directed to the zenith, 
 is, in the equatorial, parallel to the earth's axis, and therefore 
 directed to the pole of the heavens. 
 
 By means of graduated circles the instrument may be set 
 to any readings in right ascension and declination, and thus 
 its line of sight directed to any star or point in the visible 
 heavens. 
 
 14. Dimension and Form of the Earth. 
 
 If the earth were motionless and alone in space it would 
 undoubtedly take the fotm of a sphere, as that is the only 
 form in which the attractions would be all satisfied. 
 
 But the sun attracts the earth, and as the attraction is 
 greater upon the side nearer the sun than upon that farther 
 away, this attraction tends to elongate the earth along the 
 line of attraction. The moon exerts a similar efifect; and 
 although the resulting efifect upon the form of the earth is 
 exceedingly minute, cases will arise in which it must be con- 
 sidered (tides). 
 
 But the earth is not motionless, but rotates about its axis. 
 And this brings in centrifugal force, especially about the 
 equatorial parts, and this tends to bulge out these parts and 
 to contract the length of the axis form pole to pole, that is, 
 it tends to give to the earth the form of an oblate spheroid. 
 
 It is evident, then, that to find the exact dimensions and 
 the true form of the earth is not a very simple problem. 
 
 The deviation from the spherical form is small, however, 
 and for a first approximation to its radius we may quite 
 safely assume the earth to be a sphere. 
 
 15. The formula s—rO. 
 
 In this well-known trigonometrical formula, which we 
 shall have occasion to use quite frequently, i' denotes the 
 length of an arc of a circle, in any convenient length-unit; 
 is the radian measure that this arc subtends at the centre ; 
 and r is the radius of the circle ; and in this formula these 
 
34 
 
 ASTRONOMY. 
 
 are so connected that if any two are given the third can be 
 found. 
 
 Let Z and Z' be the zeniths of two 
 places A and B situated on the same meri- 
 dian. Then if ZA andZ'B be produced 
 downwards they will meet at the centre 
 of the circle of which the meridian AB is 
 a part. Let 5" be a star at its culmination. 
 The angle ZAS is the zenith-distance of 
 the star as seen from A, and Z'BS is the 
 zenith-distance as seen from B, and these 
 two angles are got by observation on S 
 when on the meridian. 
 
 Then it is easily seen that the differ- 
 ence of these zenith-distances is the angle 
 at C, or 6. 
 
 The next thing is to measure the arc 
 AB. This is usually done on some extensive tract of level 
 country, and every known refinement in the process of length 
 measurement is employed. This measure gives the value of 
 s, and thence r is found. 
 
 For a mean value it is necessary to choose the places A and 
 B at mean latitudes, as the extremes of radii are at the 
 equator and the pole. 
 
 16. The Earth's Radius. 
 
 Taking now a practical case : In England at latitude about 
 52°N. it was found that a distance of 364,971 feet subtended 
 an angle of 1°, or tt/ISO radians. 
 
 Then r=364971Xl80A=20911300 feet=3960.4 miles. 
 
 And 3960 miles may be taken as a close approximation to 
 the earth's mean radius. 
 
 This value for the radius of a spherical earth gives the fol- 
 lowing results : 
 
 Length of the equator, 24884 miles. 
 
 Length of 1 ° in latitude, 69. 1 miles. 
 
 Length of 1' in latitude, 1.517 miles, or 6081 feet. 
 
 Length of 1" in latitude, 101 feet very nearly. 
 
SPHEROIDAL EARTH. 
 
 35 
 
 This gives for the velocity of a point on the equator, 
 owing to the axial rotation of the earth, about 1040 miles an 
 hour, or over 17 miles a minute. 
 
 But how do we know that the earth is an oblate spheroid 
 and not a sphere, for as yet we have had only theory ? 
 
 17. A Spheroidal Earth. 
 
 Measurements of arcs, by measuring rods and triangula- 
 
 tion, have been carried out in many parts of the world and 
 
 in different latitudes, and in the following table we have some 
 
 of the results : 
 
 Country. Latitude. Feet in 1° of lat. 
 
 Peru r31'S. 362808 
 
 India 16° 18'N. 363004 
 
 America 39° 12'N. 363786 
 
 France 44° Sl'N. 364535 
 
 England 52° 3S'N. 364971 
 
 Sweden 66° 20'N. 365782 
 
 This table shows clearly that for a given constant angle, 1°, 
 the length of the arc increases as we go from the equator 
 towards the pole. And considering the arcs as small parts 
 of circles, we see that near the pole the meridian belongs to 
 a greater circle than when near the equator, or, in other 
 words, the meridian is less curved at the pole than at the 
 equator. 2_b 
 
 
 
 FT 
 
 "^■^vJ^ 
 
 
 
 / ■* 
 / d 
 
 plane of x-c^uat. 
 
 i 
 
 
 \ 
 
 
 Kerid.iona.1 
 I taction 
 \ Of tl.e ." 
 \ Xarth. * 
 
 ' N 
 
 A* - — ■ 
 
 7 
 
 
 
 a. 
 
 ^ 
 
 / 
 
 Fig*21. 
 
 Let ABA'B' be a section through a meridian of the earth 
 considered as an oblate spheroid. Take B, B' the points of 
 
36 ASTRONOMY. 
 
 the shorter axis as the poles, and then A and A', the end- 
 points of the longer axis, will be points on the equator. 
 
 Then it is evident that the meridian is less curved at B 
 than at A, as it should be. And if bQ, aP be normals to the 
 meridian at b and a, and be so taken that the angles BQb 
 and APa are equal and each 1° say, then it is evident that 
 the arc Bb at the pole is longer than the arc Aa at the equa- 
 tor ; and as a consequence BQ is greater than AP. 
 
 If we know Aa and Bb, we can find AP and BQ by the 
 formula s^=r6. And what we wish finally to find are the 
 radii AC and BC, or a and b. 
 
 From the table, by interpolation, we find Aa to be 362740 
 feet, and Bb to be 366410 feet. 
 
 Thence we obtain the values of AP and BQ ; and finally 
 by means of a property of the ellipse, which cannot well be 
 given in this work, we get 
 
 ^C=a=3962.8 miles, 
 BC=b=i9A9.S " ; 
 and these are respectively the values of the equatorial radius, 
 and of the polar radius of the earth. 
 
 This gives a difference of 13.3 miles between the equato- 
 rial radius and the polar radius of the earth, or 26.6 miles 
 between the two corresponding diameters. 
 
 Now this 26.6 miles is only about one-three-hundredth 
 part of the whole diameter, and this is expressed by saying 
 that the earth's oblateness is one-three-hundredth, or 1/300. 
 
 To form a proper conception of this we may represent a 
 meridian of the earth by drawing an ellipse, or oblong circle, 
 having its diameters respectively 6 in. and 6.02 in. ; and if 
 such a figure were accurately drawn it would require careful 
 measurement to prove that it was not a circle. 
 
 This protuberance of the equatorial parts is a positive 
 proof that the earth rotates on its axis. 
 
 This oblateness, small as it is, has some interesting results. 
 (1) Tivo latitudes. The most important result to be men- 
 tioned at present is that every place on the earth, unless it 
 be at a pole or on the equator, has two latitudes. We have 
 defined the latitude of a place as its angular distance from 
 
SPHEROIDAL EARTH. 37 
 
 the plane of the equator. Now in Fig. 21, let if be a place 
 on the meridian. The plumb-line 7.K produced downwards 
 does not pass through C, the centre of the earth, but through 
 a point iV on the plane of the equator. The definition gives 
 either of the angles KNA or KCA as the latitude of K. But 
 as the altazimuth is adjusted by the level, which is equivalent 
 to the plumb-line, the angle KNA is the one determined by 
 the instrument. This is accordingly called the observed or 
 apparent latitude, while the angle KCA is the geocentric lati- 
 tude, or the latitude as seen from the centre of the earth. 
 The difference, the angle CKN, is called the correction of the 
 latitude, or the angle of the vertical. It will be sufficient here 
 to say that the greatest value of this angle is about 11' 30", 
 which occurs at latitudes about 45°. Apparent latitude is 
 always greater than geocentric, except as before mentioned. 
 
 (2) As the pole is nearer the centre of the earth than the 
 equator is, attraction is stronger at the pole than at the 
 equator. So that if a body which, by a spring balance, 
 weighs 194 pounds at the equator, be taken northward, it 
 continually increases in weight until the pole is reached, when 
 it weighs 195 pounds. 
 
 Also, the time taken by a pendulum of given length to 
 make one oscillation depends upon the pull of gravity upon 
 the bob of the pendulum. And on account of the earth's 
 oblateness a pendulum clock that keeps correct time at the 
 equator would gain about 4^^ minutes daily if taken to the 
 pole. As the surface of the sea may be considered as repre- 
 senting the form of the earth, this form might be determined 
 by timing the oscillations of a standard pendulum made at 
 the seashore in different latitudes. 
 
 It is interesting to follow the sequence of small effects 
 which result from the revolution of the earth upon its axis. 
 Some of these have been given in what precedes ; others will 
 follow in the proper place. 
 
 As the oblateness of the earth is so very small it is quite 
 sufficient for general purposes, as has been said before, to 
 regard the earth as a sphere with a radius of 3960 miles ; 
 but where accuracy is required the oblateness must be taken 
 into account. 
 
38 
 
 ASTRONOMY. 
 
 THE MOON. 
 
 The moon, as our nearest neighbor and our dependent, and 
 at the same time the heavenly body that ministers to our 
 comfort and enjoyment more than any other celestial body 
 except the sun, should be of sufficient interest to us to merit 
 our next consideration. 
 
 Owing to its proximity to the earth, the problem of finding 
 its distance is not a difficult one, and its features are readily 
 and satisfactorily studied by means of even a moderate-sized 
 telescope, an assertion that can be made of no other heavenly 
 body. 
 
 It is true that its alwaji-s presenting the same face to our 
 view is somewhat of a handicap to our knowledge of it, but 
 this peculiarity is not confined to our moon, and there is no 
 reason for believing that the invisible hemisphere is mate- 
 rially different from the visible one. 
 
 Before dealing with the problem of finding the moon's dis- 
 tance it is necessary to consider the subject of 
 
 18. Parallax. 
 
 A person at A has in front of him at some distance a tele- 
 graph pole P, and at a considerably greater distance a picket 
 fence. 
 
 He sees the telegraph pole projected on the fence at a ; that 
 is the pole hides from his view a certain picket at a. 
 
PARALLAX. 39 
 
 The observer now changes his position from A to B, and 
 then sees the pole projected on the fence at b. And thus as 
 the observer changes his position from A to B, the pole is 
 apparently displaced from a to b. 
 
 This displacement of the pole is called parallax; and we 
 may accordingly define parallax as an apparent displacement 
 of an object due to a real displacement of the observer. 
 
 The angular displacement of the pole along the fence is 
 the angle aAb, as seen from A. And if the fence were at an 
 infinite distance this angle aAb would become aAC, where 
 AC is parallel to Bb. 
 
 In the only cases with which we are concerned, the fence 
 becomes the surface of the heavens with the stars as pickets, 
 and is practically at an infinite distance. So that the angle 
 of parallax becomes the angle APB^aPb^aAC, since b and 
 C are coincident at the surface of the heavens. 
 
 When the parallax of a celestial body is large the body is 
 relatively near, and when it is small the body is relatively dis- 
 tant, provided the same base, AB, is employed in each case. 
 
 The moon has by far the greatest parallax of all the 
 heavenly bodies and is therefore the nearest to us. 
 
 Some of the stars have parallaxes of less than 1" when the 
 diameter of the earth's orbit, a length of over 180 million 
 miles, is taken as a base. And even with this enormous base 
 the majority of the stars have no appreciable parallax. 
 
 Limb. When a heavenly body presents a circular disc the 
 edge of the disc is called the limb, and different parts of the 
 edge are distinguished by naming them, as the upper limb, 
 the eastern limb, etc. As it is not practicable to observe the 
 centre of the disc, there being no point or mark to distinguish 
 it, observations are made upon the limb intsead. Thus, to 
 find the altitude of the sun, we measure the altitude of its 
 upper limb, and apply a correction for its semi-diameter. 
 
 19. Moon's Parallax. 
 
 If, when the moon is on the meridian we could suddenly 
 shift our position from one point to another many miles 
 north or south of the former, the displacement of the moon 
 amongst the stars, due to parallax, would be conspicuously 
 
40 ASTRONOMY. 
 
 evident. Or, if two observers on the same meridian, and 
 many miles apart, observe the moon when on their common 
 meridian, its position among the stars will not be the same 
 for each observer. 
 
 Now, Berlin in Germany, and the Cape of Good Hope are 
 nearly on the same meridian, while one is north of the equa- 
 tor and the other is south, and at each place there is a well- 
 equipped astronomical observatory. 
 
 In the diagram B is Berlin, C is the Cape of Good Hope, 
 and M is the moon. 
 
 Fig. 23. 
 
 The observer at B sees the moon projected amongst the 
 the stars at b, and the observer at C sees it projected at c. 
 
 To the observer at B the moon is south of the star T and 
 at a considerable distance from the star S, while to the ob- 
 server at C the moon is north of the star T and near the 
 star 6". 
 
 If we can find the parallactic angle BMC and the distance 
 BC as well as the angle MBC, we can calculate the distance 
 MB by simple trigonometry. 
 
 But the stars being practically at infinity, we have — 
 BMC=bMc—bBc= I QBS— L PBS. 
 So that if the observers zt BC each measure the angular dis- 
 tance of the star 5 from the upper or lower limb of the 
 moon, the difference of these measures is the parallactic 
 angle required. 
 
 The true place of the moon amongst the stars is its pro- 
 jection as seen from the earth's centre, and this is technically 
 called the Geocentric place of the moon. Considering the 
 earth as a sphere, to a person so situated as to have the moon 
 at his zenith, its observed place is also its true or geocentric 
 
PARALLAX, 41 
 
 place. But as seen from every other point the moon is dis- 
 placed by parallax, and the displacement increases as the 
 moon gets farther from the observer's zenith. The greatest 
 displacement is when the moon is on the observer's horizon. 
 This is called the moon's horizontal parallax, and its average 
 value is a trifle over S7'. 
 
 It is readily seen that the moon's horizontal parallax is the 
 angle subtended by the radius of the earth as seen from the 
 moon. Similarly the angle subtended by the earth's radius 
 as seen from the sun is called the sun's horizontal parallax. 
 
 An observer upon the earth is carried around by the earth's 
 diurnal rotation, and his position in regard to the moon is 
 continually changing ; which means that the moon's parallax, 
 with regard to any one place on the earth, is subject to con- 
 stant variation, which partly, at least, repeats itself in every 
 lunar day. 
 
 • :s 
 
 Fig. 24. 
 
 Thus if C be the centre of the earth, m be the moon, not 
 on the celestial equator, and 5'5' be the celestial sphere, the 
 geocentric place of the moon is at c. To a person situated 
 on the equator, as at A, and carried by diurnal rotation along 
 the equatorial circle AWB, the moon would appear to move 
 in an ellipse eawh having its center at c, except that only one- 
 half of this ellipse could be observed. 
 
 If the moon were on the celestial equator this ellipse would 
 become a straight line passing through c. If the observer 
 moved towards the north pole the ellipse would move south- 
 wards and diminish in size; and when the north pole was 
 reached the ellipse would become a point, with a maximum 
 downwards displacement. 
 
 All these displacements taken together are sometimes 
 spoken of as the moon's diurnal parallax. 
 
42 
 
 ASTRONOMY. 
 
 When we consider, then, these parallactic displacements of 
 the moon, and bear in mind that the moon is at the same 
 time moving eastwards among the stars, we can understand 
 that the moon's apparent motion in the heavens from the 
 time of its rising to that of its setting is one of considerable 
 complexity. 
 
 The moon's true place is independent of the position of the 
 observer, and is recorded in the ephemeris from hour to hour, 
 and its apparent place is to be got by the application of a 
 number of corrections depending upon the latitude of the 
 observer, the moon's declination, its distance from the local 
 meridian, etc. 
 
 When the moon is on the horizon its parallax is the hori- 
 rontal parallax, and when it is at the zenith its parallax is 
 zero. 
 
 At any altitude, not 90°, the moon is displaced downward, 
 and this is called the moon's parallax in altitude. 
 
 20. Moon's distance. 
 
 If we could find the moon's horizontal parallax directly by 
 observation, nothing would be easier than to find the moon's 
 distance by application of the formula s^=r6. This might be 
 done under certain special arrangements, but as observatories 
 are situated, not at special, but at convenient points, it is 
 more practicable to follow another course, as follows : 
 
 Fig. 25. 
 
 C is the earth's centre and m is the moon's northern limb, 
 and the problem is to find Cm. 
 
 Let A and B be two observers on the same meridian, or 
 nearly so, as at Berlin and the Cape of Good Hope. And let 
 
MOON'S DISTANCE. 43 
 
 their latitudes be denoted by / and /'. Then the angle ACB is 
 l-\-l'. The observers measure the zenith distances ZAm and 
 Z'Bm respectively. Denote these by s and s'. Also let r be 
 the radius of the earth, and denote the distance Cm by x, the 
 angle AniC by a, andSwC by (8. 
 
 From the sine formula of plane trigonometry, 
 
 sin a^(r/x)sm s, and sin p=(r/x)sm :::'. 
 .'. sin a-j-sin ^^(r/x) (sin s+sin s'). 
 But by a well-known formula, 
 
 sin a+sin;8=2 sin4(a+y8)cos ^(a — p). 
 And a — ;8 is necessarily a small angle, and -J (a — ^) will not 
 exceed 10', so that cos^(a — ^^)^1 without any appreciable 
 error. Thence by substitution, 
 
 x^^r(sm z-\-sm .s')/sin -Jfa-f-yS). 
 But ACBM is a quadrangle and the sum of its angles is four 
 right angles; and these angles are 
 
 a+^, 180°— ,s, 180°— s', and /+/'. 
 .-. a^l3=z^s'—l—l'. 
 And finally, 
 
 A'=-Jr(sin s+sin z') /s\n^{s-\-z' — / — /'). 
 
 Illustration. Suppose for illustration that /=30°N., /'= 
 20°S., and that z and ^ are found to be 35° and 15° 48' re- 
 spectively. Then sin .s-j-sin .^'=0.84586, 
 
 sin i {s-\-z'—l—l' ) =sin 24'=0.00698. 
 
 And x=JrX0.84586/0.00698=60.6r. 
 
 This makes the moon's distance from the centre of the 
 earth to be 60.6 times the radius of the earth, or about 
 240,000 miles if the earth's radius is taken as 3960 miles. 
 And this is about correct. 
 
 Spectroscopic illustration. This is an illustration of the 
 effects of parallax. We have two pictures, of two stars and 
 the moon between them, separated by a vertical line. But 
 the moon is represented as being displaced by parallax, with 
 reference to the stars, to the left in the left picture and to the 
 right in the right picture. Consequently the moon should ap- 
 pear nearer than the stars if the left picture is viewed by the 
 
44 ASTRONOMY. 
 
 right eye and the right picture by the left eye. And the moon 
 should appear more distant than the stars if the left picture 
 be viewed by the left eye and the right by the right eye. 
 
 o 
 
 o 
 
 Fig. 26. 
 
 To view the pictures properly, (1) cut a rectangular hole 
 about 1 in. by f in. through a piece of cardboard. Hold the 
 page fairly before the eyes about 12 in. distant, and look at 
 it through the opening in the cardboard, it being about 5 in. 
 in front of the eyes with its longer dimension right and left, 
 and so situated that the left eye can see only the right figure, 
 and the right eye, the left figure. A little practice will unite 
 the figures, when the moon will appear to come forwards and 
 leave the stars in the distance. (2) Cut a slip of cardboard 
 about 1^ in. wide and 4 in. long. Holding the book as before, 
 hold the slip of cardboard with its longer dimension vertical, 
 and in such a position that the right eye can see only the right 
 figure, and the left eye only the left one. Upon now uniting 
 the figures the stars appear to come to the front and leave 
 the moon in the background. 
 
 In this illustration the stars become the fence, the moon 
 the telegraph pole, and the eyes become the observers at A 
 and B. In (1) the telegraph pole is in front of the fence, and 
 in (2) behind it. 
 
 21. Moon's diameter. 
 
 The angle subtended by the disc of the moon, or the 
 moon's angular diameter, is about 31', and its distance is 
 240.000 miles. 
 
MOON'S DISTANCE. 
 
 45 
 
 Plence the moon's diameter = (31/60) X240000Xt/180 
 =2160 miles. 
 
 The moon's diameter is thus three-elevenths of that of the 
 earth. And as the volumes of spheres are proportional to 
 the cubes of their diameters we find the volume of the earth 
 to be about 50 times that of the moon. 
 
 Variation in moon's distance. The average angular dia- 
 meter of the moon is about 31', but this angle is variable, 
 ranging from 29^' to 33', as represented in the diagram. 
 
 2S I OOO m. 
 
 Z2SOOO m. 
 
 Fig. 27. 
 
 Now, as the moon does not change its linear diameter, it 
 must change its distance from the earth ; and by the applica- 
 tion of the formula s-=rd we readily find that when the angu- 
 lar diameter is 29 J' the distance is 251,000 miles, and when 
 33' the distance is 225,000 miles. These distances are repre- 
 sented by the relative lengths of the lines in the diagram. 
 
 The mean of these two extreme distances is 238,000 miles, 
 and this we shall take as the average distance of the moon. 
 
 The rising and setting of the moon, as of the sun and stars, 
 is due to the rotation of the earth on its axis. 
 
 Fig. 28. 
 
46 
 
 ASTRONOMY. 
 
 22. Moon's diurnal augmentation. 
 
 Let A'' be the north pole of the earth, and M be the moon, 
 and for simplicity of explanation suppose the moon to be on 
 the celestial equator. To the observer at A the moon is on 
 the horizon and is rising. When, by the earth's rotation, the 
 observer comes to B he is nearly 4000 miles nearer to the 
 moon than he was at A, and the moon must appear larger 
 than at A. This increase in the moon's apparent diameter is 
 known as the moon's diurnal augmentation, as it is repeated 
 in every lunar day. Its greatest amount is about one-half a 
 minute of angle. 
 
 To most people the moon appears to be larger when rising 
 and setting than when far up in the heavens. This, however, 
 is an optical illusion arising from the fact that when the 
 moon is on the horizon we have objects such as trees and 
 
KEPLER'S LAW L 47 
 
 buildings with which to compare it, while there are no such 
 objects for comparison wlien the moon is far up. In like 
 manner the distance across a considerable body of water ap- 
 pears less than the same distance on land where there are 
 various intervening objects. 
 
 In the illustration the two circles are exactly of the same 
 size, but upon viewing them carefully the upper circle appears 
 to be the smaller one. 
 
 23. Kepler's law, I. 
 
 John Kepler lived from 1571 to 1630. By a persistent 
 course of trial, extending over many years, and involving an 
 immense amount of arithmetical computation, he discovered 
 three laws in regard to the motions of planetary bodies; and 
 these go under his name. 
 
 Newton was not born until 1642, so that Kepler knew 
 nothing of the law of gravitation as developed by Newton, 
 and yet all his three laws have subsequently, by means of 
 mathematical analysis in the hands of Newton himself 
 been proved to be correct. 
 
 The first law is — All the planets move in ellipses having 
 the sun at a focus. 
 
 This may be more fully stated as follows : A body re- 
 volving under the pull of a central force whose intensity 
 varies inversely as the square of the distance, describes a 
 conic section with the centre of force as a focus. 
 
 For all the planets and satellites the conic is an ellipse, so 
 that, barring disturbing influences, the moon's path is an 
 ellipse with the earth at a focus. 
 
 The Ellipse. The ellipse is so common a curve in astro- 
 nomy that it is impossible to proceed intelligently without 
 knowing some of its more obvious properties. 
 
 Put a sheet of white paper on a smooth table and pin it 
 down by two pins S and F. 
 
48 
 
 ASTRONOMY. 
 
 Make a loop of thread, not too large but so that it will 
 drop over the pins easily. With a pencil, as at P, draw the 
 thread until the loose parts PS, SP, and PP become straight. 
 Under these conditions, the pencil, upon being moved over 
 the paper, will mark out or describe an ellipse. 
 
 B' 
 
 Fig. 30. 
 
 The points 5" and P are the foci. The point C, bisecting 
 SP, is the centre, and the curve is symmetrical, for opposite 
 points, about the centre. AA', drawn through the foci and 
 centre, is the axis major ; and BB' drawn through C, perpen- 
 dicular to AA', is the axis minor ; and the ratio CP/CA is the 
 eccentricity. 
 
 With a fixed length of loop it is readily seen that when 5' 
 and F come near together the ellipse approaches the form of 
 a circle, becoming a circle when S and F are coincident. On 
 the other hand, as 5" and P get further apart the ellipse tends 
 to become long and narrow, and the eccentricity, which is 
 zero in the circle, approaches unity. 
 
 To describe an ellipse which properly represents the form 
 of the moon's orbit we should put the pins 1 unit apart and 
 make the double loop 9.7 units long, or containing 19.4 
 units of thread, where the unit may be any length unit con- 
 venient. 
 
 This ellipse will be found to be scarcely distinguishable 
 from a circle, but it is quite readily seen that the earth is not 
 at the centre (Fig. 31). 
 
MOON'S ORBIT. 
 
 49 
 
 The point P, where the moon is nearest the earth, is the 
 perigee, and when the moon is at this point in its orbit it is 
 said to be in perigee. The opposite point, A, where the moon 
 
 is farthest from the earth, is the apogee. And the line con- 
 necting these points is the apsis line or line of apses. 
 
 24. Mass-centre. 
 
 Observations certainly show that the moon appears to re- 
 volve about the earth, moving from west to east amongst the 
 stars so as to complete its circuit in a little less than a month, 
 but how do we know that this is not a deceptive appearance 
 arising from the revolution of the earth about the moon? 
 The question is quite a proper one to be answered. 
 
 (D- 
 
 Fig. 32. 
 
 A and B are two leaden balls of which A is much larger 
 than B, and they are held together by a rod AB which, for 
 
50 ASTRONOMY. 
 
 simplicity of explanation may be supposed to be without 
 weight. A thread, CC, is attached to the point C about which 
 the system balances. By twisting the thread, without other- 
 wise displacing the system, the balls may be made to revolve 
 about one another. 
 
 It will be noticed that while the balls travel around in cir- 
 cles, the point C remains still. This point about which the 
 revolutions take place is the mass centre or centre of gravity 
 of the system. This centre divides the distance between the 
 centres of the balls into parts which are inversely propor- 
 tional to the weights of the balls. Thus if A is 10 times as 
 heavy as B, C is 10 times as far from the centre of B as it is 
 from the centre of A. 
 
 The system described is not like a piece of mechanism. 
 There is nothing to keep C in position or to restrain it from 
 moving from side to side, the only purpose of the thread 
 being to keep the system from obeying the pull of gravity 
 and falling to the floor. If the string were cut while the 
 balls were revolving, their relative motions would not be in- 
 terfered with in any way, while the point C would move 
 directly along the line of the earth's attraction. 
 
 Now various considerations have shown that the earth is 
 about 80 times as heavy as the moon, being apparently 
 formed of denser or more compacted material, so the mass 
 centre of the two bodies is Vso of 240,000 miles, or 3000 
 miles from the earth's centre, or at a point 1000 miles below 
 its surface. Generally speaking, then, it would savor of 
 pedantry to say that the moon does not revolve about the 
 earth, but about a point 1000 miles below its surface, ^al- 
 though the latter statement would be the correct one. And, 
 in fact, it would be quite right to say that the earth revolves 
 about the moon, if anything in the way of explanation were 
 to be gained thereby, for in either case outside phenomena 
 would be but little, if at all, interfered with. 
 
 We see, then, that the path of the earth's centre as it 
 moves along in its orbit about the sun, is not a smooth line 
 or curve, but a wavy one, in which a wave is completed at 
 every revolution of the moon. This throws the centre out 
 
THE TIDES. SI 
 
 to the extent of nearly 3000 miles, first to one side of the 
 ideal orbit and then to the other, besides alternately retarding 
 and accelerating its motion. 
 
 Here, then, is a source of small displacements and disturb- 
 ances which must be taken into consideration wherever ac- 
 curate observations and results are concerned. And it is a 
 blessing to the astronomer that the stars are so far away as 
 to suffer no parallax from these numerous small displace- 
 ments. 
 
 25. The Tides. 
 
 As has been already pointed out, the attraction of the 
 moon upon the earth tends to elongate the earth in the line' 
 of attraction, and so also does the attraction of the sun. But 
 it has been shown in a variety of ways that, while the sur- 
 face of the earth is largely covered with a light mobile liquid, 
 water, the body of the earth in itself is as rigid as steel. So 
 that while the pull of the moon may affect the whole earth 
 to a very minute extent, it is chiefly expended in raising two 
 heaps of water, one facing the attracting body, and the other 
 upon the opposite side of the earth. These are known as 
 the tides. 
 
 ?«A?7 of -thg. WOOft 
 
 ^3 
 
 Fig. 33. 
 
 On account of the proximity of the moon to the earth the 
 tides due to lunar influence are much greater than those due 
 to solar influence. For the formation of the tides is due not 
 so much to the relative force of the attraction itself, as to 
 the difference of attraction on the opposite sides of the earth, 
 and therefore to the ratio of the earth's diameter to the dis- 
 tance of the attracting body. 
 
 As the earth rotates on its axis these heaps of water, tend- 
 ing to keep beneath the moon and also on the side of the 
 earth opposite the moon, sweep over the surface of the sea 
 from east to west, something like two very broad and shallow 
 
52 ASTRONOMY. 
 
 waves. They are not, however, properly waves, and do not 
 possess the prominent property of waves, the recurrence after 
 short periods of time. 
 
 Upon the open ocean the tides do not rise to a height of 
 more than two or three feet, and instead of being a visible 
 wave with a crest, it is merely a slight elevation of the sur- 
 face of the sea, which thins out in every direction for hun- 
 dreds, and possibly for thousands of miles, where the ocean 
 is sufficiently extended. 
 
 When this tidal accumulation of water, in its onward pro- 
 gress, encounters some properly disposed shore and is di- 
 rected into a wedge-shaped estuary, the water may rise from 
 30 to 60 feet, and rush rapidly for some distance up the 
 channels of properly exposed rivers, thus forming an inrush 
 of water known as the bore. These phenomena are to be 
 seen in the Bay of Fundy and the St. John's river, and in fact 
 upon any eastern shore of a continent. 
 
 The eastern shore of a continent is met by the tide with 
 full force, while there is no counteracting influence on the 
 western shore, as the tide there is less pronounced, and 
 mostly the result of reflex action. This must act as a sort 
 of break to the earth's rotation and should tend to lengthen 
 the day. But it is generally held that the heaving up of 
 moimtain ranges and some other related phenomena are due 
 to a contraction of the earth through a slow loss of its inter- 
 nal heat. This contraction tends to increase the rate of 
 diurnal rotation and thus to shorten the day. These oppo- 
 site tendencies pretty much annul one another, and it does 
 not appear that the day has changed its length by as much 
 as one second in the last hundred years. 
 
 When the sun, moon, and earth are in line the solar tides 
 augment the lunar ones, and we have high tides known as 
 spring tides. And when the directions of the sun and moon 
 are at right angles as seen from the earth, the solar tides tend 
 to reduce the lunar ones, and we have low or neap tides. 
 
 People, like fishermen, who have much to do with the sea 
 notice many peculiarities in the tides. Thus the two tides 
 which occur about 12^ hours apart are usually not of equal 
 
THE TIDES. 53 
 
 magnitude, the one under the moon being sometimes greater 
 and sometimes less than the tide opposite the moon, the 
 change from greater to less, and back again, taking place in 
 about a month. Of course all these variations are logically 
 explainable. Consider a seaport in north latitude at about 
 45° say. When the moon is on the equator the two tides will 
 be about of equal size. As the moon goes south from the 
 equator the tide under the moon grows less than the one op- 
 posite the moon, and as the moon goes northwards from the 
 equator the opposite effect is produced. And the moon in its 
 orbit crosses the equator twice in each revolution. 
 
 To dwellers inland the times of high water are of only 
 secondary importance. But in many seaport towns the ar- 
 rival and departure of vessels of large size can be safely 
 effected only near the time of high water, and in such places 
 the times of high water are given publicly from day to day. 
 
 26. Moon's one face. 
 
 Long ago in the past ages of the earth, when the moon 
 was )'oung, it must have been soft and plastic, with more or 
 less liquified matter upon its surface. The attraction of the 
 earth upon the moon under these conditions must have raised 
 immense tides upon the lunar surface, for the power of the 
 earth to raise tides upon the moon is somewhere about 500 
 times the power of the moon to raise tides upon the earth. 
 These lunar tides acting as a gigantic break upon the axial 
 rotation of the moon has brought it to rest relatively to the 
 earth. So that now the moon rotates on its axis in the same 
 time as it revolves about the earth, and thus presents, prac- 
 tically, always the same face to the earth. And this is the 
 fate, whether as yet realized or not, of every moon which 
 revolves about a planet much larger than itself. 
 
 THE SUN. 
 
 Astronomical symbol O. 
 
 The sun is a fixed star. And although it does not take 
 rank as one of the hottest, or the brightest, or the largest of 
 
54 ASTRONOMY. 
 
 the stars of the universe, it is to us the all-important one — 
 the great centre of attraction — the bountiful dispenser of 
 light and heat to every creature which dw^ells in this solar 
 universe. One of the first questions, then, that we are dis- 
 posed to ask in regard to this wonderful luminary is as to 
 its distance from us. How far away is the sun? 
 
 27. The Sun's distance. 
 
 The finding of the distance of the sun is one of the old 
 and difficult problems of astronomy, and it is only in com- 
 paratively recent times that any real success has been 
 achieved in its solution. Much of this success has come 
 through channels which were quite unknown to ancient and 
 mediaeval astronomers. 
 
 The sun is so far distant and its parallax is accordingly so 
 small that methods like those applied to the moon are quite 
 useless, for the unavoidable errors of observation hold so 
 large a ratio to the whole parallax as to vitiate and render 
 untrustworthy any results arrived at. 
 
 As we are not yet prepared to show how the sun's hori- 
 zontal parallax is found, we shall in the meantime assume its 
 value to be 8".8, leaving it to a future occasion to show how 
 so small an angle is determined. 
 
 As the sun's horizontal parallax is the angle subtended by 
 the earth's radius as seen from the sun, we apply the formula 
 s=zr6 and obtain : 
 
 3960=Z?X8.8XV(3600X180) 
 whence £»=92,900,000 miles, nearly. 
 
 And for the average distance of the sun we shall take 
 £>=:93,000,000 miles. 
 
 This is easily shown to be nearly 400 times the distance of 
 the moon. 
 
 Owing to these large numbers it is not practicable to draw 
 to scale a diagram or plan representing the system of the sun, 
 the moon, and the earth. 
 
EARTH AND SUN. 55 
 
 For, if the earth were represented by a small circle one- 
 tenth of an inch in diameter, the moon would be represented 
 by a circle only one thirty-sixth of an inch in diameter, at 
 the distance of three inches from the earth, while the sun 
 would be a circle 10.8 inches in diameter at a distance from 
 the earth of about 98 feet. 
 
 These considerations make it clear that diagrams repre- 
 senting astronomical sizes and distances, as they actually 
 appear in illustrated books, however necessary they may be 
 as illustrations, must unavoidably be, at times, exaggerated 
 along certain lines if they are to appear at all. 
 
 Thus the figures picturing the comparative sizes of the 
 planets are usually on a scale many times as great as that 
 upon which comparative distances are pictured. And some 
 comparisons of astronomical distances cannot be properly 
 made upon any scale whatever, great or small. 
 
 Thus, as the sun is about 400 times as far from the earth" 
 as the moon is, if the distance of the moon be represented by 
 one-tenth of an inch the sun's distance would become 40 
 inches, and that of the most distant planet, Neptune, about 
 100 feet, measures altogether impracticable in graphic illus- 
 tration. 
 
 28. Sun's Diameter. 
 
 Knowing the mean distance of the sun, it is an easy matter 
 to find the sun's angular diameter and then to find its dia- 
 meter in miles by using the formula s=rd. For r is 93,000,000 
 miles, and 6 is the radian measure of 32', which is the mean 
 angular diameter of the sun, and this gives about 850,000 
 miles for the sun's linear diameter. 
 
 This is nearly 108 times the diameter of the earth, so that 
 it would require 108 earths placed side by side to reach 
 across the sun. 
 
 As a consequence, to represent truthfully the comparative 
 sizes of the earth and the sun, we may take a small circle 
 one-twelfth of an inch in diameter to represent the earth, 
 and a circle of 10.8 inches in diameter for the sun, as in the 
 diagram, where only a part of the sun's disc is shown. 
 
56 ASTRONOMY. 
 
 ^ Ear't'li 
 
 Ltmb al the Su. 
 
 Fig. 34. 
 29. Volume of the Sun. 
 
 As the volumes of the spheres are proportional to the cubes 
 of their diameters, the volume of the sun is(108)^=l,250,000 
 times, nearly, that of the earth; in other words, it would 
 require one and a quarter millions of bodies like this earth 
 to make one body equal in bulk to the sun. 
 
 These illustrations show us clearly the insignificance in 
 size of this great round world of ours, where so many things 
 are done, where so many human beings live, and work, and 
 jenjoy themselves, and suffer, and die, in comparison with 
 the mighty sun, which warms us, and lights us, and cheers 
 us, and gives us all the material comforts that we possess. 
 
 And yet for untold ages people believed that the sun actu- 
 ally performed a daily journey around the earth in order to 
 give us the alternation of day and night. And no doubt a 
 few ignorant people believe it still, in spite of the absurdity 
 of such a view in the presence of the comparative sizes of 
 the two bodies. 
 
 However, as explained in connection with the moon, the 
 earth and sun revolve about their common mass centre, which 
 is a point about 300 miles from the centre of the sun, and if 
 explanations are rendered more simple by doing so, there is 
 no objection, but rather an advantage, in considering the 
 sun as travelling around the earth once in a year to bring 
 in the seasons. 
 
 Only one view is consistent with the principles of physics, 
 namely, that the bodies revolve about their common mass 
 centre, but which view we adopt as a matter of explanation 
 is in many cases quite immaterial, as all motion is relative, 
 and phenomena are unchanged. 
 
 In consideration of these facts, we shall adopt that view 
 which may at the time be most convenient. 
 
EARTH'S ORBIT. 57 
 
 30. Sun's angular diameter. 
 
 The angular diameter of the sun, like that of the moon, is 
 not constant, but varies from 32' 36".4 at its greatest, to 
 31' 31".8 at its least, giving a difference of 1'4".6. 
 
 This shows that the distance of the sun is variable. Work- 
 ing out the greatest and least distances as given by the least 
 and greatest apparent diameters, we get : 
 
 Date. Angular diam. O 's distance. 
 
 Jan. 1st 32' 36".4 91,197,000 miles. 
 
 July 1st 31' 31".8 94,312,000 " 
 
 31. Earth's Orbit. 
 
 The earth's orbit is an ellipse, with the sun at one of the 
 foci, thus satisfying the first law of Kepler. The distance 
 of the sun from the centre of the ellipse is about 1,600,000 
 miles. 
 
 The point where the earth is nearest the sun is the peri- 
 helion, and the point at which it is most distant is the 
 aphelion. 
 
 At present the earth is in perihelion on Jan. 1st, and in 
 aphelion on July 1st. And thus, strange as it may appear, 
 inhabitants of the northern hemisphere are nearer the sun 
 in the depths of winter than they are in the warmth of sum- 
 mer. For those in the southern hemisphere the case is, of 
 course, just the reverse. 
 
 This may have some effect on the seasons in the different 
 hemispheres in the way of making the extremes of tempera- 
 ture in the southern hemisphere somewhat greater than in 
 the northern one, but such effect, if any, does not appear to 
 be very strongly marked. 
 
 32. Kepler's law, II. 
 
 In orbital motion of one body about another, as the moon 
 about the earth, or the earth about the sun, etc., the line 
 joining the two bodies is called the radius vector ; and it is a 
 physical principle in astronomy, known as Kepler's second 
 law, that the radius vector sweeps over equal areas in equal 
 times. 
 
58 ASTRONOMY. 
 
 Let ABP represent the earth's elliptic orbit, necessarily 
 much exaggerated in eccentricity in order to strengthen the 
 illustration, and let 5 be the sun, P the perihelion and A the 
 aphelion. 
 
 Starting from P, let the earth arrive at Q at the end of 
 one week, say, at R at the end of two weeks, at T at the end 
 of three weeks, etc. Then Kepler's law II tells us that the 
 sectorial areas PSQ, QSR, EST, etc., are all equal. 
 
 Fig. 35. 
 
 But SP is less than SQ, and SQ is less than SR, which is 
 again less than ST, and each is less than SA. 
 
 Hence PQ is greater than QR, QR is greater than RT, etc. 
 
 But as these arcs are each described in the same time of 
 one week, the earth must move more rapidly from P to Q 
 than from Q to R, etc. Or, in other words, the earth moves 
 most rapidly at the perihelion P, and its motion is gradually 
 retarded until it reaches aphelion at A, at which point it 
 moves most slowly. After passing A its velocity is gradually 
 accelerated until it arrives at P again. 
 
 Consistently with this theoretical inference, observations 
 made upon the sun's apparent daily motion along its path in 
 the heavens — that is, the earth's real motion in its orbit — 
 gives 61' 9" on January 1st, and 57' 11" on July 1st, the 
 mean daily motion for the whole year being 59' 8". 2. 
 
ECLIPTIC AND EQUATOR. 
 
 59 
 
 33. The Ecliptic. 
 
 The plane of the earth's orbit, extended out indefinitely, 
 meets the sphere of the heavens in a great circle which is 
 called the ecliptic. This plane, and consequently the ecliptic, 
 holds the same position in regard to the stars as a whole, or 
 to the celestial sphere, from year to year and presumably 
 from age to age, as any slight variations in its position appear 
 to be very limited in magnitude, periodic, and more apparent 
 than real. 
 
 As a consequence the ecliptic is the one and only fixed and 
 permanent element of reference in astronomy, and all other 
 elements are finally referred to the ecliptic. 
 
 The other great circle in the heavens which, for our pur- 
 poses, is equally as important as the ecliptic, but not equally 
 as fixed, is the celestial equator. 
 
 These two great circles intersect at opposite points in the 
 heavens at an angle of 23° 27', which is known as the angle 
 of obliquity of the ecliptic. 
 
 The ecliptic and the equator. In representing these circles 
 upon the plane of the paper, as is often necessary, some of 
 them will appear in the diagram as ellipses. And we must 
 assume the impossible condition that we are viewing the 
 universe from some outside standpoint. But these things 
 should not mislead any intelligent reader. 
 
 Let E be the earth and 5' the sun, and let the line XF be a 
 section of the plane of the ecliptic, passing, as it does, through 
 the centres of the earth and the sun. 
 
60 ASTRONOMY. 
 
 Let KF be a section of the plane of the equator, making 
 the angle KEX^SEF=23° 27', and if P be in the direction 
 of the celestial pole, making the angle PES=66° 33', this 
 latter being the inclination of the earth's axis to the ecliptic. 
 
 Now let GH be a section of a plane through the sun's cen- 
 tre and parallel to the plane of the equator. 
 
 The two planes of which KF and GH are sections meet at 
 the surface of the heavens to form one and the same great 
 circle, the celestial equator. So that as far as the celestial 
 equator is concerned it is immaterial whether we consider the 
 plane of the equator as passing through the centre of the 
 earth, or through that of the sun. 
 
 But with the terrestrial equator it is different. For this 
 curve should be the intersection of the surface of the earth 
 by the plane of the celestial equator. So that if we wish to 
 consider this plane as being fixed it is simpler to look upon 
 the earth as being fixed, and the sun as making an annual 
 journey around it in the plane of the ecliptic; and this is the 
 view usually taken in illustrations. 
 
 That the phenomena concerned are independent of which 
 view is taken is shown by the fact that the idea of a fixed 
 earth prevailed for thousands of years before the modern 
 and correct state of affairs became known, and yet the same 
 phenomena are present now as then, and have been present 
 during all the past time. 
 
 34. Nodes and Solstices. 
 
 The diagram (Fig. 37) shows the earth E at the centre, the 
 celestial equator QQ'. the poles of the heavens Np, Sp, and 
 the ecliptic Ws, Ss. P is the pole of the ecliptic. 
 
 As the ecliptic and the celestial equator are both great cir- 
 cles in the heavens, they intersect in two opposite points A 
 and D on the sphere of the heavens. The sun, S, is repre- 
 sented as moving along the ecliptic, the arrow showing the 
 .direction of motion, and it is in the position that it would 
 have about the latter part of February. 
 
NODES AND SOLSTICES. 
 
 61 
 
 The half of the celestial sphere which lies north of the 
 equator is said to be above the equator, and the other half 
 belozv. As the sun moves onwards it comes to A, the ascend- 
 ing node, about March 20th or 21st. Here it passes from 
 below to above the equator, and hence the name of the node. 
 For the next three months the sun rises higher and higher 
 above the equator until it reaches the highest point, Ss, about 
 
 Fig. 37. 
 
 June 23rd. This is called the summer solstice, because the 
 season of summer begins, and the sun having ceased to rise 
 higher towards the pole, begins to descend. The day is now 
 the longest in the year for those dwelling in the northern 
 hemisphere, and the night is the shortest. 
 
 For the next three months the sun gradually works south- 
 wards until it reaches the descending node on Sept. 22nd or 
 23rd. Here it crosses from above the equator to below. 
 Working southwards for another three months, the sun ar- 
 rives at the winter solstice, Ws, on Dec. 21st. Winter now 
 begins, and the sun, turning northwards again, arrives in due 
 
62 
 
 ASTRONOMY. 
 
 time at the point from which it set out, and the circle of the 
 year is complete. 
 
 The point A is also called the vernal equinox, because 
 when the sun reaches this point spring begins, and the days 
 and nights are of equal length. For similar reasons the point 
 D is called the autumnal equinox. 
 
 In the next diagram we have the ecliptic as seen from its 
 pole, with the earth at its centre. 
 
 Fig. 38. 
 
 The full radial lines divide the circle into 12 parts corre- 
 sponding to the 12 months of the year, but instead of mark- 
 ing the beginnings of the months they indicate from the 20th 
 to the 23rd of the month, and the round dots indicate the 
 positions of the sun at these dates. The months are denoted 
 by their initial letters. Thus M at the ascending node means 
 March 20th, S at the descending node, Sept. 23rd, etc. 
 
 The dotted line is the line of apses joining the perihelion 
 and the aphelion. 
 
 As the sun moves most rapidly near perihelion and most 
 slowly about aphelion, it is readily seen that the sun will 
 move from the descending node around by the winter solstice 
 
THE ZODIAC. 63 
 
 to the ascending node, in less time than it will do the remain- 
 ing half of the orbit. Or, in other words, as the summer 
 solstice is north of the equator, the sun should be north of 
 the equator for a longer period than it is south of the 
 equator. This will be practically shown by counting as fol- 
 lows : 
 
 Sun north of Equator Sun south of Equator 
 
 March 11 days. September-.. .. 7 days. 
 
 April 30 days. October 31 days. 
 
 May 31 days. November 30 days. 
 
 June 30 days. December 31 days. 
 
 July 31 days. January 31 days. 
 
 August 31 days. February 28 days. 
 
 September .. ..23 days. March 20 days. 
 
 Total 187 days. Total 178 days. 
 
 It thus appears that in the northern hemisphere the spring 
 and summer together are about nine days longer than the 
 autumn and winter together. In the southern hemisphere 
 matters are. of course, reversed. 
 
 It might appear, at first, that the earth receives more heat 
 from the sun while the sun is north of the equator than it 
 does while the sun is south of the equator, since the former 
 period is nine days longer than the latter. But as the sun 
 is farther away during the former period than it is during 
 the latter the difference in time is compensated by the differ- 
 ence of distance, and the amount of heat received during 
 each period is the same. 
 
 35. The Zodiac. 
 
 Five planets, not counting the earth, which was supposed 
 to be the centre, or the moon, were known to the ancients, 
 namely, Mercury, Venus, Mars, Jupiter and Saturn. These, 
 while appearing to travel around the earth, really travel 
 around the sun, each in its own respective orbit, and the 
 planes of these orbits extended to the heavens give us five 
 great circles ; and the plane of the moon's orbit gives us a 
 sixth. These six circles, while each crossing the ecliptic at 
 two opposite points called their respective nodes, yet lie so 
 
64 ASTRONOMY. 
 
 near the ecliptic that none of them depart from it at any 
 point by an angle as great as 9°, while for the most of them 
 the angle of departure is far below this limit. 
 
 If, then, we consider a belt about the heavens, extending 
 
 in breadth to 9° on each side of the ecliptic, or 18° in all, 
 
 this belt forms a pathway, or highway, so to speak, along 
 
 which the sun, the moon, and all the older planets appear to 
 
 travel. This belt is called the zodiac. 
 
 
 ^er'^iy r 
 
 ^ _-—-=--.. ^ -w ci , fit.: f 
 
 ...--- "' 
 
 
 o'. ■"•»■" 
 
 Vp- 
 
 Fig. 39. 
 
 The figure represents the zodiac as if cut across and 
 opened into a flat belt, which should be in the proportion of 
 20 in length to 1 in breadth, but of which the width is exag- 
 gerated in order to make it more distinct. The line through 
 the middle is the ecliptic or apparent path of the sun. The 
 dotted curved line represents the track of the moon, and the 
 curved line of short strokes, the path of the planet Mercury, 
 both for the year 1880. The points at which the paths cross 
 the ecliptic are the nodes and are marked by round dots. 
 
 The origin of the zodiac is lost in the obscurity of the past. 
 But it probably originated with the early Chaldeans or Baby- 
 lonians, if not even earlier, as picture drawings of the zodiac 
 are found in prehistoric and ancient remains in parts of the 
 world far removed from one another, as in Babylonia, 
 Egypt, India, Mexico, etc. 
 
 That the zodiac should be of singular importance in 
 ancient times is quite natural. For the only bodies in the 
 celestial vault that appear to possess the power of moving 
 from place to place at will, and thus seem to be endowed with 
 life, are the sun, the moon, and the visible planets. To the 
 ancient priest-astronomer, then, these appeared to be gods 
 or the dwellings of gods ; and next to the gods themselves. 
 
THE ZODIAC. 65 
 
 what could be of greater interest than the broad and well- 
 travelled pathway which they followed in their march 
 through the field of stars ? 
 
 ^ As to the division of the zodiac into parts or regions, it 
 appears to have been at first divided into 6 parts, which were 
 afterwards increased to 12 ; however, there is some uncer- 
 tainty about this. In later times, however, the zodiac was 
 divided into 12 parts, thus forming 12 constellations, or 
 groups of stars, known as the 12 signs of the zodiac. These 
 are mostly named after animals which they were supposed to 
 represent, although the real significance of the names is prob- 
 ably to be traced much further back. The name zodiac is 
 from the Greek word for an animal. 
 
 The zodiac has come down to us almost unchanged, and 
 the names of the constellations and the symbols which stand 
 for them are here given : 
 
 Aries, or the Ram. 
 Taurus, or the Bull. 
 Gemini, or the Twins. 
 Cancer, or the Crab. 
 Leo, or the Lion. 
 Virgo, or the Virgin. 
 Libra, or the Balance. 
 Scorpio, or the Scorpion. 
 Sagittarius, or the Archer. 
 Capricornus, or the Goat. 
 Aquarius, or the Waterbearer. 
 Pisces, or the Fishes. 
 
 The English names are also very neatly introduced in the 
 accompanying rhyme : 
 
 The Ram, the Bull, the heavenly Twins, 
 And next the Crab, the Lion shines, 
 The Virgin, and the Scales, 
 The Scorpion, Archer, and he-Goat, 
 The man who bears the Watering-pot, 
 And Fish with glittering tails. 
 
 1. 
 
 T 
 
 2. 
 
 « 
 
 3. 
 
 n 
 
 4. 
 
 s 
 
 5. 
 
 a 
 
 6. 
 
 m 
 
 7. 
 
 ,^ 
 
 8. 
 
 HI 
 
 9. 
 
 t 
 
 10. 
 
 YS 
 
 11. 
 
 /v^ 
 
 12. 
 
 K 
 
66 ASTRONOMY. 
 
 These constellations, like all others, are irregular in out- 
 line, of no definite form, they over-reach the limits of the 
 zodiac belt, and fail to fill in to such an extent that other 
 constellations, not of the zodiac, occasionally trespass on the 
 belt in order to avoid open spaces in the heavens. 
 
 The scheme, as it stands, can scarcely be called scientific, 
 and any scheme that could be adopted would labor under 
 unavoidable difficulties. 
 
 The sun, as seen from the earth, appears to travel through 
 these 12 constellations or signs of the zodiac in each year, 
 thus entering a new constellation every month. Some 2000 
 years ago the beginning, or first point, of Aries marked the 
 vernal equinox or ascending node ; that is, the equator 
 crossed the ecliptic at the line of division between Pisces and 
 Aries. 
 
 But slow changes in the heavens, the nature of which will 
 be more fully considered hereafter, cause the equinoxial 
 points, and hence the beginnings of the seasons, to slide back- 
 wards, as it were, along the ecliptic; so that no relation in 
 position between the equinoxes and the constellations of the 
 zodiac can be a permanent one. 
 
 During the past 2000 years the equinoxes have shifted 
 backwards nearly a whole sign, so that the vernal equinox is 
 now at the beginning of the constellation Pisces. In 2000 
 years more it will be at the beginning of Aquarius ; and 
 .something over 4000 years ago, when the ancient Babylonian 
 empire was predominant, spring began when the sun entered 
 Taurus, 
 
 As crude and unscientific as this scheme may seem to be, 
 it is so woven into ancient history and chronology, and into 
 the whole usage of astronomy, that it would not be profitable 
 to change it. or to throw it aside, even if we could. 
 
 The best that we can do is to adopt, for certain purposes, 
 a sort of conventional system which connects permanently 
 the names and symbols of the zodiacal signs with the seasons 
 of the year. 
 
THE ZODIAC. 
 
 67 
 
 Thus it is a usual thing to say that the first meridian passes 
 through the first point of Aries, or that spring begins when 
 the sun enters Aries ; and in the names tropic of Cancer and 
 tropic of Capricorn we are using the words Cancer and Ca- 
 pricorn in this way. But we must bear in mind tliat Aries, 
 Cancer, Capricorn, etc., when used in this conventional sense 
 do not mean the same things as when applied to the constel- 
 lations of stars. 
 
 Fig. 40. 
 
 The diagram gives a perspective view of the zodiacal belt 
 as seen from without, if such a thing were possible, showing 
 the ecliptic, the equator crossing it at the no'des, and the path 
 of the moon, the latter being variable. This is according to 
 the conventional zodiac, for according to the constellational 
 one the equator would cross the ecliptic at 5£ and TTg. 
 
 The zodiac, marking as it does the courses of the sun, 
 moon, and planets throughout the year, and thus connecting 
 itself in a prominent way with the holidays, the feasts, the 
 variation of the seasons, and almost everything which comes 
 into closest relation with human life, exercised a sort of 
 mystic influence over all primitive people who had entered 
 upon the early stages of civilization, and many of their ideas 
 are still current amongst us in a more or less modified form, 
 as for instance, the supposed influence of the moon or 
 planets when in certain signs. 
 
68 ASTRONOMY. 
 
 The accompanying figure represents a zodiac which is now 
 in the museum of the Louvre in Paris, but which was found 
 buih into an ancient temple at Denderah in Egypt. 
 
 Besides the signs of the zodiac, which are easily traced by 
 the animals representing them, the figure apparently pictures 
 
 Fig. 41. 
 
 all the constellations visible at that locality, mixed up with 
 mythological and other symbols ; for early astronomy and 
 mythology were quite intimately connected. 
 
 A figure of a man surrounded by the signs of the zodiac 
 is usually to be found upon the second or third page of 
 every cheap almanac. This is a remnant of old astrology, 
 and has reference to the influence which the moon was sup- 
 posed to have over the different parts of the body, according 
 as it was in one or other of the signs of the zodiac when the 
 person was born. 
 
THE SEASONS. 69 
 
 36. The Seasons. 
 
 It is to the obliquity of the ecliptic that we are indebted 
 for our orderly rotation of seasons. 
 
 If the ecliptic coincided with the equator, or, what is the 
 same thing, if the earth's axis were perpendicular to the 
 plane of the ecliptic, the sun would not swing from north 
 to south and back again as it does now, but would be per^ 
 petually over the equator. And thus, holding daily through- 
 out the year the same relation to any one given place, there 
 could be no seasons, but spring, summer, autumn, and winter 
 would be merged into one dead uniformity. 
 
 This does not necessarily mean that such a state of matters 
 might not be very good indeed, nor does it mean that there 
 would be no variations in the state of the weather from day 
 to day. But it does mean that things would seem somewhat 
 strange to us who are accustomed to revel in the ever-varying 
 scenes of the changing seasons. 
 
 In the accompanying figure E is the earth, S the sun, and 
 Ec the ecliptic. 
 
 Fig. 42. 
 
 As seen from 6" the earth appears at E' in the ecliptic, and 
 as seen from E, the sun appears at S' in the ecliptic. But S' 
 and E' are opposite points, so that when the sun appears to 
 be in Aries we would have to say that the earth is in Libra, 
 as seen from the sun. 
 
 Now as we have to make our observations from this earth 
 as our standpoint, this continual reverting from the place of 
 the sun to that of the earth would be, not only troublesome 
 and confusing, but a serious disadvantage. 
 
 And as motion is relative, and phenomena are unchanged, 
 astronomers long ago decided to take things in this connec- 
 tion as they appear to be, to look upon the earth as being 
 
70 
 
 ASTRONOMY. 
 
 fixed, and to record the positions and motions of the sun 
 instead of those of the earth. Thus in any good ephemeris 
 one finds recorded the right ascension, declination, and longi- 
 tude of the sun, and not of the earth. 
 
 In this sense, then, the right ascension of the sun is zero 
 when at the vernal equinox and 180° when at the autumnal 
 equinox. And this is the usage that we shall here follow. 
 
 The earth's axis is inclined at the angle 66° 33' to the plane 
 of its orbit, and its direction in space is fixed, except as to 
 a very slow change to be considered later on. As a conse- 
 quence, whether we consider the earth as going around the 
 sun or the sun as going around the earth, the radius vector 
 will be, at certain times, perpendicular to the earth's axis, and 
 at other certain times be inclined to the axis at the minimum 
 angle of 66° 33', while at intermediate times the angle will 
 be intermediate. 
 
 Spring. The beginning of spring is when the sun arrives 
 at the vernal equinox, about March 20th or 21st, depending 
 on the occurrence of leap year. 
 
 The earth's radius vector is then perpendicular to the axis. 
 
 Fig. 43. 
 
 and the sun is accordingly vertical over the equator and it 
 illuminates one-half of the earth's surface from pole to pole. 
 As the earth rotates daily upon its axis every place on its 
 surface, except the poles, has 12 hours day and 12 hours 
 night. Hence the term equinox, when the time from sunrise 
 to sunset is equal to that from sunset to sunrise. 
 
THE SEASONS. 71 
 
 Both the northern and the southern hemispheres are now 
 enjoying the same length of day, but the southern is coming 
 out from its summer of long days, and passing on to its 
 winter of short days, while the northern is leaving its winter 
 of short days and moving onwards to its summer of long 
 days. And thus spring in the northern hemisphere is con- 
 temporaneous with autumn in the southern. 
 
 Summer. Summer begins when the sun arrives at the 
 summer solstice, about June 23rd. The radius vector is now 
 inclined to the axis at the angle 66° 33', and the north pole 
 leans towards the sun. 
 
 Fig. 44. 
 
 The sun is vertical over the point T which, by the rotation 
 of the earth on its axis, determines the circle Tt, 23° 27' from 
 the equator. This is called the tropic of Cancer, the name 
 being due to the circumstances that the sun, having arrived 
 at its farthest position north, is turning (rpeTreiv, to turn) to 
 go back, and this takes place when the sun enters the con- 
 ventional sign of Cancer, or the crab. It has been said, in 
 fact, that the constellation was so named because the crab 
 has a habit of walking backwards. 
 
 The rays of sunlight reach beyond the north pole to the 
 point C, which determines the circle CC, 23° 27' from the 
 pole, and which is called the Arctic Circle. 
 
 On the other hand, the rays of the sun fail to reach the 
 south pole, coming only to D, which determines the Antarctic 
 Circle DD' at the distance 23° 27' from the south pole. 
 
 As the circle COD, which separates between day and night, 
 bisects the equator, as at and 0', upon the opposite side of 
 
72 ASTRONOMY. 
 
 the earth, all places on the equator have equal day and night. 
 But as one goes northwards from the equator the day gets 
 longer and the night shorter until the Arctic Circle is 
 reached. Beyond this the sun does not set, but moves in a 
 circle around the horizon without passing below it, and thus 
 it is all day and no night. And finally when the pole is 
 reached the sun travels around in a circle parallel to the 
 horizon and 23° 27' above it. 
 
 As one goes south from the equator the day grows shorter 
 and the night longer until the Antarctic Circle is reached, 
 and beyond this it is perpetual night. 
 
 The north point of Norway is north of the Arctic Circle, 
 so that anywhere near the 23rd of June one can, from North 
 Cape, see the midnight sun for a number of days (for there 
 are no nights) in succession. There is no inhabited country 
 within the Antarctic Circle. 
 
 The foregoing is a description of the extreme case, when 
 the sun is farthest north, or at the summer solstice. But the 
 intelligent reader will understand how the description will 
 have to be modified to suit the case where the sun is on its 
 way northward, or on its way southward, after having passed 
 the summer solstice. Also it will be easy to comprehend the 
 state of affairs when the sun is at the autumnal equinox or 
 at the winter solstice. 
 
 Autumn. This season begins when the sun reaches the 
 autumnal equinox. The relative positions of the earth and 
 sun are exactly as they were at the vernal equinox, that is, 
 the sun shines from pole to pole and the days and nights are 
 equal throughout the world. But there is the difference, 
 which shows itself in the whole aspect of the vegetable king- 
 dom, that the northern hemisphere is now passing from sum- 
 mer into winter, and the southern, from its winter into its 
 summer. 
 
 Winter. Winter begins when the sun arrives at the winter 
 solstice, about December 21st. The radius vector is again 
 inclined to the earth's axis at an angle of 23° 27', but the 
 south pole is now turned towards the sun. 
 
THE SEASONS. 
 
 73 
 
 The sun is vertical over the circle T't', called the Tropic of 
 Capricorn, because the sun is turning to go north and is en- 
 tering the conventional sign of Capricornus. 
 
 Fig. 45. 
 
 In the northern hemisphere the days are short and the 
 nights are long, while the very opposite condition exists in 
 the southern hemisphere. The Antarctic Circle is all light 
 and the Arctic Circle is all dark. 
 
 A number of north pole seekers have spent long, dark 
 winters in the Arctic Circle, and a good description of such 
 an experience is to be found in " Kane's Arctic Explora- 
 tions." 
 
 I n 
 
 Fig. 46. 
 
 In figure 46 we have the seasons illustrated from both 
 
 points of view. In I the earth is represented as being at the 
 
 centre and the sun S travels around it. N is the north pole, 
 
 and the illuminated hemisphere is always next the sun, and 
 
74 ASTRONOMY. 
 
 covers one-half the circle ABCD. As the sun and illuminated 
 hemisphere move around together it is easily seen how the 
 north pole changes its relation to the light and dark parts, 
 and in these changes brings in the seasons. 
 
 In II, the sun is at the centre and the earth travels around 
 it. And as the earth's axis is fixed in direction the position 
 of the pole is the same for all the positions A, B, C, and D. 
 And it will be noticed that the illuminated hemisphere travels 
 around the globe exactly as in I. 
 
 One sees from this diagram that, as far as explanation of 
 phenomena is concerned, it is immaterial which view is 
 taken. 
 
 37. Celestial Longitude and Latitude. 
 
 We have already considered two systems of indicating the 
 position of a body in the celestial sphere. First, by giving 
 its altitude and its azimuth. This is known as the horizontal 
 system of coordinates, the horizon being the equator of the 
 system and the zenith being the pole. Second, the equator 
 system of coordinates, where the celestial equator is the 
 equator of the system and the celestial north pole is the pole. 
 The measures having reference to these are right ascension 
 and declination. 
 
 We have now a third system known as the ecliptic system 
 in which the ecliptic is the equator of the system and the pole 
 of the ecliptic, a point in the constellation Draco, 23° 27' 
 from the celestial north pole in the direction of the winter 
 solstice, is the pole. 
 
 The measures in this system are Longitude, which is 
 measured in angle from the vernal equinox around the eclip- 
 tic in the direction in which the earth travels, and Latitude 
 which is measured from the ecliptic towards the pole of the 
 ecliptic. Thus celestial latitude and longitude are quite dif- 
 ferent from terrestrial measures of the same names. 
 
 The sun has longitude zero when it is at the vernal equi- 
 nox, and in the Nautical Almanac its longitude is given for 
 every day in the year. 
 
 As the sun apparently moves in the ecliptic, its latitude is 
 zero constantly, except for a slight disturbance produced by 
 
LONGITUDE AND RIGHT ASCENSION. 7S 
 
 the planets, but as this disturbance never reaches more than 
 a single second of angle, it need not be considered here. 
 
 The sun's longitude does not increase uniformly from day 
 to day, because the sun's velocity is greater at perihelion than 
 at aphelion. Thus a reference to the Nautical Almanac 
 shows that the increase in the sun's longitude from Jan. 1st 
 noon to Jan. 2nd noon, or in 24 hours, is 61'. 9", while from 
 July 1st noon to July 2nd noon it is only 57' 12"; and these 
 quantities are proportional to the sun's apparent velocities 
 at these times. 
 
 Referring again to the quantities recorded in the ephem- 
 eris, we find, at the times of the equinoxes and the solstices, 
 the following peculiarities in the daily increase of the sun's 
 right ascension as compared to its daily increase in longitude : 
 
 Change in long. Change in rt.ascen. 
 in 24 hrs. in 24 hrs. 
 
 Sun at vernal equinox 59' 33" S3' 55" 
 
 " " summer solstice 57' 13" 62' 22" 
 
 " " autumnal equinox .... 58' 47" 53' 12" 
 
 " " winter solstice 61' 6" 66' 38" 
 
 We notice that the increase in longitude does not vary very 
 much, and that it is greatest at the winter solstice, which is 
 near the perihelion, and least at the summer solstice, which 
 is near the aphelion, as we would expect it to be. But it is 
 different with the right ascension, the increase being nearly 
 the same at each equinox, but greater and considerably dif- 
 ferent at the solstices. 
 
 Also the increase in longitude is greater than in right 
 ascension at the solstieesr jl^*^^ •kw-^<u-^ 
 
 The irregularity in the increment of longitude is due to the 
 elliptic form of the earth's orbit and the sun being at a focus, 
 as has already been pointed out. But the irregularity in the 
 increase of right ascension, while partly due to the same 
 cause, is also partly due to another matter which we now 
 propose to explain. 
 
 In the figure P is the north pole of the heavens, and P' is 
 the pole of the ecliptic, P'P being a part of the solstitial 
 colur€. 
 
76 ASTRONOMY. 
 
 VE is the equator and VC is the ecliptic. Then V is the 
 vernal equinox. Let the sun be at V, some time on March 
 20th, and 24 hours afterwards let is be at 5". 
 
 Draw the meridian PSS', to meet the equator at S'. 
 
 ■P 
 
 Fig. 47. 
 
 Then the arc VS represents the sun's increase in longitude 
 for 24 hours at the vernal equinox, and VS' represents the 
 sun's corresponding increase in right ascension. 
 
 But as SVS' is nearly a plane triangle, and SS'V is a right 
 angle, VS is greater than VS' . Or, at the equinoxes longi- 
 tude increases faster than right ascension. But when the 
 sun comes to C its longitude is 90°, and so is its right ascen- 
 sion. Hence at and near the solstices the sun's right acsension 
 increases faster than its longitude. And the second cause for 
 the irregularity of increase in the right ascension of the sun 
 is the circumstance that longitude and right ascension do not 
 belong to the same coordinate system; and it would be a 
 problem in spherical trigonometry to change the one into the 
 other. 
 
 However, we see that the motion of the sun is not uniform 
 in either longitude or right ascension, and this has an import- 
 ant bearing upon our next subject. 
 
TIME. 
 
 n 
 
 TIME. 
 
 Time is measured naturally by the sequence of events con- 
 nected with certain motions of the heavenly bodies. 
 
 The revolution of the earth on its axis is the best realiza- 
 tion known of an ideal uniform motion; and the apparent 
 rotation of the sphere of the heavens about the earth, which 
 is an equivalent for the rotation of the earth about its axis, is 
 necessarily of equal uniformity. Thus any fixed star, from 
 its rising to its setting, measures out angle with absolute 
 uniformity. And the local meridian of any given place on 
 the earth travels along the celestial equator at a perfectly 
 uniform rate. We must adopt some means, then, to make 
 this uniform motion our measurer of time. 
 
 38. Siderial Time. 
 
 Let PhP be the local meridian of a place K upon the earth, 
 E, where P, P' are the north and south poles of the celestial 
 
 equator, and h the point where the local meridian crosses the 
 equator. Then as the earth rotates on its axis, the point h 
 sweeps along the equator with a uniform motion, measuring 
 out equal angles in equal times. 
 
78 ASTRONOMY. 
 
 Let the local meridian pass through the star S at any par- 
 ticular time. Then the period of time occupied by this meri- 
 dian in passing from 6" around to 5 again is the time required 
 for one rotation of the earth on its axis, and this is called a 
 siderial day. The siderial day is divided into 24 siderial 
 hours, and each of these into 60 siderial minutes, etc., thus 
 giving that system known as siderial time. 
 
 If the celestial equator were a real line in the heavens and 
 were graduated into 24 hours, and again into minutes and 
 seconds, the line Oh would become the hour hand of a great 
 siderial clock which would indicate time with the utmost pre- 
 cision. But instead of this we have only the stars as indi- 
 cating figures upon our celestial dial and the plane of the 
 local meridian as the hour hand of the clock. And the stars 
 are not distributed at equal distances from one another or 
 according to any known system, but are apparently scattered 
 haphazard over the surface of the heavens, and yet the astro- 
 nomer has finally to appeal to the stars for the determination 
 of his time. 
 
 But for a number of reasons which cannot be given here, 
 although some of them will appear in the sequel, the appeal 
 to the stars is not always as simple an operation as it may 
 be thought to be. Besides, the stars are not always visible. 
 Hence the astronomer brings to his aid 
 
 39. The Siderial Clock. 
 
 The siderial clock, if correct, reads zero whenever the 
 local meridian passes through the vernal equinox, or, in 
 other words, the vernal equinox is on the local meridian. So 
 also the siderial clock reads 6 hours when the summer solstice 
 is on the local meridian, and 18 hours, when the winter sol- 
 stice is on this meridian. 
 
 In short, the hour hand of the siderial clock, in its passage 
 ov.er the dial, represents the local meridian in its passage 
 over the heavens. And if the clock be so placed as to have 
 the arbor of its hand parallel to the earth's axis, and its face 
 turned northwards, and the hour hand set to point to the 
 first celestial meridian, it will always point to that meridian. 
 
 Let h be the vernal equinox. The local meridian is at h at 
 
SIDERIAL TIME. 
 
 79 
 
 time 0. Let it require H hours for the local meridian to pass 
 from h to h' . Then hh' measured in time is the right ascen- 
 sion of t, a star on Ph', and it is also H hours. Hence the 
 right ascension of a star is the siderial time at which the star 
 comes to the meridian, or culminates. Thus, if the right 
 ascension of the star Regulus be 10* 2™ 1«, this is the siderial 
 time of the star's culmination ; or the star will be ' on- the 
 meridian ' at that time by the siderial clock. 
 
 A clock, however, cannot be made to go with the uniform- 
 ity of the earth in its axial rotation, and has therefore to be 
 corrected from time to time. Suppose that the altazimuth is 
 set exactly in the meridian, and through it a star whose right 
 ascension is given in the almanac as 3'' 8™ 43« is seen to cross 
 the central thread at 3* 4™ 52* by the siderial clock. Then 
 as the clock should have shown 3* 8™ 43' when the star was 
 on the meridian, the clock is 0* 3™ 51* slow. 
 
 The form of altazimuth used for this purpose has no ver- 
 tical axis, but a horizontal one only. It is called an astrono- 
 mical transit, and is one of the chief, instruments of the 
 astronomer. 
 
 The transit is adjusted with great care so as to have its 
 line of sight trace out the meridian, and its field is usually 
 crossed with equidistant vertical threads, 
 and two horizontal ones near together. 
 The purpose of having a number of 
 vertical threads is to furnish the ob- 
 server with the mean of a number of 
 ' readings, as this will in all probability 
 be more accurate than a single reading 
 would be. Thus, suppose a star is seen 
 Fig. 49. to cross the five threads at the following 
 
 times as shown by the clock: A.. .8'' 3™ 27», 5.. .8* 5™ 14«, 
 C...& 7-'" 2\ D.. .8" 8™ SO*, £.. .8" 19™ 36*. The mean of 
 these is 8'' 7" 1*.8, differing by 0*.2 from the reading of the 
 middle thread. 
 
 40. Mean Time. 
 
 If the star 5" had a slow but uniform movement in right 
 ascension, say 1° per day, we could still count our time by 
 
80 ASTRONOMY. 
 
 that star, if circumstances required it, the only difference 
 being that the day would not mean the time taken by the 
 earth to make an axial rotation, but a length of time depend- 
 ing upon this and the motion of the star. But all days would 
 still be of uniform length. 
 
 The siderial day is an exact unit of time and is of great 
 importance in astronomy, but it is not adapted to the common 
 business of life. For this purpose we need a day having a 
 relation to light and darkness, and hence to the sun's position 
 with respect to our local meridian. 
 
 Now, we cannot put the sun in the place of 5 as a moving 
 star, for, as we have seen, the sun is irregular in its motion 
 in longitude and still more so in its motion in right ascension. 
 
 To get over these difficulties we adopt the following fic- 
 tions : 
 
 (1). We suppose a sun, which we shall call the dynamic 
 sun, to move uniformly in the ecliptic, so as to coincide with 
 the true sun at perihelion and at aphelion only. We theif 
 calculate the errors in the position of the true sun as com- 
 pared with this dynamic sun. These are the errors due to 
 eccentricity of the earth's orbit, and these taken as a whole 
 will be called the eccentricity error. 
 
 (2) We assume a sun, called the mean sun, which moves 
 uniformly along the celestial equator, coinciding with the 
 dynamic sun at the equinoxes and the solstices. We calcu- 
 late the errors in the position of the dynamic sun as com- 
 pared with the mean sun. These errors are due to the 
 obliquity of the ecliptic, and taken as a whole will be called 
 the obliquity error. 
 
 Then the algebraic sum of the eccentricity error and the 
 obliquity error gives us the error of the true sun as compared 
 with the mean sun, and as the mean sun increases its right 
 ascension uniformly it can replace the moving star S. 
 
 We shall have much to do with the mean sun, and we speak 
 of this fiction as if it were a reality. 
 
 When the mean sun is on the local meridian it is mean 
 noon, and the interval between two consecutive mean noons 
 is a mean day, and all mean days are exactly of the same 
 length. The mean day is divided into 24 mean hours, each 
 
SOLAR TIME. 
 
 81 
 
 into 60 minutes, etc., and time so reckoned is called mean 
 time. 
 
 Clocks used for domestic purposes are mean time clocks, 
 and are supposed to keep mean time. 
 
 41. Solar Time. 
 
 When the real sun is on the local meridian the time is solar 
 noon, and the time elapsing between two consecutive solar 
 noona is a solar day. As the sun is irregular in its motion of 
 right ascension, solar days are not of equal length, and clocks 
 and watches are not constructed or intended to keep solar 
 time. 
 
 The difiference between mean and solar time is called the 
 equation of time. The equation of time is given in the 
 ephemeris from day to day, and it expresses at any time the 
 error in the position of the real sun as compared to the mean 
 sun. 
 
 • The mean sun, being a fiction, cannot be observed, so that 
 what we obtain directly from observations on the real or 
 true sun is solar time, and this is brought to mean time by 
 adding or subtracting the equation of time as the occasion 
 may require. 
 
 •«-+R. ft 
 
 Fig. SO. 
 
 Lef£, in the figure, be the polar projection of the earth 
 showing the north pole, CQ be a part of the celestial equator, 
 
g2 ASTRONOMY. 
 
 S be the position of the real sun as referred to the equator, 
 M be the mean sun on the equator, and ER be the local meri- 
 dian of a given place. 
 
 The meridian, and S, and M, all move in the same direc- 
 tion, as indicated by the arrows. 
 
 In the case represented the true sun is ahead of the mean 
 sun. But when the local meridian R reaches M it is mean 
 noon, and it is not solar noon until the meridian comes to S, 
 so that the true sun appears to be late in coming to the meri- 
 dian, or slow. And so we have the seeming paradox : 
 
 When the sun's place, referred to the equator, is ahead of 
 the mean sun, the sun is slow, and when behind the mean 
 sun, the sun is fast. Or, the sun is slow or fast on mean 
 time according as its right ascension is greater or less than 
 that of the mean sun. 
 
 Graph of Eccentricity Error. As the true sun moves fast- 
 est at perihelion on January 1st, and slowest at aphelion on 
 July 1st, it must be ahead of the mean sun and therefore 
 slow from January 1st to July 1st, and behind the mean sun, 
 and therefore fast during the remaining half of the year. 
 
 This error is represented in the accompanying diagram, 
 which shows a graph of the eccentricity error for the year. 
 
 
 
 .ec"n<r,-,,Vj, COir..'..*.. 
 
 
 
 
 
 
 ~^ 
 
 
 ■ ; 
 
 
 ' ' '■■^'H'i^uiiv ..■■■-'''"'— ^ £iii£_ 
 
 • 
 
 
 fl 
 
 ; P«e. 
 
 
 
 ■ T«k. 
 
 Fig. 51. 
 
 The straight line represents the time kept by the dynamic 
 sun and extends from January to January again, the months 
 being named. The curve line, by its departure from the 
 straight one, shows the error of the true sun in relation to 
 the dynamic sun throughout the course of the year. When 
 the curve is below the line the sun is slow, and when above 
 the line, the sun is fast. 
 
Page 83. Graph of Obliquity Error. After the fourth line read: 
 And as time and right ascension of the mean sun are both measured 
 out uniformly on the equator, it is easy to see that, starting from the 
 vernal equinox, the right ascension of the dynamic sun falls behind 
 that of the mean sun, catching up to it again at the solstice ; so that 
 the dynamic sun is fast from the vernal equinox, Mar. 20th, to the 
 summer solstice, June 23rd. Then slow from June 23Td to Sept. 23rd, 
 then fast from Sept. 23rd to Dec. 21st, and slow again from Dec. 
 21st to March 20th. 
 
EQUATION OF TIME. 83 
 
 The greatest departure, and therefore the greatest eccen- 
 tricity error, is between 7 and 8 minutes. 
 
 Graph of Obliquity Error. We have seen that, starting 
 from the vernal equinox, the sun's longitude increases faster 
 than its right ascension, but that they are the same, each 
 being 90°, when the summer solstice is reached. And a^ 
 time and right ascension are both measured by motion in thel 
 equator, we see that the dynamic sun is ahead of the meanj 
 sun, and therefore slow, from the vernal equinox to the sum-/ 
 mer solstice, that is, from March 20th to June 23rd. Simi-/ 
 larly, the dynamic sun is fast from June 23rd to Septemben 
 23rd, slow from September 23rd to December 21st, and fast\ 
 from December 21st to March 20th, / 
 
 This is represented in the dotted graph. 
 
 Graph of Equation of Time. The error known as the 
 equation of time is the sum of the two foregoing errors. So 
 that to obtain the graph of the equation of time we must 
 combine these two graphs, by taking the first graph and 
 bending its straight line so as to make it coincide with the 
 curved Hne in the second graph, or, what comes to the same 
 thing, by taking the algebraic sum of the corresponding 
 ordinates of the two graphs with which to form a new curve. 
 The result is represented in the third graph. 
 
 Tables are sometimes given of the equation of time for 
 every day in the year, but these tables are of little use where 
 accuracy is required. For, on account of slow changes, the 
 same table would not be correct for any two consecutive 
 years. To be of use, except as an approximation, such a 
 table would have to be reconstructed for each current year. 
 
 We notice from the third graph that the sun agrees with 
 the mean time clock only four times in the year, namely, 
 about April 15th, June 13th, September 1st, and December 
 24th, and that it is about 14^ minutes slow on February 11th, 
 and about 16^ minutes fast on November 2nd. 
 
 Noon Mark. A mark drawn along the edge of the shadow 
 cast by a vertical line or upright post upon a level floor when 
 the sun is on the meridian, is called a noon mark. It indi- 
 cates the return of solar noon from day to day throughout 
 
84 
 
 ASTRONOMY. 
 
 the year, and the equation of time gives the correction by 
 which we change solar noon into mean noon. So the coun- 
 tryman who boasted of his clock because it always coincided 
 with the noon mark was not possessed of a very good clock. 
 To regulate a clock or a watch by a noon mark the equation 
 of time must be applied. Thus, when the shadow is at the 
 noon mark on February 10th, the clock should indicate about 
 14J minutes past 12. 
 
 Similar observations apply to the use of the sun-dial,' 
 which is of the nature of a peculiarly extended noon mark. 
 
 The following table gives the equation of time to the 
 nearest tenth of a minute for every third day of the year 
 1910, and it will be sufficiently exact for correcting the time 
 given by a noon-mark or a sun-dial for any year. 
 
 The letter .r indicates that the sun is slow, or comes to 
 the meridian after 12 o'clock noon, and the letter / that the 
 sun is fagt and comes to the meridian before 12 o'clock noon. 
 
 TABLE OF EQUATION OF TIME. 
 
 Day of the Month. 
 
 Month. 
 
 1 
 
 4 
 
 7 
 
 10 
 
 13 
 
 16 
 
 19 
 
 22 
 
 25 
 
 28 
 
 Jan.- 
 
 ... 3.4s 
 
 4.5s 
 
 6.2s 
 
 7.5s 
 
 8.6s 
 
 9.7s 
 
 10.7s 
 
 11.6s 
 
 12.4s 
 
 13.0s 
 
 Feb 
 
 ... 13.7s 
 
 14.0s 
 
 14.3s 
 
 14.4s 
 
 14.4s 
 
 14.3s 
 
 14.1s 
 
 13.7s 
 
 13.3s 
 
 12.8s 
 
 Mar 
 
 ... 12.6s 
 
 12.0s 
 
 11.3s 
 
 10.6s 
 
 9.8s 
 
 9.0s 
 
 8.1s 
 
 7.2s 
 
 6.3s 
 
 5.4s 
 
 Apr 
 
 ... 4.1s 
 
 3.2s 
 
 2.4s 
 
 1.5s 
 
 0.7s 
 
 0.0 
 
 0.7f 
 
 1.4f 
 
 2. Of 
 
 2.5f 
 
 May 
 
 ... 2.9f 
 
 3.3f 
 
 3.5f 
 
 3.7f 
 
 3.8f 
 
 3.8f 
 
 3.7f 
 
 3.6f 
 
 3.3f 
 
 3. Of 
 
 June 
 
 ... 2.5f 
 
 2.0f 
 
 1.5f 
 
 l.Of 
 
 a.3f 
 
 0.3s 
 
 0.9s 
 
 1.6s 
 
 2.2s 
 
 2.8s 
 
 July 
 
 , .. 3.4s 
 
 4.0s 
 
 4.5s 
 
 5.0s 
 
 5.4s 
 
 5.8s 
 
 6.0s 
 
 6.2s 
 
 6.3s 
 
 6.3s 
 
 Aug 
 
 ... 6.2s 
 
 6.0s 
 
 5.7s 
 
 5.3s 
 
 4.8s 
 
 4.3s 
 
 3.7s 
 
 3.0s 
 
 2.2s 
 
 1.3s 
 
 Sept 
 
 . . . 0.2s 
 
 O.Sf 
 
 1.8f 
 
 2.8f 
 
 3.9f 
 
 4.9f 
 
 6. Of 
 
 7. Of 
 
 8.1f 
 
 9. If 
 
 Oct 
 
 ... lO.lf 
 
 ll.Of 
 
 11. 9f 
 
 1.2.8f 
 
 13. 5f 
 
 14.2f 
 
 14.8f 
 
 15.3f 
 
 15. 8f 
 
 16.1f 
 
 Nov 
 
 ... 16.3f 
 
 16.3f 
 
 16.2f 
 
 16.0f 
 
 15.7f 
 
 15.2f 
 
 14.7f 
 
 13. 9f 
 
 13. If 
 
 12.2f 
 
 Dec 
 
 ... 11. If 
 
 9.9f 
 
 8.7f 
 
 7.4f 
 
 6.0f 
 
 4.6f 
 
 3. If 
 
 1.6f 
 
 O.lf 
 
 1.4s 
 
SIDERIAL YEAR. 85 
 
 42. The Siderial Year. 
 
 The time occupied by the sun in making one complete 
 apparent circuit of the heavens, from a star to the same star 
 again, is called a siderial year, and in this relation it is imma- 
 terial whether we consider the mean sun or the true sun, as 
 each completes its circuit in the same length of time. 
 
 If we could observe the sun when it passes over and hides 
 a particular star on two consecutive occasions, we would 
 have a direct way of arriving at the length of the siderial 
 year. But as this method is not practicable we must resort 
 to some method which is. 
 
 The difference between the siderial clock and the mean 
 time clock, that is, between siderial time and mean time, in- 
 creases uniformly throughout the year. At the completion 
 of a year this difference amounts to exactly one day. So 
 that if we can find the amount of this increase for a given 
 length of time, we can easily calculate the length of time 
 required for the increase to equal one day. For if we record, 
 in mean time, the meridian passage of a star, at any date, 
 the same star will cross the meridian again at the same mean 
 time, exactly one siderial year after that date. 
 
 Suppose, then, a certain star is observed to cross the meri- 
 dian on March 14th at 11* 44™ 32^4 p.m., and that 30 days 
 afterwards, on April 13th, the same star is observed to cross 
 the meridian at 9'' 46" 3.S*.4 p.rn., both records being made 
 in mean time. 
 
 As the star crosses the meridian at the same siderial time 
 on both occasions, we have: 
 
 Gain of siderial time on mean time, 1" 57"^ 57*, 
 Period of time elapsed, 29* 22* 2™ 3«. 
 
 And our problem is, how long a time must elapse to make 
 the gain one whole day? By putting these time quantities 
 into seconds, and denoting the length of the year by y we 
 have: 
 
 3;=2584923/7077=36S''.257 nearly. 
 
 By taking the mean of a great number of observations, 
 at longer intervals apart, the result obtained is : 
 y=365.25636 days=365« 6" 9'" 9».6. 
 
86 ASTRONOMY. 
 
 This length of the siderial year is expressed in mean days. 
 And as the stars gain one revolution on the sun, or in other 
 words, siderial time gains one day on mean time in a year, 
 the siderial year contains 366.25636 siderial days. 
 
 The accompanying diagram may serve to make matters 
 somev^rhat plainer. 
 
 Fig. 52. 
 
 £ is a polar view of the earth's northern hemisphere. NL 
 is the local meridian, 5' and S' the positions of the sun in the 
 ecliptic at the first and the second observations respectively, 
 and T the position of the star. 
 
 As L sweeps around in the direction of the arrow, on 
 March 14th it takes 11" 44'" 32^.4 to go from 6" to T. But 
 on April 13th the sun has moved forwards to S', and it 
 now requires 9* 46™ 35*.4 for L to pass from S' to T. 
 
 The increase is the angle SNS', and elapsed time is 30 days 
 minus SNS'. 
 
 It is readily seen that in one complete revolution oi S, L 
 will pass T once oftener than it will pass S. So the number 
 of siderial days in the year is one greater than the number 
 of solar days. 
 
 To regulate a clock or watch by the stars. Siderial time 
 gains one day on mean time in 365.256 days, nearly; so that 
 
STANDARD TIME. 87 
 
 it gains 1/365.256, or 0.00273 days, nearly, in one day. This 
 amounts practically to 3™ 56*. 5. 
 
 But a star keeps siderial time ; so that a given star will set 
 3" 56*. 5 earlier each evening when compared with the mean 
 time clock. 
 
 ,-* 
 
 Place a post P at some distance east of a building B, and 
 observe when some conspicuous star, not a planet, disappears 
 below the roof or chimney of the building, keeping the eye 
 in line with the top of the post and the top of the building, 
 as represented. The time of the disappearance of the star 
 will be 3™ 56* earlier each evening. Thus if the watch shows 
 10" 13"" 42* when the star disappears on Monday evening, it 
 should show lO'' 9™ 46* on Tuesday evening, 10* 5" 50* on 
 Wednesday evening, etc. 
 
 Of course this does not give you any help in setting your 
 time-piece to the true time, but only in correcting its rate of 
 running. 
 
 43. Standard Time. 
 
 What is known as standard time is commercial in its idea 
 and application rather than astronomical. In fact, it is some- 
 what of a nuisance to the practical astronomer, although of 
 great benefit to the traveller. To illustrate it we will take a 
 concrete example. 
 
 The longitude of Montreal is 4* 54" W., and of Toronto 
 5ft \ym yq ^ and the Grand Trunk Railway goes from the one 
 
88 ASTRONOMY. 
 
 to the other. Suppose that the railway time-tables were 
 made out for these two cities in terms of their respective 
 mean astronomic times, and that a person at Montreal is 
 supplied with a good watch correct to time. When this pas- 
 senger arrives in Toronto his watch is 23*^ fast, and unless 
 he sets it to Toronto time, it is useless in directing him to 
 the times of arrival and departure of trains at Toronto as 
 given in the Toronto time-table. The case is similar when a 
 person goes from Toronto to Montreal, except that his watch 
 would be 23" too slow on Montreal time, and confusion 
 would be likely to follow. 
 
 The difficulty, as far as these two cities are concerned, 
 might be got over by Toronto keeping Montreal time or re- 
 ciprocally. But civic pride would come in here; besides it 
 would not be the best solution of the difficulty. 
 
 The 5*, or 75°, meridian passes near Cornwall, between 
 Montreal and Toronto, and by adopting the time of this 
 meridian for both places Montreal time as so changed be- 
 comes 6" slower than its mean astronomic time, while 
 Toronto time becomes 17"* faster than its astronomic time, 
 and neither of these changes or errors in time would be felt 
 in commercial life, while the traveller would find his watch 
 in agreement with the station clocks and the time-tables at 
 both places. This is known as standard time ; and the stand- 
 ard time for all Ontario and a good part of Quebec is the 
 time of the 5* meridian, or is exactly S hours behind Green- 
 wich time. 
 
 Now this principle may be applied throughout the world 
 theoretically as follows: All places between long. 0* 30" E., 
 and long. O* 30™ W., to take Greenwich time; all places be- 
 tween 0" 30™ E., and 1» 30'" E., to take the time of the V 
 meridian ; between P 30™ E., and 2* 30™ E., to take the time 
 of the 2* meridian, etc. ; all places between 0* 30™ W., and 
 V 30™ W., to take the time of the 23* meridian; between 
 1» 30™ W., and 2" 30™ W., the time of the 22* meridian, etc. 
 
 This, which is the principle of standard time, has been 
 adopted by the majority of civilized nations, and where it 
 
STANDARD TIME. 89 
 
 prevails all business and local time-pieces indicate the same 
 minute and differ only by a whole number of hours. 
 
 In the practical application of the principle, departures 
 from the theory have often to be made, the change of hour 
 being more or less dependent upon circumstances. The 
 change in the hour cannot well be made within the limits of 
 a city or in the immediate vicinity of one, and is conveniently 
 made at a boundary between nations or states, or along open 
 stretches of country. Thus the standard time-piece goes back 
 one hour in passing from Windsor to Detroit, or from Sar- 
 nia to Port Huron. 
 
 Five different times, as far as the hours are concerned, 
 reach across the continent of North America, namely : Inter- 
 colonial time. Eastern time, Central time. Mountain time, and 
 Pacific time. And Pacific time is exactly 4 hours behind 
 Intercolonial time, and 8 hours behind Greenwich time. 
 
 It must be remembered that the heavenly bodies may not 
 accommodate themselves to any such artificial arrangements, 
 and that every observatory must have its mean time clock 
 regulated to astronomical time. 
 
 Standard time at Kingston is 5™ 55* ahead of local astro- 
 nomic time. 
 
 PRECESSION OF THE EQUINOXES. 
 
 It' has already been pointed out that while the ecliptic is 
 the most immovable circle in the heavens, the conventional 
 first point of Aries, or the ascending node, or the vernal 
 equinox, is not a fixed point in the ecliptic. And as all the 
 signs of the zodiac have a fixed relation to Aries, the con- 
 ventional zodiac, so to speak, must shift along the ecliptic; 
 or, the conventional zodiac slides around slowly over the 
 constellational zodiac. 
 
 The cause of this motion will be referred to later on. At 
 present we shall confine ourselves to a discussion of the 
 nature and extent of the movement and the various pheno- 
 mena dependent thereon. 
 
90 ASTRONOMY. 
 
 S, in the figure, is the sun, moving from right to left along 
 the ecliptic and approaching the ascending node A. AQ is 
 the equator, and Am ihe meridian passing through the as- 
 cending node, that is, the first meridian. 
 
 This is in 1910, say, and the meridian passes through the 
 star m. In 1920, 10 years after, A has moved to A', the 
 
 north 
 
 1910 iS20 ^930 
 
 ^oath 
 
 Fig. 54. 
 
 equator is now A'Q' and the first meridian is A'm' and passes 
 through the star m'. In 1930, after another 10 years, A 
 has come to A", the equator is A"Q" and the first meridian 
 A"m" passes through star in" ; and so on from decade to 
 decade, the movement of the node being in a direction oppo- 
 site to that of the sun. 
 
 The precession of the node, which is in reality a retrogres- 
 sion, does not go on uniformly, being the outcome of the 
 superposition of a number of slow cyclic changes which, in 
 general, run their cycles in a few years. But upon the 
 average the node travels backwards along the ecliptic at the 
 rate of 50". 1 per year. 
 
 Now 50". 1 is contained in 360° about 25860 times. So 
 that if this movement continues unchanged it will carry the 
 node completely around the ecliptic in 25860 years. This is 
 called the annus magnus, or great year. 
 
 This motion, as slow and inconspicuous as it is, has far 
 reaching consequences which we shall proceed to study. 
 
 The siderial year is an exact and easily determined period 
 of time, but it is not adapted to the common purposes of life. 
 For it is evidently necessary that the year be so adjusted to 
 
PRECESSION OF EQUINOXES. 91 
 
 the seasons that the beginning of the year shall always be 
 in the same season, and in the same part of that season. 
 
 But on account of the precession of the equinoxes it is 
 impossible to make the round of the seasons coincide with 
 the sun's motion amongst the stars for any great length of 
 time. What we are compelled to do, then, is to institute a 
 year of such a length that it will run concurrently with the 
 seasons for all time to come. 
 
 But the seasons are connected with the arrival of the sun 
 at the vernal equinox, and hence we must make the year to 
 include the time taken by the sun to pass from the vernal 
 equinox to the vernal equinox again. This is 
 
 44. The Tropical year, or Equinoctial year. 
 
 The node or equinox comes backwards 50". 1 annually to 
 meet the sun, and hence the tropical year must be shorter 
 than the siderial year by the space of time required by the 
 sun to pass over SO".l. 
 
 Now the sun describes 360° in the heavens in 365.25 days, 
 nearly, and a little arithmetic shows that it passes over SO^TlT 
 in 20™ 19*. 9, and this is the difference in length between the 
 siderial year and the tropical year. Hence the 
 
 Tropical year=365* 5" 48™ 49^.7=365.242242 days. 
 
 Leap year. The tropical year consists of 365.242242 days, 
 which is not a whole number of days, and of which the frac- 
 tional part is not an aliquot part of a day. 
 
 And yet, commercially and practically, we must make the 
 year to consist of a whole number of days, which means that 
 the practical year cannot be of invariable length. 
 
 Now 400 yrs. of 365.242242 days= 146096.897 days 
 and 400 yrs. of 365 days =146000 
 
 Difference 96.897 " 
 
 So that 400 years of 365 days each would fall behind by 
 96.987 days. Adding one day to every fourth year, making 
 it 366 days, will add on 100 days in the 400 years. This is 
 3.103 days in excess, so that we must take away 3 days in 
 400 years. The error will then be only 1 day in 4000 years. 
 
92 
 
 ASTRONOMY. 
 
 a date too far ahead to concern ourselves about now. These 
 corrections are provided for as follows : 
 
 1. Every year not evenly divisible by 4 consists of 365 
 days, and is a common year. 
 
 2. Every year evenly divisible by 4 consists of 366 days, 
 and is a leap year. 
 
 Except, if it be a century year it is a leap year only when 
 the number of the century is evenly divisible by 4. 
 
 Thus 1913 will be a common year; 1924 will be a leap 
 year ; 2000 will be a leap year, but 2100 will be a common 
 year. 
 
 45. The Two Zodiacs. 
 
 We have two zodiacs, (1) the zodiac of the constellations, 
 in which the names Aries, Taurus, etc., are connected with 
 and denote fixed groups of stars, which' groups are un- 
 changed from generation to generation, and which were prac- 
 tically the same to the ancient Babylonian astronomer as they 
 
 are to-day. 
 
 s-ta-rry 
 
 •S'eavens 
 Fig. 5S. 
 
 This is represented in the diagram by the outer ring, 
 marked with star groups and the symbols of the constella- 
 tions. 
 
PRECESSION OF EQUINOXES. 93 
 
 (2) The conventional zodiac, in which the symbols and 
 names no longer apply to groups of stars, but to divisions of 
 the tropical year, and are preserved on account of their con- 
 venience and their historical value. This zodiac is repre- 
 sented by the inner circle of the diagram. 
 
 The outer circle remains fixed, and the inner circle, — car- 
 rying with it the equinoxes, the solstices, the equator, the 
 meridians, the poles, the circles of declination, and the con- 
 ventional signs of the zodiac, — revolves within the outer 
 circle from left to right at the slow rate of 50". 1 per year. 
 
 But even at this slow rate, the inner circle shifts, to the 
 extent of one day's motion of the sun, in about 70 years, or 
 to the extent of 30°, or one whole sign in 2150 years. 
 
 The limits of the constellations in star maps are not usually 
 well defined, so that it is not easy to say where the constella- 
 tions began and ended in early times. But this is certain, 
 that if the vernal equinox coincided with the first point of 
 Aries 2150 years ago, it must now coincide with the first 
 point of Pisces. So that from this point of view the conven- 
 tional sign of Aries agrees with the stellar sign of Pisces, 
 
 Some of the common almanacs ignore the conventional 
 zodiac and tell you that the sun enters Pisces on March 20th, 
 or at the beginning of spring. Such a view is highly objec- 
 tionable. For if it be entertained, the sun will enter Pisces 
 on March 21st in 70 years from now, and on April 1st in 
 about 700 years from now. Or, in other words, if the equi- 
 nox is at the first point of Pisces now, it will be at the 20th 
 degree of Aquarius in 700 years from now. And thus the 
 equinox will travel backward through the zodiac from year 
 to year, and will have no fixed place among the signs. Only 
 confusion can be the result. 
 
 The British Nautical Almanac adopts the more sensible 
 view of keeping to the conventional signs of the zodiac and 
 thus fixing the first point of Aries perpetually at the vernal 
 equinox. 
 
 Some 4300 years ago, or about 2400 B.C., the old Babylo- 
 nian empire was in the midst of its power, and it is probable 
 
94 ASTRONOMY. 
 
 that the zodiac was brought into a definite form about that 
 time. 
 
 But the vernal equinox was then at the beginning of 
 Taurus. And we can well understand that the strength and 
 subduing power of the sun-god at the beginning of spring — 
 in overcoming the death-like gloom of winter, in freeing the 
 brooks and ponds from their icy chains, in banishing to un- 
 known parts the snow and sleet and chilling winds, in resur- 
 recting again the tender plant and spreading out the verdant 
 fields, and covering all by a radiant sky as an earnest of 
 another season of warmth and comfort and plenty — was well 
 typified by the Bull, the greatest and strongest of all domestic 
 animals. 
 
 These ancient people represented the constellations through 
 which the sun travelled during the gloomy and disagreeable 
 parts of autumn and winter, when skies were lowering and 
 surroundings dull and depressing, as species of monsters who 
 held the sun in a sort of bondage and prevented it from send- 
 ing down its rich gifts to man. Thus there was the scorpion- 
 man, who guarded the gates of the underworld, the archer, 
 who was half man and half some lower animal, the goat- 
 man, as appears in the picture of the ancient zodiac, and the 
 fish-man. And some writers hold that the Babylonian story 
 of Marduke overcoming and subduing the monster Tiamut, 
 a myth which in some form or other is of almost universal 
 extent as symbolizing Creation, is only a mythological state- 
 ment of the spring sun overcoming the rigorous terrors of 
 winter. 
 
 46. Movement of the pole and consequent changes. 
 
 The precession of the equinoxes or the backward motion 
 of the node is due to the shifting of the earth's axis in space. 
 
 Let P be the pole of the ecliptic, and Np be the north ce- 
 lestial pole. 
 
 Let Np move in the circle NpR, having P' as its centre 
 and an angular radius of 23° 27', and let it complete its cycle 
 in 25860 years. Then, as Np is the pole of the celestial 
 
POLE STAR. 95 
 
 equator, this motion causes the equator to swing around so 
 as to make D and A move backward along the ecliptic, while 
 preserving unchanged the angle at which the ecliptic and the 
 equator intersect. 
 
 The Pole Star. The star which is, at present, nearly at the 
 celestial north pole is Polaris or a Ursae Minoris, and is in 
 the tail of the Little Bear. It is about 1°.3 from the pole, but 
 the motion of the earth's axis, will carry the pole somewhat 
 nearer to the star for a number of years to come. The pole, 
 however, will pass the star at the distance of about a half 
 degree, at its nearest approach, and will then move away 
 upon its long journey of 25860 years before completing its 
 circuit. 
 
 About 4000 years ago the nearest bright star to the north 
 pole was in the constellation Draco ; in a thousand years to 
 come the pole star will be a small star in Cepheus; and in 
 13000 years the pole will be quite near to a conspicuous star 
 in Hercules. 
 
96 
 
 ASTRONOMY. 
 
 Change in declination and right ascension. 
 
 As the pole moves along its circular path its distance from 
 a given fixed star is constantly changing, unless the star be 
 at the pole of the ecliptic. That is to say, that the polar dis- 
 tance of the star, and hence its declination, is in a state of 
 slow change owing to the precession of the equinoxes. 
 
 The change in declination is least, in fact zero, for stars 
 situated on that meridian which is perpendicular to the path 
 of the pole for the time being, that is, upon the solstitial 
 colure. And from this it increases as the star is farther 
 away until the maximum is reached for stars on the equi- 
 noxial colure. 
 
 Fig. 56. 
 
 Thus if P be the pole, and P' be the pole of the ecliptic, 
 PP' is a part of the solstitial colure, PT perpendicular to this 
 is a part of the equinoxial colure. But SP, the north polar 
 distance of 5", is scarcely affected by a very small motion of 
 P along the circle, while TP experiences the maximum effect. 
 
 In other words, this change in declination is least for stars 
 whose right ascension is 6" or 18*, and greatest for those 
 whose right ascension is 0" or 12*. 
 
 Also, owing to the motion of the vernal equinox the first 
 meridian sweeps around the whole ecliptic in a retrograde 
 
POLE STAR. 91 
 
 direction, so that the right ascensions of all the stars are 
 upon the average slowly increasing. 
 
 As the ecliptic and its pole are the only elements that hold 
 fixed relations to the stars, the latitude of a star is invariable, 
 except for changes in the position of the star itself ; but the 
 longitude increases at the average rate of 50". 1 or 3«.34 each 
 year. 
 
 Circle of perpetual apparition. The centre of this circle- is 
 the celestial pole, and its radius is the latitude of the place. 
 As the pole changes place, so the circle of perpetual appari- 
 tion must change its centre and the groups of stars which it 
 includes. 
 
 Similar changes occur in the circle of perpetual occultation. 
 
 47. Causes of Precession. 
 
 We may say, in the beginning, that a perfectly spherical 
 earth would have no precession. So that the remote cause of 
 the precession is the earth's axial rotation, which causes the 
 earth to become protuberant at the equator; and it is this 
 protuberant mass which gives rise to the precession. 
 
 A rigid discussion of the reason for the precession cannot 
 be given without the use of mathematics far beyond the 
 scope of this work. But we can get a reasonable and in- 
 structive illustration of the matter which may, to some 
 extent, take the place of demonstration, by experiments upon 
 the behaviour of certain bodies in motion. 
 
 The really difficult part, however, of the problem is as to 
 why the bodies in the experiment do as they do. 
 
 A is a top supposed to be rapidly spinning in the direction 
 of the arrow, and to be in a position of equilibrium, with its 
 axis vertical and at rest. 
 
 If a force, F, be brought to act for a little upon P, as by 
 blowing a strong current of air against the axis, the pole will 
 not respond in the direction of the force but will begin to 
 move along a line R perpendicular to F. And R is the re- 
 sultant direction of the rotation of A combined with the 
 force F. 
 
98 ASTRONOMY. 
 
 If the top have an iron spindle and be suspended from the 
 pole of a magnet, as at 5, and a force F be applied as before, 
 we have the same phenomena as with A except that the re- 
 sultant R is turned in the direction opposite to what it had 
 at A. Aloreover, if in A the spindle be inclined to the ver- 
 tical, as at C, the pole P will undergo precession, travelling 
 in a circle PQ about the vertical, in the direction in which 
 the top turns. This is seen in a top that is wabbling. 
 
 ma^aet 
 
 Fig. 57. 
 
 But, if the spindle be inclined to the vertical in B the pre- 
 cession will be in the direction opposite to that in which the 
 top turns, that is, it will be retrograde. 
 
 It is not difficult to see why the cases A and B differ as 
 they do. The position of equilibrium for the spinning top is 
 that in which the axis is vertical. 
 
 But in the case of A this equilibrium is unstable, and if it 
 be disturbed by pushing the axis out of the vertical the force 
 of gravity tends to increase the disturbance and bring the 
 pole farther out of the centre. 
 
CAUSES OF PRECESSION. 99 
 
 In B, on the other hand, the equihbrium is stable, and the 
 force of gravity tends to correct any disturbance of equi- 
 librium that may take place. 
 
 Fig. 58. 
 
 Now, in figure 58, let SC be a string attached to the centre, 
 C, of a heavy circular disc D. Let PC be the axis of the 
 disc, and let the angle PCS be less than a right angle. 
 
 If C is made to revolve rapidly about 5" as a centre, in a 
 horizontal orbit, the centrifugal force will keep the string 
 stretched, and the centrifugal force at F will be greater than 
 that at /, as F moves in the larger circle ; and the tendency 
 will be to bring the plane of the disc to coincide with the 
 plane of the orbit, or to bring PC to be perpendicular to SC. 
 
 Before this is effected, suppose that the disc is set in rapid 
 rotation about its axis. Then, as we have seen in the case 
 of the top B, the axis will undergo precession in a direction 
 opposite to that of the orbital motion. 
 
 Finally, in the application, let 5" be the sun, and the disc D 
 represent the protuberant mass along and around the earth's 
 equatorial parts. The sun's attraction takes the place of the 
 string and matters go on much as in our assumed experiment. 
 
 The pull of the sun tends to bring the plane of the equator 
 into coincidence with the plane of the ecliptic, which would 
 be a position of stable equilibrium, and the axial rotation of 
 the earth so modifies the effect as to produce a retrograde 
 precession of the axis and hence of the nodes. 
 
100 ASTRONOMY. 
 
 We thus see that the effect of the sun in producing pre- 
 cession is zero when the sun is at the nodes and a maximum 
 when the sun is at the solstices. 
 
 48. The Anomalistic year. 
 
 The time required by the earth to pass from the perihelion 
 around to the perihelion again is called the anomalistic year. 
 The sun's distance from the perihelion point is called the 
 sun's anomaly, and is measured from 0° to 360°, and hence 
 the name given to the year. 
 
 Now, the perihelion point in the earth's orbit is not fixed 
 but moves in the same direction as the sun at the rate of 
 11". 25 per year. And as the sun requires 4*" 33*. 7 to move 
 11". 25, the anomalistic year is 4" 33*. 7 longer than the si- 
 derial year. We have accordingly : 
 
 Tropical yr. Siderial yr. Anomalistic yr. 
 Motion of O . . 359°.9861 360°.0000 360°.0031 
 Length in days. 365^.2422 36S«.2S67 365«.2595 
 As ir'.25 is contained in 360° 115000 times, it requires 
 115000 years for the perihelion point to make one complete 
 revolution. But as the equinox moves backwards one revo- 
 tion in 25860 years, we get from the formula ab/(a-\-b), 
 which is adapted to this problem, where a= 11 5000 ajid 6= 
 25860, the quantity 21000 years; and this is the time that it 
 requires the perihelion to move from the ascending node to 
 the ascending node again. 
 
 49. Eccentricity of Earth's Orbit and variations in climate. 
 
 The eccentricity of the earth's orbit is at present about 
 0.01677 or ^/^„. This quantity has a very long period of 
 variation. It is at present growing less and the orbit is be- 
 coming more nearly a circle. The eccentricity will never 
 reach zero, however, and the orbit will never be a circle. 
 After passing the minimum the eccentricity will continue to 
 increase for something like a hundred thousand years until 
 it reaches a maximum, after which it will again decrease. 
 
 Variations in climate. At present the earth's perihelion 
 passage is in winter in the northern hemisphere, and this has 
 
VARIATION IN CLIMATE. 101 
 
 some effect in modifying the cold of winter and the heat of 
 summer and thus bringing in a somewhat more equable cli- 
 mate than would otherwise be the case. 
 
 In the southern hemisphere matters are reversed, and the 
 tendency is towards a short hot summer and a long cold 
 winter. And this seems to be borne out by the facts that the 
 south pole is surrounded by ice to a' greater extent than the 
 north pole, and for a given high latitude the mean tempera- 
 ture is lower for the southern hemisphere than for the 
 northern. 
 
 In ten or eleven thousand years matters will be quite 
 changed around, the perihelion passage will be in July, the 
 southern hemisphere will be enjoying a moderate climate, 
 and the northern one will be subject to extremes. 
 
 If the earth's orbit were a circle, differences between the 
 mean temperatures would not be so marked as at present, 
 although the different distribution of land and water in the 
 two hemispheres would undoubtedly have some effect. But 
 if the eccentricity were much increased and the perihelion 
 were at a solstice, the difference would be increased. 
 
 And it is easy to understand that with a high eccentricity 
 we might have a winter so long that the following summer, 
 although hot, would be too short to clear away the accumu- 
 lation of snow and ice of the preceding winter. And this 
 accumulation going on from year to year would bring in a 
 veritable ice age in the polar regions of that hemisphere 
 which had the perihelion passage in its summer. 
 
 As long as this high eccentricity existed there would be a 
 succession of ice ages, shifting from one pole to the other, 
 through intervening periods of moderation, as the perihelion 
 passed through an equinox. 
 
 These periods of cold and ice would each last for some 
 thousands of years, and would recur at either pole after 
 lapses of about 21000 years. 
 
 Mr. James Croll has adopted this explanation of the occur- 
 rence of past ice ages in his " Climate and Time," and whe- 
 ther it is generally accepted by geologists or not, it seems 
 very reasonable as, at least, a partial explanation. 
 
102 ASTRONOMY. 
 
 THE MOON. 
 
 The moon, being the most conspicuous celestial object next 
 to the sun, and undergoing such wonderful changes every 
 month, has always been an object of particular interest to 
 mankind. And we have not, as yet, fully dropped our faith 
 in the moon's power over many things pertaining to man and 
 his interests. 
 
 The word ' month ' is connected with ' moon,' and cer- 
 tainly no more convenient measure of time, for periods 
 longer than a day, is to be found in the motions of the heav- 
 enly bodies, than is presented in the consecutive changes of 
 the moon. 
 
 Many people, such as the Indians of North America, 
 counted their time and registered their events by moons, and 
 many African tribes do so still. And in Captain Speke's 
 travels in Africa he gives an interesting description of the 
 feast of the new moon as kept by certain of the African 
 chiefs. 
 
 50. The Moon's Motion. 
 
 A very little observation will show that the moon moves 
 from west to east amongst the stars. For it is only necessary 
 to compare the position of the moon with that of some bright 
 star, near which it passes in its course, for a few evenings, 
 or even for a few hours upon the same evening. 
 
 By measuring the angular distance of the star from the 
 limb of the moon at about the same hour on consecutive 
 evenings, we can readily make out that the moon moves for- 
 ward in its orbit at a rate of a little over 13° in 24 hours, or 
 a little above one-half a degree in an hour. And as the 
 moon's angular diameter is about 31', the moon apparently 
 moves over a distance equal to its own diameter every hour. 
 This apparent motion of the moon amongst the stars is far 
 from being uniform. For the moon is sufficiently close to 
 the earth to have its apparent position materially affected by 
 parallax arising from the earth's axial rotation. Thus, while 
 the moon is moving forwards in its orbit, the observer is also 
 being carried forwards, and the effect is to displace the moon 
 
MOON'S SIDERIAL PERIOt). 103 
 
 in a retrograde direction. And thus the moon appears to 
 move faster when rising or setting than when high in tlie 
 heavens. 
 
 Besides there are real irregularities in the moon's orbital 
 motion arising from the eccentricity of its orbit and from 
 other causes. 
 
 The moon passes over and hides, or occults, as it is said, 
 every star in its course, and the disappearance of the star be- 
 hind the moon's disc is so sudden as to form a very distinct 
 point of time. 
 
 By noting the elapsed time between two similar occulta- 
 rions of the same star after some hundreds of revolutions of 
 the moon about the earth, it is not difficult to arrive at a close 
 approximation to the moon's siderial period. 
 
 But as the moon's orbit is not fixed, but undergoes con- 
 stant changes of one kind and another, the problem is some- 
 what more difficult than it might at first appear to be. 
 
 From a very large number of observations, and numerous 
 corrections, extending over some hundreds of years, the 
 moon's siderial period is accepted as being 
 
 27.32166 days, or 27^ 7" 43™ 1P.4. 
 Taking the mean radius of the moon's orbit as 238000 miles, 
 we readily find that the moon moves in its orbit at the aver- 
 age speed of 
 
 2280 miles an hour, or 38 miles a minute. 
 
 51. Moon's Synodic Period. 
 
 Let the earth E, the moon M, the sun S, and a star T be in 
 
 si. 
 
 Fig. 59. 
 
 line. While the moon moves from T around to T again the 
 sun has gone forwards from 5' to S' And our problem is to 
 
104 ASTRONOMY. 
 
 find how long it will take the moon to go from S, not to 5"', 
 but to the position where 5" will be when the moon over- 
 takes it. 
 
 We solve this by the formula t^=ab/{a — b), for two bodies 
 revolving about the same centre, when a is the time of revo- 
 lution of the slower moving body, and b is the time of re- 
 volution of the other. 
 
 In the present 0=365.25674, the number of days in the 
 siderial year, and b=27. 32166, the moon's siderial period. And 
 the result of substitution is : 
 
 ^=29.53059 days, = 29* 12* 44™ 3», nearly. 
 
 This quantity of time is the moon's synodic period, or one 
 lunation ; and it is the interval of time between two consecu- 
 tive new moons, or two consecutive full moons, etc. 
 
 52. Lunations in a year — Epact. 
 
 There are 365.2422 days in a tropical year and 29.5306 
 days in a lunation. And 365.2422/29.5306 gives 12 luna- 
 tions with 10.875 days remaining. So that there are 12 new 
 moons in a year, as also 12 full moons, etc. 
 
 The excess of 10.875 days lacks }i oi a day of 11 days. 
 If we consider 11 days as the excess we will be one day out 
 in 8 years. But if at the same time we take 30 days instead 
 of 29.53 days for a lunation, the error will be only about 4 
 days in a century. 
 
 Now the Epact is the moon's age — that is, the number of 
 days since thq last new moon^ — on the first day of January. 
 And we see that this number increases by 11 days annually. 
 And when the increase makes it to be over 30, 30 is rejected 
 and the remainder forms the epact. Thus the epact for 1910 
 is 19; for 1911 it will be found by adding 11 to 19, giving 
 30; for 1912 it becomes 11, etc. 
 
 These results, although only approximate, are sometimes 
 convenient, as they serve to fix the dates of the new moons 
 throughout the year, and they are seldom more than a day 
 astray. The epact, which is given in the almanac for every 
 
MOON'S PHASES. 
 
 105 
 
 53. Moon's Phases. 
 
 year, is calculated through the Golden Number, which will 
 be considered later on. 
 
 The most distinctive and interesting phenomena connected 
 with the moon are the incessant changes in its visible form. 
 These are due to the moon's being a dark body, shining only 
 by the reflected light of the sun, and to the varying relative 
 positions of the sun, the moon, and the earth, during a 
 lunation. 
 
 
 
 Fig. 60. 
 
 As the sun's distance from the earth is 400 times that of 
 the moon, and the sun's diameter is nearly twice the diameter 
 of the moon's orbit, the rays of the sun, as they come to the 
 moon, may be considered as being parallel, in whatever part 
 of its orbit the moon may be. 
 
 The diagram represents the earth E at the centre, the moon 
 in 8 equidistant positions in its orbit, showing in each case 
 the Hghted half turned towards the sun, and in the positions 
 
106 ASTRONOMY. 
 
 A\ B', C, D', E', etc., the lighted portion of the moon as seen 
 from the earth. 
 
 At A the sun and the moon have the same right ascension, 
 and the moon is invisible, as at A', because its dark side is 
 wholly turned towards us, and also it is lost in the glare of 
 the sun. This, as an astronomical event, is new moon; but 
 popularly the term is applied to the moon when it is a couple 
 or three days old, or when first seen in the west as a slender 
 crescent. 
 
 At B the moon has completed one-eighth of its revolution 
 and is in the First Octant. The figure B' shows that as seen 
 from the earth the lighted part appears as a crescent facing 
 westward, and covering about one-fourth of the moon's 
 whole disc. 
 
 Moving on in its orbit the crescent grows wider until C is 
 reached, when the moon has passed over one-fourth of its 
 orbit, and the lighted portion has become a semi-circle. The 
 moon is now in the First Quarter. Leaving this position, the 
 face of the moon becomes gibbous, that is, one edge of the 
 lighted portion is circular and the other edge elliptical. This 
 is well seen at D and £)'. 
 
 The elliptical edge is known as the terminator, and it 
 undergoes a continuous change of form as the moon pursues 
 its course. 
 
 At E the right ascension of the moon is 180° in advance 
 of that of the sun, and it presents to us a full circle of light, 
 and we have Full Moon. From this around to new moon 
 again these phenomena and changes occur in a reversed 
 order, and the lighted portion of the moon now faces' east- 
 ward. 
 
 It is seen, then, that we have New Moon, First Quarter, 
 Full Moon, and Last Quarter, according as the right ascen- 
 sion of the moon is 0^ 90°, 180°, and 270° in advance of 
 that of the sun. 
 
 Also a very little consideration will show that from new 
 to full the moon rises some time during the day and sets 
 some time during the night, while from full to new it rises 
 during the night and sets during the day. 
 
MOON-LIGHT AND EARTH-LIGHT. 107 
 
 54. Moon-light and Earth-light. 
 
 The earth and the moon are both dark bodies, and the 
 earth, as well as the moon, shines by reflecting the sun's rays. 
 Moon-light whenever present is always a pleasure in the re- 
 lief that it gives from dark and gloomy nights, and the appar- 
 ent gliding of the moon through broken clouds upon a 
 summer evening is a thing of poetic beauty. And yet, ac- 
 cording to Zollner, the brightness of the full moon is only 
 about one-six hundred thousandths (1/600000) of that of 
 the sun. 
 
 The reflecting surface of the moon is of solid material, 
 but of the earth it is nearly three-fourths water, and we 
 cannot be certain as to how the ocean reflects the light of 
 the sun. But as the moon's angular diameter is only 31', 
 while that of the earth as seen from the moon is 114', the 
 area of the earth's disc as seen from the moon is about 12 
 times that of the moon as seen from the earth. So that if 
 the earth's albedo, or power of reflecting light, be one-half 
 that of the moon's, the earth must give six times as much 
 light to the moon as the moon does to the earth. We would 
 expect, then, that when the moon's dark face is largely 
 
 SU.H5 rays 
 
 Fig. 60a. 
 
 turned towards us and is lighted by the full disc of the earth, 
 the moon should be visible in earth-light. These conditions 
 are fulfilled soon after new moon when we have the moon 
 
108 ASTRONOMY. 
 
 as a slender crescent in the west after sunset, and again when 
 it appears as a similar crescent in tiie east a little before 
 sunrise. 
 
 In both cases the whole surface of the moon is visible with 
 a faint ashy light bordered towards the sun by a narrow and 
 brilliant crescent. This phenomenon, especially the evening 
 one, is known as the old moon in the new moon's arms. 
 
 55. The Moon's Orbit. 
 
 As has already been said, the moon's orbit is an ellipse 
 with the earth at one of the foci, and it accordingly has an 
 apsis line, perigee, apogee and nodes. 
 
 The orbit is inclined to the ecliptic at an angle of 5° 6', so 
 that it has two nodes where it crosses the ecliptic, one being 
 the ascending node and the other the descending node. These 
 nodes, as is the case with the equinoxes, have a retrograde 
 motion which carries them through a complete circuit of the 
 ecliptic in about 18.6 years. 
 
 As the ecliptic is inclined to the equator at the angle 
 23° 27', the inclination of the moon's orbit to the equator 
 varies between the limits 18° 21' and 28° 33', running its 
 whole course in 18.6 years. 
 
 We are now in a position to explain some interesting things 
 in regard to the moon's presentation. 
 
 55. Wet, and Dry, Moon. 
 
 It will probably be a long time before the credulity of man 
 will allow him to give up altogether his faith in the moon's 
 influence over the weather. And the belief in a wet moon 
 and a dry moon is a part of that faith. The serious difficulty 
 is that followers of the cult are not always agreed among 
 themselves ; some holding that when the new moon lies well 
 upon its back it is a dry moon, and some holding the very 
 reverse. For our purpose we shall call the first of these cases 
 a dry moon. And a wet moon will be when the crescent 
 stands well up upon one of its horns. 
 
WET AND DRY MOON. 109 
 
 In the figure, (I), the line NS represents the western hori- 
 zon just after sunset, when the sun is near to and approach- 
 ing the vernal equinox, which is on the horizon and just 
 setting. 
 
 \ ^^^ \" 
 
 MfitH n«Mr Moan 
 
 r t til nCiv neo 
 Sapt ZOtti 
 
 Fig. 61. 
 
 The latitude is supposed to be 45 °N, so that the equator 
 rises at an angle of 45° from the south; and the ecliptic rises 
 at the angle 68° 27' from the south. The sun is below the 
 horizon, at S, and the new moon is near the ecliptic, at m. 
 And it is easily seen that the crescent moon lies well upon its 
 back, and being capable of holding water, is a dry moon. 
 
 In (II) we have the western horizon and the equator the 
 same as in (I), but it is September, with the sun approach- 
 ing the autumnal equinox, which is on the horizon and just 
 setting. 
 
 The ecliptic is now inclined to the horizon at the angle 
 21° 33' from the south. The sun has set, as at .S", and the 
 new moon, at m near the ecliptic, is standing upon its horn 
 so as not to be able to hold water. This then is a wet moon. 
 
 These are the extreme cases. But they occur in a less 
 marked degree when the sun is anywhere near one of the 
 
no ASTRONOMY. 
 
 nodes of the earth's orbit. In fact, starting from the vernal 
 equinox, when the new moon is well on its back, the crescent 
 becomes more and more tilted up until the case of the second 
 figure is reached at the autumnal equinox; after which the 
 tilting becomes less and less as the sun gets around towards 
 the vernal equinox again. 
 
 But the important point is that we always have a dry new 
 moon in March and a wet one in September. And the regu- 
 larity in the sequence of variations should, to any intelligent 
 person, be sufficient to throw discredit upon the whole theory 
 of wet and dry moons. 
 
 57. The Harvest Moon. 
 
 The average time elapsing between the risings of the moon 
 upon two consecutive nights is about 48 minutes. But for 
 the full moon in September, and especially when it happens 
 near the time of the autumnal equinox, the interval between 
 consecutive risings may be as low as 27 minutes or even 21 
 minutes ; so that to superficial observers the moon appears 
 to rise almost at the same hour for several nights in succes- 
 sion. Long years ago, before the true explanation of this 
 peculiarity was known, it was attributed to a special dispen- 
 sation of Providence intended to assist the agriculturist in 
 saving his harvest; hence the name of harvest moon. The 
 full moon of October exhibits the same peculiarities but less 
 extensively, and is sometimes called the hunter's moon, be- 
 cause it occurs in what is known as the hunting season. 
 
 We give here the explanation of the harvest moon for 
 latitude 45 °N. 
 
 In the autumn, when the sun is near Libra, the full moon, 
 being opposite the sun, is near Aries. 
 
 The diagram illustrates the eastern horizon with the full 
 moon on the horizon on September 23rd or thereabouts. The 
 vernal equinox, T, is rising, and the equator, the ecliptic, 
 and the two positions of the moon's orbit, when inclined in 
 opposite sides of the ecliptic, are shown as they would be 
 projected on the eastern sky under certain circumstances. 
 
HARVEST MOON. Ill 
 
 Suppose that on September 23rd, say, the full moon is 
 rising as at h, and that it is moving in the ecliptic. Then on 
 the 24th at the same hour the moon will be at c, and will rise 
 when the horizon sinks through the distance he by the earth's 
 diurnal rotation. 
 
 Fig. 62. 
 
 Now in the triangle hbc, bhc is 135°, hbc is 45°— 23°27', 
 or 21° 33', and the angular distance be traversed by the moon 
 in 24 hrs. is about 13°. Hence we readily find that the dis- 
 tance ch is about 6° 45', equivalent to 27™ in time. 
 
 And thus the rising of the full moon at e on the 24tli would 
 be only 27 minutes later than the time of its rising at b on 
 the 23rd. Similar explanations will apply to its rising when 
 at a, and at d. 
 
 If the moon's orbit is situated as ikTAf' ,whSre M'bd is 5° 6', 
 the conditions are most favorable, and the difference between 
 consecutive risings becomes only 21 minutes. And with the 
 orbit situated as LL' the conditions are least favorable, the 
 difference in consecutive risings working out to about 33 
 minutes. And we have an alternation of most favorable 
 harvest moons with least favorable every 18.6 years. 
 
 And thus the harvest moon, while always favorable to 
 agricultural interests, is a most natural outcome of the con- 
 ditions prevailing, and varies from most favorable to least 
 favorable and back again in 18.6 years. 
 
 For a latitude higher than 45° the harvest moon is still 
 more favorable, and less so for a lower latitude. 
 
112 ASTRONOMY. 
 
 58. Moon's Apsis line. 
 
 The line joining the apogee and perigee of the lunar orbit 
 has a slow motion forwards, completing a revolution in about 
 9 years. 
 
 The relative distances of the moon at apogee and at peri- 
 gee are as 9 : 8. the distances themselves being about 252000 
 miles and 224000 miles. This means a variation in angular 
 diameter from. 33' to 29' 30". Now, the sun's angular dia- 
 meter varies from 32' 36" to 31' 32". So that, although upon 
 the average the moon appears to be somewhat smaller than 
 the sun, the moon, when near perigee, appears to be larger 
 than the sun, and if interposed between us and the sun would 
 completely hide the latter. 
 
 59. Moon's Libration. 
 
 As everybody knows, the moon practically presents the 
 same face to the earth, the reason of which has been already 
 explained under the heading of ' The Tides.' On this ac- 
 count it is sometimes said that the moon does not rotate upon 
 an axis. This is true in relation to the earth, but in relation 
 to' space, or absolutely, the moon rotates once on its axis in 
 the same time as it makes its revolution about the earth. 
 
 In viewing a ball whose diameter is much greater than the 
 distance between the eyes, we see somewhat less than half 
 the surface of the ball. But if the ball were turned slightly 
 on one side and then on another, we might be able to see 
 somewhat more than half the surface, considering all the 
 positions. 
 
 That shifting which enables us to see more than one-half 
 of the moon's surface is called the moon's libration. 
 
 There are three causes for the libration, namely: 1. The 
 eccentricity of the moon's orbit; 2. The inclination of the 
 moon's axis to the plane of its orbit ; and 3. The axial rota- 
 tion of the earth. 
 
 1. A rotating planet cannot undergo a sudden change in 
 its velocity of rotation, or in the direction of its axis. So 
 
MOON'S LIBRATION. 
 
 113 
 
 that although the moon rotates slowly, only once in 27 days, 
 yet its rate is uniform. But, from Kepler's law II, this is 
 not the case with the moon's motion in its orbit. 
 
 The diagram shows the moon's orbit with the earth at a 
 focus, exaggerated in eccentricity in order to accentuate the 
 illustration. 
 
 The moon is shown at perigee, at apogee, and half-way 
 between these in time. Then, as the moon rotates uniformly, 
 
 Fig. 63. 
 
 the tangent line ab, at P, will be as shown in the four posi- 
 tions. But PQ is greater than QA, and PR greater than 
 RA. So that at Q we see beyond ah to cd on the a side, and 
 at R we see beyond ah to cd on the b side. 
 
114 ASTRONOMY. 
 
 This is called the moon's libration in longitude, and its 
 amount is about 7° 30' on each side of a central position. 
 
 2, The moon's axis is inclined about 6° 30' from a normal 
 to the plane of its orbit, so that when the north pole of this 
 axis leans towards the earth we can see 6^ degrees beyond 
 the north pole ; and 14 days later the south pole leans towards 
 the earth and we see 6^ degrees beyond the south pole. 
 
 This is the moon's libration in latitude. 
 
 3. If we change our position on the earth, not only is the 
 moon affected by parallax, but we can see a Httle distance 
 around the limb of the moon. If the moon passes through 
 our zenith, we are carried, by the earth's rotation, between 
 moon-rise and moon-set, through an angle, as seen from the 
 inoon, equal to twice the moon's horizontal parallax, or about 
 1° 54', and we are enabled to see this far around the edge. 
 
 This is the moon's diurnal libration, and its amount de- 
 pends upon the position of the observer upon the earth. 
 
 The result of all this is that, although we do not see quite 
 one-half of the moon's surface at any one time, we see some- 
 thing more than one-half taken all together. 
 
 Stereograph of the Moon. By taking two photographs of 
 the moon when in the same phase but, as near as is practica- 
 ble, at extremes of libration, and uniting these in a stereo- 
 scope, we obtain a realistic view of the moon as a solid globe 
 some 2 or 3 feet in diameter and 12 or 15 feet distant. The 
 view is something such as would be obtained by a giant 
 whose head was in the position of the earth and whose eyes 
 were some thousands of miles apart. 
 
 The author has such a stereograph from negatives by L. 
 M. Rutherford, and in it the moon appears to be somewhat 
 of a prolate-spheroid form with the longer axis directed 
 towards the earth ; and this is probably the form which it 
 would assume by virtue of the earth's attraction. 
 
 60. Nutation. 
 
 The moon attracts, not only the waters of the ocean to 
 form the tides, but also the protuberant mass about the equa- 
 tor to produce a sort of precession of the equinoxes in much 
 
ECLIPSES. 
 
 lis 
 
 the same way as the sun does, except that on account of the 
 smallness of the moon, and the rapid change in its orbit, the 
 efifects are very small. This effect is known as the lunar 
 nutation. 
 
 The effect is much the same as if the pole of the heavens 
 travelled about a small ellipse, once in 18.6 years, while the 
 centre of the ellipse moved in a complanar circle 23° 27' 
 from the pole of the ecliptic, making its circuit in 25860 
 years. The path of the pole is thus a sinuous motion imposed 
 upon a circular one, there being about 1400 sinuosities in the 
 circuit. 
 
 The dimensions of the ellipse are 7" by 9", so that the 
 sinuosities are too small to be detected except by careful 
 measurement. 
 
 ECLIPSES. 
 
 An Eclipse in astronomy is the passing of one heavenly 
 body through the shadow of another. 
 
 We are concerned just now with what are called eclipses 
 of the sun and of the moon. The bodies to be considered, 
 then, are the sun which supplies the light, and the earth and 
 moon which cast shadows. 
 
 The Shadow. S represents the sun and E the earth, or 
 moon. The shadow cast by E consists of two cones. The 
 
 h ' f'"" 
 
 Fig. 64. 
 
 one COD from which all light is excluded is the umbra of 
 the shadow, and the inverted cone, bounded in section by Ce 
 
116 ASTRONOMY. 
 
 and Df, from which only a part of the light is excluded, is 
 the penumbra. 
 
 A normal section of the shadow made by the plane mn is 
 shown at X. The umbra gives the central dark portion, and 
 the penumbra surrounds it, beginning with the darkness of 
 the umbra and growing lighter as we pass outwards until the 
 distinction between the penumbra and the full light is lost. 
 
 At 0, the angles subtended by AB and CD are equal, and 
 E just covers S and no more, as at W. At u, a point be- 
 tween and E, CD subtends a greater angle than AB, and 
 E appears large enough to cover 5" and to lap over to some 
 extent, the extent being greater as u is nearer to E, as repre- 
 sented by Y. From any point to the right of O, £ appears 
 too small to cover S, and when superposed leaves a ring of 
 5" visible about £, as at Z. 
 
 At a point /»', near the border of the penumbra, the body 
 E appears to cut a small segment out of S, as at U ; and at 
 p", near the border of the umbra, E appears to cover all but 
 a small crescent of S, as at V. 
 
 If we suspend a ball in the rays of the sun, and cut the 
 shadow by a piece of white cardboard held normal to the axis 
 of the shadow, by moving the cardboard back and forth, 
 we can study the character of the shadow with ease and 
 satisfaction. 
 
 The earth and the moon, being dark bodies, cast their long 
 black shadows far into space in a direction opposite to that 
 of the sun, so that when the sun is in Aries the earth's 
 shadow is in Libra, and vice-versa. 
 
 Preparatory to the study of eclipses, we must first find the 
 dimensions of the shadows of the earth and moon. This is 
 effected by simple geometry. But as some of the elements 
 which we have to consider are variable between certain 
 limits, all we can here expect to do is to get an average esti- 
 mate, and accordingly very great accuracy is not a necessity. 
 
 As no angle with which we are concerned in the investiga- 
 tion is greater than 33' or a little upwards, we can use the 
 formula s^r6 wherever required without sensible error, and 
 we may safely look upon an arc of 33' as being a line. 
 
SHADOWS OF EARTH AND MOON. 
 
 117 
 
 Let S denote the sun's radius, 425000 miles. 
 
 E 
 M 
 D 
 d 
 
 X 
 
 earth's radius, 3960 miles. 
 
 moon's radius, 1080 miles. 
 
 sun's distance, 93,000,000 miles. 
 
 moon's distance, 238,000 miles. 
 
 the length of the umbra of the earth's 
 
 shadow, 
 the length of the umbra of the moon's 
 
 shadow, 
 the radius of the umbra of the earth's 
 
 shadow at the moon's distance, 
 the radius of the penumbra of the earth's 
 
 shadow at the moon's distance. 
 
 s 
 
 1 B """--. P'. 
 
 1 r.--'T 
 
 A 
 
 / ,^--'L^ 
 
 .y I C:p 
 
 i_ 
 
 Fig. 6S. 
 
 In the diagram AB is S, CF is E, CO is x, AC is D, aC 
 is d, ah is h, and ac is h'. 
 
 From similar triangles: 
 
 x:x-\-D^E:S; whence ^^^ §ZZ£ 
 
 M 
 
 Putting M for E in this gives x'=D j^^ 
 
 -M 
 
 .(a) 
 
 Agaxn h:E=x—d:x; whence h=E—^ (S—E) (y) 
 
 And in a similar way by putting y to denote O'C we get 
 y=.D/iS+E) ; 
 
 and h' : E=y+d : y ; whence h'=E+ ^ {S+E) (S) 
 
118 ASTRONOMY. 
 
 Putting in the numbers denoted by the letters and perform- 
 ing the arithmetical calculations necessary we get : 
 
 .r=z874600 miles, the length of the umbra of the earth's 
 shadow. 
 
 x'=227000 miles, the length of the umbra of the moon's 
 shadow. 
 
 ^=2880 miles, the radius of the earth's umbra at the dis- 
 tance of 238000 miles away. 
 
 /;'=S030 miles, the radius of the earth's penumbra at the 
 distance of 238000 miles away. 
 
 In what follows we shall use the word shadow for umbra, 
 as is customary, and where the penumbra is concerned it will 
 be specially mentioned. 
 
 We infer: (1) That as the distance of the moon is 238000 
 miles, and the length of the earth's shadow is 874600 miles, 
 the earth's shadow reaches far beyond the moon's orbit. 
 
 (2) That as the radius.of the moon is 1080 miles and that 
 of the shadow at the distance of the moon's orbit is 2880 
 miles, or nearly three times that of the moon, the moon 
 might pass through the shadow and be totally eclipsed for 
 some length of time. 
 
 (3) That as the average length of the moon's shadow is 
 237000 miles, while the distance from the moon to the earth's 
 centre is 238000 miles, the point of the moon's shadow does 
 not reach to the centre of the earth by 1000 miles, but it 
 reaches nearly 3000 miles beyond that surface of the earth 
 which faces the moon. 
 
 Of course, these numbers are means or averages. When 
 the moon is in perigee the apex of the moon's shadow reaches 
 about 13000 miles beyond the earth's centre; and when in 
 apogee the apex of the shadow lacks about 11000 miles of 
 reaching the earth's surface. 
 
 When the moon is at one of the nodes of its orbit it is in 
 the plane of the ecliptic ; and if a full moon happens at that 
 time, the sun, the earth, and the moon are in line, with the 
 earth between the sun and the moon, so that the moon must 
 necessarily pass centrally through the earth's shadow and be 
 totally eclipsed. This is represented at a in the diagram, 
 
LUNAR ECLIPSE. 119 
 
 where EE' is the ecliptic ; MM', the moon's orbit ; the point 
 where these cross, the node ; the large circle, a section of the 
 earth's shadow; and the small circle, the moon at the full. 
 If the full moon happens when the moon is near the node, 
 but not near enough to give a total eclipse, as at h or b' , the 
 
 Fig. 66. 
 
 moon may cut into the side of the shadow and present us 
 with a partial eclipse. And if the full moon happens still 
 farther from the node, as at c or c', the moon grazes the 
 shadow, but there is no eclipse other than such darkening as 
 may be produced' by the penumbra of the earth's shadow. 
 These are the cases of lunar eclipses. 
 
 On the other hand, if a new moon happens when the moon 
 is at one of its nodes, the sun, the moon, and the earth are 
 in line, with the moon between the sun and the earth. 
 
 So that as seen from some place on the earth, the moon 
 will appear to be centrally imposed on the sun. If the moon 
 is near the perigee it will, for a few minutes, completely hide 
 the sun, thus producing a total solar eclipse at the place of 
 observation. But if the moon is near the apogee it will 
 appear too small to cover the sun, and when centrally im- 
 posed will leave a ring of the sun about the dark body of 
 the moon, thus producing an annular eclipse. 
 
 The foregoing are general statements as to how eclipses 
 occur. What we have now to do is to consider, in more de- 
 tail, some particular cases. And from a consideration of the 
 cases of the central eclipse, others can easily be inferred. 
 
 61. The Lunar Eclipse. 
 
 Let C7 be a section of the shadow where it is traversed by 
 the moon, P be a section of the penumbra at the same place, 
 and let the small circles denote the moon in six positions in 
 its orbit. These circles should have their diameters as the 
 
120 
 
 ASTRONOMY. 
 
 numbers 51, 29, and 11. The shadow is at the moon's as- 
 cending node, and the moon moves through it from right to 
 left, as seen from the earth. 
 
 Position 1. The moon has first contact with the penumbra. 
 As the penumbra brightens rapidly as we pass outwards 
 from the umbra, no visible effect is produced upon the moon 
 until it has entered well into the penumbra, when a hazy and 
 illy-defined darkening becomes observable on the moon's 
 eastern limb, as at a. 
 
 Fig. 67. 
 
 Position 2. The limb of the moon has reached the shadow, 
 and the eclipse is said to begin. The darkening on the ad- 
 vancing limb is quite apparent, and its curved outline is 
 readily seen. As the eclipse progresses, the curved black 
 shadow of the earth, with its poorly defined outline, gradu- 
 ally creeps over the surface of the moon, as at b. In 
 
 Position 3, the whole surface is obscured, and totality 
 begins, as at c. 
 
 In positions 4, 5, 6 we have but the phenomena of 1, 2 and 
 3 reversed, as the eclipse is passing away. 
 
 Even in the midst of totality the place of the moon is not 
 lost, as it is seen to shine with a faint coppery light sufficient 
 to make its position visible. This effect is due to the 
 earth's atmosphere. The light of the sun which penetrates the 
 atmosphere and passes near the earth is affected in two ways ; 
 first, the more refrangible blue violet rays are filtered out and 
 
LUNAR ECLIPSE. 121 
 
 absorbed in undue proportion, and second, the reddish rays, 
 which succeed in passing, are refracted inwards so as to 
 traverse the distant parts of the umbra, and these, falling 
 upon the moon, give to it its faint and weird illumination. 
 As seen from the moon under these conditions the earth 
 would be surrounded by a narrow halo of ruddy light. 
 
 62. Duration of a Lunar Eclipse. 
 
 The eclipse may be of any duration from nothing, when 
 the moon just grazes the shadow, to the maximum when the 
 moon passes centrally through the shadow. We shall con- 
 sider the latter case only. 
 
 It is necessary first to find the velocity of the moon rela- 
 tively to the shadow, that is, to find how fast the moon 
 approaches or leaves the shadow. 
 
 As the moon gains one revolution on the shadow in one 
 lunation, or 27rX238000 miles in 29.5306 days, a little calcula- 
 tion will show that the moon's relative velocity is about 35 
 miles per minute. 
 
 (I). The distance from the centre of 1 to that of 6 (Fig. 
 67) is 12220 miles, and at 35 miles per minute the moon 
 passes over this in 350™, nearly, or 5'' 50™. And this is the 
 average time between the first and the last contacts with the 
 penumbra. 
 
 (2). The distance between the centres of 2 and 5 is 7920 
 miles, which divided by 35 gives 226™, or 3'' 46™. And this 
 is the whole duration of the eclipse, if we regard the eclipse 
 in relation to the umbra only, as is usually done. 
 
 On account of the indefinite boundary of the umbra, how- 
 ever, it is difficult to say practically just when the eclipse 
 begins and when it ends. 
 
 (3) The distance between the centres of 3 and 4 is 3600 
 miles, and divided by 35 this gives 103™, or 1* 43™, which is 
 the average length of totality, for the central lunar eclipse. 
 
 63. The Solar Eclipse. 
 
 The phenomena attendant upon a solar eclipse are con- 
 siderably different from those of the lunar eclipse, because 
 
122 
 
 ASTRONOMY. 
 
 of the difference in the points of view of the observer in the 
 two cases. 
 
 In the kinar eclipse the observer is situated upon the body 
 that casts the shadow, while in the solar eclipse he is placed 
 upon the body upon which the shadow falls. 
 
 In other words, in the lunar eclipse the watcher looks at 
 the shadow as it passes over the face of the moon, while in 
 the solar eclipse the shadow passes over him and hides, either 
 partially or totally, the sun from his view. 
 
 To completely harmonize the two the solar eclipse should 
 be viewed from the moon, and we shall adopt this supposition 
 in our illustration. 
 
 We have seen that when the moon is near apogee its 
 umbra does not reach to the surface of the earth, and the 
 moon is too sma!ll in angular diameter to cover the sun, so 
 that we can have only an annular eclipse of the sun. 
 
 For this reason, and for greater generality, we consider 
 the moon to be in perigee, at the distance 225000 miles from 
 the earth's centre, or thereabouts. 
 
 06 
 
 Fig. 68. 
 
 ^ w 
 
 By a comparatively easy investigation we find the radius 
 of the penumbra of the moon's shadow, at the position of the 
 
SOLAR ECLIPSE. 123 
 
 earth, to be about 2120 miles, and the radius of the umbra 
 to be about 70 miles. 
 
 If the moon were in apogee the radius of the penumbra 
 would be over 2200 miles, and there would be no umbra. 
 
 Draw a circle with radius 57 to represent the earth, and 
 mark the equator and the poles. Through the centre draw an 
 indefinite line, inclined to the earth's axis at any angle greater 
 than about 62°, to represent the moon's orbit, and conse- 
 quently the path of the centre of the moon's shadow. On 
 this as a line of centres draw the circles 1, 2, 3, 4, as in the 
 diagram, with a common radius 30, to represent four posi- 
 tions of the penumbra ; and at the centres of these the black 
 dots, with radius 1, to represent the umbra of the moon's 
 shadow. 
 
 As seen from the moon the 'shadow moves from left to 
 right across the earth, and the earth turns in the same direc- 
 tion. Thus every solar eclipse comes in from the west and 
 moves eastward or nearly eastward across the earth. 
 
 Position L The penumbra touches the earth at r, and the 
 eclipse begins on the earth, since to a person at r the limb of 
 the moon has just come into apparent contact with that of 
 the sun. At r the sun is on the eastern horizon and is rising 
 so that here the eclipse begins at sunrise. , 
 
 Position 2. The umbra has come into contact with the 
 earth, and to observers now at r the total eclipse is beginning 
 at sunrise. 
 
 Position 3. The umbra has arrived at s, which has the sun 
 on the western horizon, and the total eclipse begins at sunset. 
 And finally the penumbra leaves the earth at position 4, that 
 is, the eclipse ends at sunset, or to the observer at j the moon 
 has completely withdrawn from hiding any part of the sun. 
 
 The penumbra, in its course, traces out a kind of belt 
 across the surface of the earth, and every place that lies 
 within this belt when the penumbra reaches the place will 
 witness an eclipse of the sun, while to places outside this belt 
 there will be no eclipse. 
 
 But it does not follow that every place that is within the 
 
124 ASTRONOMY. 
 
 belt when the edipse begins at r will have the eclipse. For, 
 as the earth is rotating in the same direction as that in which 
 the shadow is moving, a place situated as a will have ' turned 
 the corner ' and passed into the night before the eclipse ar- 
 rives ; and a place as b may have been carried out of the belt 
 across the northern limit. 
 
 To a place situated as c when the penumbra overtakes it 
 there will be a small eclipse on the sun's southern limb, as 
 represented at c in the diagram; to a place situated as d, a 
 small eclipse on the sun's northern limb ; at e the eclipse will 
 be large on the southern limb, and at / it will be large on the 
 northern one. 
 
 And finally all places so situated as to be in the narrow 
 belt of totality, when the eclipse comes along, will witness 
 a total eclipse of the sun. 
 
 If the moon were in or near apogee there would be no 
 belt or line of totality, but those situated along the middle 
 line of the penumbra's path would be visited with an annular 
 ecHpse of the sun, as at Z, figure 64. 
 
 The path of a central eclipse may be inclined to the equa- 
 tor at an angle as high as 28° 33', as in the diagram, where 
 the eclipse is represented as taking place at the time of the 
 autumnal equinox. If the eclipse happens at the time of a 
 solstice, it may begin and end on the equator, but as the 
 equator, seen from the moon, is then projected into an 
 ellipse, the central line of the eclipse will pass above or below 
 the equator according as it is the summer or the winter sol- 
 stice. 
 
 64. Duration of Central Eclipse of the Sun. 
 
 The distance from the centre of 1 to that of 4, (Fig. 68), 
 is about 12160 miles, and as the shadow moves practically 
 with the same velocity as the moon, 35 miles a minute, this 
 distance is travelled in 348*", or 5'' 48'", which is the total 
 duration of the eclipse, for the whole earth, from its begin- 
 ning to its end. 
 
 With the moon in apogee the motion of the shadow is 
 slower and the penumbral circle is larger, so that the total 
 length would be increased by 6 or 8 minutes. 
 
SOLAR ECLIPSE. 125 
 
 The longest duration of the eclipse at any one place on the 
 earth is for places situated near the centre of the earth's en- 
 lighted disc at the time. For such places are being carried 
 by the earth's axial rotation, at the rate of 17 miles a minute, 
 in a direction nearly coinciding with that of the shadow. So 
 that the shadow gains only 18 miles a minute. And 4240 
 miles, the diameter of the penumbral ring, divided by 18 
 gives 3* 56™ for the maximum duration of the eclipse at one 
 place. And this would be lengthened out a few minutes with 
 the moon in apogee, as already pointed out. 
 
 The rate of 17 miles a minute is for places on the equator; 
 if the central line of the penumbra passes north or south of 
 the equator, the eclipse will not last quite so long. 
 
 65. Duration of Totality. 
 
 The diameter of the umbral ring upon the earth is, at the 
 best, only about 140 miles. And 140 divided by 18 gives 
 less than 7 minutes for the duration of totality under the 
 most favorable circumstances. 
 
 If the moon is near one of the nodes of its orbit, but not 
 at it, at the time of new moon, the eclipse will not be central, 
 but will pass over the northern part of the earth, or over the 
 southern, as circumstances determine. And when the new 
 moon happens sufficiently far from the node that only a part 
 of the penumbra meets the earth, the eclipse will be a partial 
 one visible only in high northern or southern latitudes, as the 
 case may be. 
 
 When we consider that the moon's penumbra, as also the 
 umbra, is a cone which sweeps over a revolving sphere, we 
 can readily understand that the path of the shadow over the 
 earth will be bounded by a somewhat complex curve in the 
 case of even a central eclipse, and by a still more complex 
 one in that of a partial eclipse. 
 
 In the British Ephemeris or Nautical Almanac these 
 curves are calculated and plotted for every solar eclipse of 
 the year. 
 
 We present herewith maps of the courses of the eclipses 
 for May 28th, 1900, and December 31st, 1880, as these prove 
 to be two quite characteristic ones. 
 
126 
 
 ASTRONOMY. 
 
 In I, both the north and the south limits of the eclipse 
 are shown, the north one passing near the pole, and the 
 eclipse is confined to the northern hemisphere, except for a 
 
 TOTAI. EC1.IPBB 
 
 SUN 
 
 Kay 26,lSOO 
 
 Fig. 69 I. 
 
 little at the beginning. Totality begins in the Pacific Ocean, 
 at a little west of Lower California, at which place the sun 
 is then rising, and it ends in Egypt, at which place and time 
 the .sun is setting. The belt of totality is quite narrow, but 
 wider at the middle than at the extremities, as these latter 
 points are nearly 4000 miles farther from the moon than the 
 middle part of the belt is. For as the moon's umbra is a 
 cone with its apex towards the earth, its section becomes 
 smaller as we recede from the moon. The eclipse was visible 
 over the whole of North America and Europe, over a small 
 portion of South America and a limited portion of western 
 Asia. On May 28th the north pole was somewhat inclined 
 towards the sun, and the eclipse reached northwards to a 
 point beyond the pole. 
 
SOLAR ECLIPSE. 
 
 12/ 
 
 In II, the point A is near the Arctic Circle, and the earth's 
 axis, leaning away from the sun, this point is the most north- 
 ern limit of the sun's rays at this date. The umbra passes 
 north of the earth without touching it, so that the eclipse is' 
 partial only. The loops crossing at A show the angle through 
 
 AKTIXl. 
 XCI.IP6I: OTIKE 
 BVN HEC.SI.IBBO. 
 
 Fig. 69 IL 
 
 which the earth turns while the penumbra is passing over it. 
 The calculation and plotting of these curves for any par- 
 ticular eclipse is a matter of some difKculty, and beyond the 
 scope of this work, but the comprehension of what the curves 
 mean should not be difficult. 
 
 66. Occurrence of Eclipses. 
 
 An eclipse of the moon can take place only at the time of 
 full moon, and an eclipse of the sun only at the time of new 
 moon. And yet it is well known that eclipses do not happen 
 at every full and new moon. For there are 12 full moons 
 
128 ASTRONOMY. 
 
 and 12 new moons in every year, while the average number 
 of edipses in a year is only 4. 
 
 Our present purpose is to examine the conditions under 
 which eclipses take place and the order of their presentation. 
 
 The Lunar Eclipse. It would be of little service to inves- 
 tigate the conditions under which the moon first meets the 
 penumbra of the earth's shadow, for, as already stated, the 
 moon must dip to a very considerable extent into the penum- 
 bra before any visible effect is produced upon the limb of 
 the moon. 
 
 Henc€ it is usual to consider a lunar eclipse in relation to 
 the umbra only, so that the eclipse begins when the moon 
 first comes into contact with the umbra of the shadow. 
 
 On account of the variations in the distance and velocity 
 of the moon the results arrived at must be looked upon as 
 approximations which admit of variations within small limits. 
 
 EcJiptic 59' per day 
 
 Fig. 70. 
 
 Let U be the centre of the earth's shadow (umbra) moving 
 along the ecliptic in the direction UN, and let M be the centre 
 of the rnoon moving along its orbit MN, and so situated at 
 the particular moment that it just touches the shadow exter- 
 nally, as illustrated. Then N is the moon's descending node, 
 and the distance NU is called the lunar eclipse limit on one 
 side of the node, because a lunar eclipse can happen only 
 when the distance of the centre of the shadow from the node 
 is less than the eclipse limit UN. 
 
 Now UM is 2880+1080=3960 miles; and UN is UMX 
 cosec 5° 6'=44S50 miles; and this is one-half the lunar 
 eclipse limit in miles. But we wish to have it expressed in 
 days, that is. in terms of the motion of the shadow per day. 
 As the shadow moves over the moon's orbit in 365 days, the 
 
ECLIPSE LIMITS. 129 
 
 motion per day is got from 2TrX238000/36S, or 4100 miles, 
 nearly. And 44550/4100 gives 11 days to the nearest day. 
 
 But the sun is directly opposite the shadow and is the same 
 distance from one of the nodes as the shadow is from the 
 other. 
 
 Hence, if the shadow, or, what is equivalent, the sun, is more 
 than 11 days from a node at the time of full moon, no eclipse 
 of the moon takes place; and if the distance of the sun from 
 a node be less than eleven days when the moon is full, the 
 moon will be eclipsed either partially or totally. ' 
 
 Again, when the moon touches the umbra internally we 
 have the beginning of totality. The distance between the 
 centres of moon and shadow is now 2880 — 1080^1800 miles, 
 and making a calculation similar to the last we obtain 5 days 
 to the nearest day. So that the lunar eclipse will be total if 
 the sun is within five days of one of the nodes at the time of 
 full moon. 
 
 And thus the whole lunar eclipse limit is 11 days on each 
 side of the node, or 22 days in all ; and the total eclipse limit 
 is 10 days in all. 
 
 67. Solar Eclipse. 
 
 By making U the centre of the earth and M the centre of 
 the moon's penumbra, we find,' by a process perfectly analo- 
 gous to the one applied in the case of the lunar eclipse, that 
 the solar ecliptic limit is 17 days on each side of the node, or 
 34 days in all. 
 
 So that if a new moon happens when the sun is within 17 
 days of a node, there will be a solar eclipse at some place 
 upon the earth. And if the new moon happens when the sun 
 is more than 17 days from a node, there can be no eclipse at 
 that new moon. 
 
 Another Method. 
 
 The foregoing method of studying the occurrence of 
 eclipses by means of linear measures expressed in miles is 
 very explicit and easily understood, and is probably the best 
 for illustration. But in practical work a modification, in 
 which linear measurements are replaced by angular ones, is 
 
130 ASTRONOMY. 
 
 found to be more convenient, as these angular quantities, 
 with their daily variations, are tabulated in the almanac. 
 
 Thus, if P denotes the moon's horizontal parallax; p, the 
 sun's horizontal parallax ; s, the sun's angular semi-diameter ; 
 m, the moon's angular semi-diameter ; and u be the angular 
 diameter of the radius of the earth's umbral circle at the 
 distance of the moon, we have 
 
 P=E/d ; p=E/D ; u=:h/d. 
 
 And by substituting in (y) of page 117 we get 
 u=P-\-p—s. 
 
 But if at full moon the moon touches externally the umbral 
 ring in its passage, the distance of the moon's centre from 
 the ecliptic, that is, the moon's latitude, is practically u-\-m. 
 So that if / denotes the moon's latitude, we have 
 
 For external contact l^P-\-p — s-\-m. 
 Similarly " internal " l^P-\-p — .r — m. 
 
 We can accordingly state that : 
 
 At any full moon there will be a lunar eclipse if the moon's 
 latitude is less than P-)-/!— j-j-w ; and the eclipse will be total 
 if the latitude is less than P-\-p — J — m. 
 
 The letters denote angles in radian measure, but the equa- 
 tion is equally true when the angles are given in degree 
 measure. 
 
 By a similar process of reasoning we find for a solar 
 eclipse : At any new moon there will be a solar eclipse upon 
 some part of the earth if the moon's latitude is less than 
 P — p-\-s-{-m ; and the eclipse will be total or annular at some 
 places on the earth if the moon's latitude is less than 
 P — p-\-s — m. 
 
 These quantities do not vary much, and p being only 8".8 
 may be ignored unless great accuracy is required. 
 
 The average values of the others in minutes of angle are : 
 P=58', s=l6', m=16'. 
 
 Illustration 1. At the full moon on January 22nd at P 46™ 
 past midnight, 1880, the moon's latitude was about 48" south. 
 And as this is well within the limit for total eclipses, which 
 is about 26', there was a large total eclipse of the moon, it 
 being nearly central. 
 
ECLIPSE LIMITS. 131 
 
 Illustration 2. The new moon of November, 1882, hap- 
 pened at 11* 9"* 6' after mean noon at Greenwich, and the 
 moon's latitude at the time was 35' 22" south'. But the limit 
 for totality in a solar eclipse is 58'. And there was an eclipse 
 on the southern hemisphere. The eclipse was annular, and 
 visible in Australia and the South Pacific islands. 
 
 In the British Nautical Almanac, the moon's latitude is 
 given for noon and midnight on every day of the year, and 
 is easily found for any specified time. 
 
 68. Eclipse Periods. 
 
 We have seen that an eclipse can happen only at new 
 moons and full moons, and then only when the sun is within 
 a given distance from one of the moon's nodes, 17 days from 
 the node in the new moon and a solar eclipse, and 11 days 
 from the node in the case of the full moon and the lunar 
 eclipse. And as the sun passes each node once in a year, we 
 have two periods in the year at which eclipses can take place, 
 or eclipse periods. The lengths of these periods are 34 days 
 for solar eclipses and 22 days for lunar eclipses. 
 
 As the time elapsing between two consecutive new moons 
 is not quite 30 days, we see, at once, that there may be two 
 solar eclipses at the same eclipse period. 
 
 Fig. 71. 
 
 This is illustrated in the diagram, which represents mat- 
 ters as seen from the moon. N is the moon's ascending node, 
 and the ecliptic is marked off into days, that is, each division 
 represents one day's motion of the earth in its orbit. £,, is 
 the earth at 15 days before reaching the node, and E^ is the 
 earth 30 days later, both being within the eclipse limit of 34 
 days. Let a new moon happen when the earth is at E^ and 
 let Pj be the moon's penumbral circle ; then a second new 
 moon will take place at E^ with Pj ^s the penumbral circle. 
 
132 ASTRONOMY. 
 
 The first eclipse is at the south polar regions, and the second 
 one at the north polar regions. 
 
 If these conditions occur at the descending node, matters 
 are reversed in the way that the first eclipse would be at the 
 north polar regions and the second at the south polar regions. 
 
 But in either case when two solar eclipses happen at the 
 same eclipse period, they are both small and are confined to 
 polar latitudes. 
 
 As there is a full moon just half-way between two con- 
 secutive new moons, the moon will be full at the node oppo- 
 site that at which the new moon takes place, and there will 
 be a total lunar eclipse. 
 
 Thus, then, when there are three eclipses at the same 
 eclipse period, two will he small eclipses of the sun visible at 
 polar latitudes, and the third a total eclipse of the moon. 
 
 As the lunar eclipse limit is only 22 days, it is evident that 
 there cannot be two lunar eclipses at the same period, and 
 that there need not be any. 
 
 Also, as the limit of totality of a lunar eclipse is 5 days on 
 each side of the node, if there be a partial eclipse of the 
 moon at a period the moon must be more than 5 days from 
 the node, and there can be only one eclipse of the sun, and 
 therefore only two eclipses altogether at that period. 
 
 So that zvhen there are tzvo eclipses at the same eclipse 
 period, they will he a partial eclipse of the moon or a total 
 one of short duration, and an eclipse of the sun. 
 
 Finally, if there be a solar eclipse less than 4 days from 
 the node, there can be no lunar eclipse at that period. 
 
 Therefore, if there he only one eclipse at a period it will 
 he a nearly central eclipse of the sun. 
 
 klMIT9 rOfl „ 80LAH C C L I f 9 t 
 
 All of these may be illustrated by the accompanying dia- 
 gram. 
 
ECLIPSES AT A PERIOD. 133 
 
 Take three graduated rules A, M, B, A being 34 units long, 
 B 22 units, and M of indefinite length, the unit being the 
 same for each. The open circles are 30 units apart, and a 
 black circle is half-way between two open circles. The black 
 circles are referred to scale A only, and the open circles to 
 scale B. Then by sliding M between A and B all the preced- 
 ing cases of eclipses at a node may be illustrated. Thus it is 
 seen that it is possible to make two black circles (new moons) 
 fall within the limits of A, and then the intermediate white 
 circle will be near A''. But it is impossible to bring two white 
 circles to lie within the limits of B, etc. ; showing that there 
 may be two small solar eclipses and a total lunar eclipse at 
 one eclipse period. But there cannot be two lunar eclipses 
 at the same eclipse period. In like manner all the other cases 
 are illustrated. 
 
 69. Motion of Moon's Nodes. 
 
 The nodes of the moon's orbit retrogress at the rate of one 
 revolution in 18.6 years. And as the sun progresses at the 
 rate of one revolution per year, we see that the sun will pass 
 from a node around to the same node again in (18.6X1)/ 
 (18.6-f-l) years, or 346 days to the nearest day. And hence 
 the time required for the sun to go from one node to the 
 other node is 173 days. 
 
 But six lunations occupy 177 days, and thus the time re- 
 quired for the sun to pass from the one node to the other 
 is 4 days less than that required for six lunations. 
 
 So that if a new moon happens when the sun is exactly 
 at one of the nodes, giving a central solar eclipse, the sixth 
 new moon thereafter will occur when the sun is 4 days past 
 the other node, and there will be another solar eclipse, nearly 
 central. 
 
 After another term of six lunations there will be another 
 solar eclipse, with the sun 8 days past the node, and thus, as 
 yet, far within the solar ecliptic limit. 
 
 These relations give rise to a peculiar periodicity of 
 eclipses which we shall briefly consider. 
 
134 ASTRONOMY. 
 
 The figure represents portions of the moon's orbit, or of 
 the ediptic, about the moon's nodes, the extent of each por- 
 tion being such as to include the solar limits of 17 days on 
 each side of the node. These are divided into parts repre- 
 senting 4 days each, from 16 days before the node to 16 
 
 -1 — @ I I I p -1- 
 
 sf -I -4 "? -I 
 
 O O 
 
 Up un 
 
 Hit o *• 
 
 f I 
 
 •< 
 
 O 
 
 0* 
 
 •2 4l>isc.r.ooi 6 a 
 
 Fig. 73. 
 
 days after. The dates given, and the relative positions of 
 the eclipses laid down might occur at some time, but for the 
 present are merely explanatory. 
 
 Suppose that a new moon happens on May 8th, 16 days 
 before the sun reaches the ascending node. This will be a 
 small eclipse visible in the Antarctic regions. This is eclipse 
 number 1. 
 
 The next new moon after six lunations is on October 31st, 
 with the sun 12 days before reaching the descending node, 
 and the eclipse is a small one confined to northern regions of 
 the earth. This is eclipse number 2. Another six lunations 
 gives us eclipse number 3, with the sun 8 days in front of 
 the ascending node. This eclipse is on April 27th, and is 
 visible over southern temperate regions. 
 
 Eclipse number 4 occurs on October 20th, with the sun 4 
 days before the descending node. This will be visible over 
 a large part of the earth, with its centre line north of the 
 equator. The next eclipse, number 5, with the sun at the 
 ascending node, happens on April 17th, and the eclipse will 
 be central over the earth. 
 
 In a similar way ecHpses 6, 7, 8, 9, occurring on October 
 10th, April 6th, September 28th, and March 26th, may be 
 accounted for. 
 
PERIODICITY OF ECLIPSES. -135 
 
 We notice from the foregoing: 1st, That the solar eclipse 
 which began as number 1 on May 8th reappeared alternately 
 at each node, moving forwards 4 days at each appearance, 
 until it finally passed away with its ninth appearance on 
 March 26th, nearly four years after its first presentation. 
 
 Eivdently these nine eclipses do not include all the solar 
 eclipses happening in the period, as there must have been a 
 small solar eclipse about November 1st corresponding to the 
 one on May 8th, etc., but these nine, by their orderly advance 
 of 4 days at each occurrence, form a natural group, and lead 
 one to look upon the whole series as being recurring presen- 
 tations of one and the same eclipse. So that, with this view, 
 eclipses, like human beings, 
 
 " Have their day and cease to be." 
 
 Every solar eclipse, then, begins when the sun has fairly 
 entered upon the western border of a solar limit at one of 
 the nodes. It then travels eastwards through the limits alter- 
 nately at each node, until after 8 or 9 presentations it passes 
 off into space, and is succeeded by another. 
 
 And the same may be said of a lunar eclipse, except that, 
 on account of the shorter limits, the number of presentations 
 will not exceed 5, and may be only 4. 
 
 We notice, 2nd, that the eclipse periods travel backwards 
 through the year, which is, of course, due to the retrogres- 
 sion of the moon's nodes. 
 
 70. Number of Eclipses in a year. 
 
 In the case of a central solar eclipse there can be no eclipse 
 of the moon at that period. So, if the periods come in not 
 at the beginning or end of the year, we may have a solar 
 eclipse with the sun a coviple of days in advance of the node, 
 and at the next period another solar eclipse with the sun two 
 days past the node. And thus the least number of eclipses 
 in the year is two, and they are both of the sun and quite 
 central over the earth. 
 
 If the eclipse period begins with the year, so that there 
 may be a small solar eclipse on January 1st or 2nd, there may 
 
13e ASTRONOMY. 
 
 be three eclipses at this period, two of the sun and one of 
 the moon. At the next node, 173 days after, we may have 
 three more eclipses, two of the sun and one of the moon. 
 Then, after 346 days, which is 19 days before the year closes, 
 the first node comes in again in time to give another eclipse 
 of the sun before the end of the year. 
 
 And thus the greatest number of eclipses which can take 
 place in any one year is 7, of which 5 are solar and 2 lunar. 
 
 The most common number of eclipses in a year is 4. 
 
 71. The Saros. 
 
 This is a remarkable cycle in the recurrence of eclipses 
 which has been known since very early times and whose dis- 
 covery has been, by some ancient writers, attributed to the 
 old Chaldean astronomers. 
 
 The occurrence of an eclipse depends, as we have seen, 
 altogether upon the relative positions of the moon and the 
 nodes of the moon's orbit at the time of new or full moon. 
 If the moon and the node were exactly together at any new 
 moon, and if after n lunations the moon and the node were 
 again exactly together at the new moon, they would presum- 
 ably be exactly together after every period of n lunations, 
 and every eclipse of one of these cycles of n lunations would 
 be repeated in each and every cycle, so that a record of the 
 eclipses for one cycle would answer for every cycle so far 
 as the sequence and magnitudes of the eclipses were con- 
 cerned. 
 
 If this correspondence were not exact, but very approxi- 
 mately so, the character of the set of eclipses belonging to 
 one cycle would differ only slightly from that of those be- 
 longing to the preceding cycle, and although there would be 
 a slow and gradual marching of the eclipses through the 
 cycle, it might require many years to effect a very material 
 change in the main features of _ the eclipses belonging to 
 the set. 
 
 Now, the moon's siderial period is 27.32166 days, while 
 the node makes one revolution backwards in 6793.39108 
 days. Hence, we find, by the formula ah/{a-\-b), that the 
 
SAROS. 137 
 
 time required by the moon to pass from one node to the same 
 node again is 27.21222 days. And we know that the length 
 of a lunation is 29.53059 days. 
 
 Hence 223x29.53059=6585.322 days, 
 and 242X27.21222=6585.357 days. 
 
 Or, the time required for 223 lunations is shorter than that 
 required for 242 returns of the moon to the same node by 
 only 0.035 days. And as the moon moves 13°.2 per day, this 
 is equivalent to about 28', or 4' less than the moon's diameter. 
 So that if a new moon happened in any year exactly at 
 the node, the 223rd new moon after would take place when 
 the moon was 4' less than its diameter from the node, and 
 the two eclipses would be almost exactly alike in magnitude. 
 But this is not all. The perigee makes one complete revo- 
 lution forwards in 3232.5753 days. Then we find that it 
 takes the moon 27.5546 days to go from the perigee to the 
 perigee again. And 239X27.5546 is 6585.534 days, which 
 differs from 223 lunations by only 0.212 days, or an angle 
 equal to about 2° 48' or about 5 times the moon's diameter. 
 So that if a solar eclipse happened when the moon was in 
 perigee, the 223rd new moon thereafter would have the moon 
 only 5 times its own diameter from the perigee, and the two 
 solar eclipses would be almost exactly of the same character 
 as to their being total or annular. 
 
 Thus we have 223 lunations, 242 returns to the same node, 
 and 239 returns to the perigee occupy almost the same length 
 of time. 
 
 Dividing 6585.322, the number of days in 223 lunations, 
 by 365 gives 18 years of 365 days each, with 15^ days over 
 very nearly. But 18 years contain either 4 or 5 leap years, 
 and taking the 4 or 5 days from the 15^ gives us 18 yrs. 11-j 
 days, or 18 yrs. lOJ days, according as there are 4 or 5 leap 
 years in the cycle. So that a new Saros begins only 10^ or 
 11-J days later in the year than the preceding one did, and 
 the corresponding eclipses of two consecutive Saroses will 
 take place in practically the same parts of the heavens, that 
 is, in positions only 10° or 11° removed from the places of 
 the former. 
 
138 ASTRONOMY. 
 
 The number of eclipses in a Saros is about 70, of which 
 40 are solar and 30 lunar. 
 
 Although the Saros offers a remarkable relation as exist- 
 ing among the times of three particular revolutions, the 
 moon, the node, and the perigee, yet the small discrepancies 
 existing gradually and slowly carry those eclipses which are 
 near the border from one cycle into the next. 
 
 72. The Metonic Cycle. 
 
 We ask, is there any cycle of years such that the new 
 moons or full moons will repeat themselves, so as to fall 
 upon the same dates in the year? Or if there is no exact 
 cycle of this kind, what is the closest approximation we can 
 find to it ? 
 
 The equinoxial year=365.2422 days, and the mean luna- 
 tion is 29.5306 days. By forming a fraction with these 
 numbers and finding its convergents, we get 19/235 as a very 
 close approximation. Or, in other words, 235 lunations are 
 approximately equal to 19 equinoxial years. 
 
 Now 19X365.2422=6939.602 days, 
 and 235 X 29.5306=6939.690 days. 
 
 These differ by only 0.088 days or about 2^ 6"*. Thus, if 
 a new moon occurred at mean noon on January 1st in any 
 year, the 235th new moon thereafter would happen in the 
 19th year thereafter on January 1st at about 2* 6" p.m., not 
 considering the variation due to leap years. So that, prac- 
 tically, the new and full moons of any year occur upon the 
 same days of the same months as they did 19 years before. 
 This cycle of 19 years was discovered by Meton, a Greek 
 astronomer, about 433 B.C., and after him it is called the 
 Metonic Cycle. 
 
 The cycle is of some importance in chronology as far as 
 its facts have relation to the motions and places of the moon ; 
 but as the years are counted as 365 days with the necessary 
 addition of a day every four years, the times of the moon's 
 changes as given by the Metonic Cycle may be as much as 
 a whole day off at certain times, or under certain circum- 
 stances. With these unimportant discrepancies, the moons 
 
ECCLESIASTIC CALENDAR. 139 
 
 of one cycle are repeated in the next cycle with remarkable 
 faithfulness, when the whole case is considered. 
 
 But the Metonic Cycle, unlike the Saros, has no practical 
 connection with the recurrence of eclipses. 
 
 ECCLESIASTIC CALENDAR. 
 
 This article is inserted here, not because of its astronomical 
 importance, but because it has a relation to our civilized life, 
 which must make it of considerable interest to many people. 
 
 The moveable feasts of the ecclesiastic calendar are depend- 
 ent upon Easter, which itself is dependent upon a special full 
 moon. Thus, Easter Sunday is the first Sunday following 
 the ecclesiastic full moon which happens first after the vernal 
 equinox. So that Easter may fall any time between the 23rd 
 of March and the 26th of April. 
 
 By the ecclesiastic full moon is meant, not the full moon 
 of the astronomer, but the average full moon, so to speak, as 
 determined by means of the Metonic Cycle or a modification 
 of it. This is necessary if Easter is to be kept upon the same 
 Sunday throughout the Christian world. For it is easily 
 conceivable that an astronomic full moon may occur at one 
 place on a Saturday and at some distant place upon the Sun- 
 day after. And in such a case the " Sunday following the 
 fxill moon " would not be the same for both places. 
 
 That is, the ecclesiastic full moon is not an absolute event 
 for the whole earth, as the astronomic full moon is, but has 
 relation to the local time. 
 
 The determination of Easter, then, fixes the moveable 
 feasts for the year, and for this determination we make us 
 of the Golden Number, the Epact and the Sunday letter or 
 number. 
 
 73. The Golden Number. 
 
 The Golden Number for any year is the number of that 
 year in the Metonic Cycle of 19 years, and it received its 
 name from the circumstance that it was formerly printed in 
 the calendar in figures of gold. 
 
140 ASTRONOMY. 
 
 The beginning of the cycle is arbitrary, but usage has given 
 us the following rule : 
 
 Denote the golden number by G, and the year by y. 
 
 Then G is the remainder from {y-\-l)/19. Arid if there 
 is no remainder the golden number is 19, as zero does not 
 count. Thus the golden number for 1910 is 11. 
 
 74. The Epact. 
 
 This has been already explained as the moon's age on 
 January 1st, or the number of days which have elapsed on 
 January 1st since the previous new moon. 
 
 If we know the epact, E, for any year, we can readily find 
 the dates of all the new and full moons of the year. But as 
 the new moons repeat themselves every 19 years, so the epact 
 must have a cycle of 19 years, and should be determinable 
 from the golden number. We have the following rule : 
 
 The remainder from 11(G — 1)/30 is £+1, or E, accord- 
 ing as the year is a common year or a leap year. 
 
 Thus for 1910, which is a common year, 11(11— 1)/30= 
 £+1 .". £=19, the epact for 1910. 
 
 Having the epact we can calculate the date of the full 
 moon following the vernal equinox. Thus for 1910 the epact 
 is 19. Taking this from 30 leaves 11th for date of new moon 
 in January. Adding 59 (two lunations) to 11 and subtract- 
 ing 31-|-28 for January and February leaves 11th for date 
 of new moon in March. And adding 14 we get March 25th 
 as the date of full moon in March. This is after the vernal 
 equinox, and the Sunday following this was Easter. 
 
 75. The Dominical or Sunday Letter. 
 
 This is a letter, from A to G, accompanied by a number 
 and a day of the week, and indicates the date of the first 
 Sunday in the year. 
 
 The rule for finding the Sunday number is as follows : 
 The division (5v-l-19)/4 gives Q-\-a remainder. 
 
 Then 7 — Remainder from Q/7=the Sunday number 
 . =the date of the first Sunday in the year. When the 
 number comes out zero, 7 is to be taken. 
 
ECCLESIASTIC CALENDAR. 141 
 
 Applying this to 1910 gives 2, so that January 2nd was 
 Sunday, and the year came in on Saturday. 
 
 Thence it is easy to find that March 27th was Sunday, and, 
 from the foregoing, Easter Sunday. 
 
 The numbers, the letters and the days of the week are 
 connected as follows : 
 
 12 3 4 5 6 7 
 
 A B C D E F G 
 
 Sun. Sat. Fri. Thur. Wed. Tues. Mon. 
 
 Thus the Sunday letter for 1910 is B, and the year began 
 with Saturday. The Sunday letter for 1915 is C, and the 
 year begins with Friday, and the first Sunday is the 3rd. 
 
 In leap years the Sunday letter retrogrades one place after 
 February 29th, on account of the additional day in February. 
 Thus, for 1912 we have G from January 1st to March 1st, 
 and then F for the rest of the year ; so that the Sunday let- 
 ters are GF.. That is to say, that after March 1st, the Sun- 
 days follow the same order as if the year began with 
 Tuesday instead of with Monday. 
 
 The following stanza is often convenient in connecting 
 certain days of the months with the first day of the year : 
 
 The 1st of October you'll find if you try, 
 
 The 2nd of April as well as July, 
 
 The 3rd of September and also December, 
 
 The 4th day of June and no other remember, 
 
 The Sth of the leap-month, of March and November, 
 
 The 6th day of August and 7th of May 
 
 Agree with the first in the name of the day. 
 
 But do not forget that when leap year is reckoned 
 
 From the first of March on they agree with the second. 
 
 Thus, in 1910 the 3rd of December is Saturday, and the 
 24th is Saturday, so that Christmas is on Sunday. 
 
 76. The Julian Calendar. 
 
 The Julian Calendar, which was devised by an Egyptian 
 astronomer, Sosigenes, under the patronage of Julius Caesar, 
 and hence named after him, made three successive years to 
 consist of 365 days each and the fourth year of 366 days. 
 
142 ASTRONOMY. 
 
 This is the same as the present, or Gregorian, calendar, 
 with the exception of the correction for centuries, and intro- 
 duces an error of 3.104 days in 400 years. 
 
 At the time of the Council of Nice, 325 A.D., the vernal 
 equinox was on March 21st, but in the reign of Pope 
 Gregory XIII, 1582, the vernal equinox had shifted to 
 March 10th. By the advice of the astronomers of the time 
 the pontiff issued a decree that the day after the fourth of 
 October in that year should be called the fifteenth, thus 
 throwing 10 days out of the calendar of the year. 
 
 This change was adopted at once in all Roman Catholic 
 countries, but it was not adopted in Great Britain until the 
 year 1752, when by Act of Parliament 11 days were thrown 
 out between the 2nd and the 14th of September. Russia 
 adopted the changed calendar only about two years ago. 
 
 In reading dates one often finds them distinguished as 
 O.S., old style, and N.S. new style, these having reference to 
 the change in the calendar. O.S., then, means according to 
 the Julian Calendar, and N.S., according to the Gregorian 
 Calendar. 
 
 THE SOLAR SYSTEM. 
 
 The members of the solar system are : ( 1 ) the sun, which 
 is the practical centre of the system and the principal source 
 of its light and heat ; (2) a number of planets and planetoids 
 or asteroids revolving about the sun and retained in their 
 orbits mainly by the sun's attraction; (3) a number of 
 moons, or secondary planets, which revolve about certain of 
 the planets as centres; and (4) an indefinite number of 
 comets or cometary and meteoric masses which manifest 
 their presence only occasionally. 
 
 The principal planets are Mercury, Venus, Earth, Mars, 
 Jupiter, Saturn, Uranus and Neptune. The planetoids or 
 asteroids differ from these principally in regard to size, they 
 being comparatively very small. Thus the diameter of the 
 smallest planet is nearly 3000 miles, while that of the largest 
 
THE PLANETS. 143 
 
 planetoid is probably not 300 miles, and some of them are 
 very much smaller. 
 
 The principal known planetoids are Eros, a small body 
 circulating between the orbits of Earth and Mars, and a group 
 numbering over 300, which have their orbits lying between 
 those of Mars and Jupiter. 
 
 The planetoids are all telescopic on account of their small 
 size, and the majority of them can be seen only under high 
 powers of the telescope. Also, two of the known planets, 
 Uranus and Neptune, are telescopic, but not on account of 
 their small size, as they are both large planets, but on account 
 of their great distance. And recently a telescopic planet has 
 been discovered beyond the orbit of Neptune, but nothing 
 very definite is, as yet, known about it. However, whatever 
 its real size may be, it cannot be small and be visible at such 
 a distance. 
 
 77. Order of the Planets. 
 
 The accompanying list gives the order of the planets, • 
 counted from the sun outwards, together with the astrono- 
 mical symbols by which they are denoted, when there are 
 such. Those numbered are principal planets : 
 
 1. Mercury, 
 
 S 
 
 Asteroids, 
 
 
 2. Venus, 
 
 9 
 
 5. Jupiter, 
 
 n 
 
 3. Earth, 
 
 e 
 
 6. Saturn, 
 
 T? 
 
 Eros, 
 
 
 7. Uranus, 
 
 ¥ 
 
 4. Mars, 
 
 $ 
 
 8. Neptune, 
 
 w 
 
 Of the first four planets. Mercury, Venus, Earth, and 
 Mars, the largest is the earth, with a diameter of 7920 miles, 
 and of the next four, Jupiter, Saturn, Uranus, and Neptune, 
 Uranus is the smallest, with a diameter of nearly 35,000 
 miles. 
 
 So that the planets are readily divided into four minor 
 ones, which lie near the sun, and four major ones, which lie 
 farther away. This great difference in the sizes of the minor 
 
144 ASTRONOMY. 
 
 and major planets is a peculiarity of which there is no ready 
 explanation. 
 
 Eros is a small body, probably not more than 8 or 10 miles 
 in diameter, and the numerous asteroids vary in size from 
 about 300 miles down to 4 or 5 miles in diameter. These 
 are of very little interest to any one except the professional 
 astronomer, and not of much interest to him; although it is 
 thought that Eros may be of some importance in correcting 
 the present accepted distance of the earth from the sun. 
 
 78. Common Statements for the Planets. 
 
 (1). All the planets and planetoids revolve in ellipses 
 approximately circles, having the sun at one of the foci, and 
 all the moons revolve in ellipses having a primary planet at 
 one of the foci. 
 
 (2). All the planets and planetoids revolve in the same 
 direction, such that, as seen from the northern pole of the 
 ecliptic, it is opposite to that of the hands of a clock over 
 the dial. This is called the positive direction, and all the 
 moons, with one exception, revolve about their primaries in 
 the same positive direction. 
 
 (3). Every planet that rotates on its axis does so in the 
 positive direction. 
 
 (4). All the planets have orbits which are confined to the 
 zodiac, and some of them lie quite close to the ecliptic. 
 
 But this is not true of the planetoids, as about 30 per cent, 
 of them stray beyond the confines of the ecliptic. 
 
 This community of properties naturally points to a com- 
 munity of origin, and the probability is that in some way, 
 the nature of which is not certainly determined, the sun and 
 the planets have come, by a natural process of evolution, 
 from something which preceded them in time, and which 
 was the common origin of them all. 
 
 It follows, from what precedes, that the orbit of every 
 planet crosses the ecliptic at two points, and thus has an 
 ascending and a descending node; so that every planet is, 
 generally speaking, one half the time upon the northern side 
 of the ecliptic, and one half the time upon the southern side. 
 
THE PLANETS. 145 
 
 The accompanying table of the elements of the planets will 
 be found useful : 
 
 
 
 
 
 
 Mean 
 
 
 
 
 
 
 Bist from 
 
 Dist. 
 
 Period 
 
 Orbital 
 
 Rota- 
 
 Long. 
 
 
 
 Diam. 
 
 Sun in 
 
 from 
 
 of 
 
 vel. 
 
 tion Inclina- 
 
 of 
 
 
 
 in 
 
 millions 
 
 Sun 
 
 Eevol. 
 
 in mile! 
 
 5 on tion of 
 
 Ascen. 
 
 
 PlE;:et 
 
 miles 
 
 of miles 
 
 e=i 
 
 in dys. 
 
 per min 
 
 . Axis Orbit 
 
 Node Dens'y 
 
 Mercury . . 
 
 .. 3000 
 
 35M 
 
 .387 
 
 88 
 
 1773 
 
 88 dys. 70 0' 
 
 46° 
 
 6.85 
 
 Venus . . 
 
 . .. 7660 
 
 66H 
 
 .723 
 
 224.7 
 
 1296 
 
 225 dys. 3°24' 
 
 75° 
 
 4.81 
 
 Earth .. . 
 
 ... 7920 
 
 93i 
 
 1.000 
 
 365.3 
 
 1102 
 
 23.9 hrs. 0°0' 
 
 0° 
 
 5.66 
 
 Mars . . . 
 
 . .. 4210 
 
 141 
 
 1.524 
 
 687 
 
 895 
 
 24.6 hrs. 1°51' 
 
 48° 
 
 4.17 
 
 Jupiter . . 
 
 ...86000 
 
 480 
 
 5.203 
 
 4332 
 
 484 
 
 9.9 hrs. 1 = 19' 
 
 99° 
 
 1.38 
 
 Saturn . . 
 
 ...70500 
 
 881 
 
 9.539 
 
 10760 
 
 357 
 
 10.2 hrs. 2°30' 
 
 112° 
 
 0.7S 
 
 Uranus . . 
 
 ..31700 
 
 1771 
 
 19.183 
 
 30700 
 
 252 
 
 0''46' 
 
 73° 
 
 1.28 
 
 Neptune .. 
 
 ..34500 
 
 2775 
 
 30.054 
 
 60000 
 
 202 
 
 1047/ 
 
 130° 
 
 1.15 
 
 This table brings into prominence several peculiar features 
 of the solar system. 
 
 (1) The very great increase in the sizes of the planets as 
 you pass from Mars to Jupiter, and the corresponding de- 
 crease in their densities. Thus, on the average, a cubic foot 
 of the matter which composes any one of the major planets, 
 is not one- fourth as heavy as a mean cubic foot of the mate- 
 rial forming the earth ; and Saturn is so light that it would 
 float in water. 
 
 One would naturally expect the very reverse. For a large 
 planet should have more central attraction of its parts and 
 therefore be more condensed than a small one. And the only 
 feasible explanation is that these major planets are very hot 
 and that a very large proportion of their visible bodies is in 
 a gaseous state, while the solid and liquid matter forms a 
 nucleus in the centre. 
 
 We notice also that, with the exception of Mercury, all 
 the principal planets have their orbits lying quite close to the 
 ecliptic, so that their deviations from side to side includes 
 only a small part of the zodiac. 
 
 Mercury and Venus have both been stopped in their axial 
 rotation by tidal friction, so that they now present the same 
 
146 
 
 ASTRONOMY. 
 
 face continually to the sun, or they revolve on their axes in 
 the same time as they revolve about the sun. 
 
 79. Relation between Period and Distance of a Planet. Kepler's 
 law III. 
 
 Let 5 be the sun and let the planet at P be moving in the 
 direction PT zt right angles to the radius PS, and let its orbit 
 be a circle. 
 L 
 
 The attraction of the sun on the planet pulls it in the direc- 
 tion PS, and as the orbit is a circle, PQ may be taken as the 
 measure of the sun's attraction and be denoted by /, while 
 QV, denoted by v, will represent the planet's velocity in its 
 orbit; for however near F is to P the motions PQ and QV 
 brings P to V. 
 
 But by an elementary theorem on the circle PQ{2r — PQ^ 
 = QV^ And PQ being very small in comparison with PS 
 and QV, its square may be rejected when V is near P, so 
 that at the limit PQ=QV'/2r, or f=cv^/r where c is a con- 
 stant. 
 
 But if t be the time of revolution about the sun, v^^l-nr/t. 
 And m denoting the mass of the sun, f:=c-ym/r'^ where c-^ and 
 m are constants. 
 
 Whence eliminating / and v, r^/f^z. constant. 
 
 That is, for a planet moving in a circle the cube of the 
 radius of the orbit is proportional to the square of the time 
 of revolution. And as all the planets move in orbits which 
 are nearly circles, and their masses are very small as com- 
 pared to that of the sun, we may make the general statement 
 that with any two planets the squares of their periodic times 
 are proportional to the cubes of their mean distances from 
 the sun ; and this is Kepler's law III. 
 
INFERIOR PLANETS. 
 
 147 
 
 80. The Inferior Planets. 
 
 This term is applied to the two planets Mercury and 
 Venus, whose orbits are included within that of the earth. 
 The phenomena attendant upon these planets are somewhat 
 different from those attendant upon the superior planets, or 
 those whose orbits lie beyond that of the earth. 
 
 As very little can be said to be actually known of the phy- 
 sical state or condition of any of the planets except the earth, 
 we shall confine ourselves at present principally to mechani- 
 cal descriptions of movements and appearances. 
 
 \ _ 
 
 Fig. 75. 
 
 In the diagram we have the sun in the centre, and sur- 
 rounding it the orbits of Mercury, Venus, and earth. Motion 
 takes place in the direction indicated by the arrows, but for 
 the sake of simplicity of explanation we may, for the present, 
 suppose the earth to remain at rest. 
 
148 ASTRONOMY. 
 
 When Venus is at A, or B, so that a line from the earth is 
 tangent to the orbit of Venus, the planet appears to be com- 
 ing directly towards the earth, as at A, or to be moving 
 directly away from the earth, as at B. In both of these posi- 
 tions the planet is said to be stationary. Also, the planet is 
 then said to be at its greatest elongation, east of the sun 
 when at A and west of the sun when at B. 
 
 For the angle of greatest elongation we have AS/ES 
 =sm.AES._ Whence AES=A6° 18'. This angle is, of 
 course, subject to small variations, but upon the average 
 Venus never departs much more than 46° from the sun, and 
 in its journey about the sun it appears, to us, to oscillate 
 eastward and westward from side to side of the sun. 
 
 At C and C Venus is in conjunction with the sun, C being 
 inferior, and C superior conjunction. 
 
 While the planet moves through the arc BC'A, it appears 
 to move forwards among the stars, and is said to have 
 direct motion, while in the remainder of its course it appears 
 to move backwards among the stars, and is, said to have 
 retrograde motion. As the earth is all the while moving for- 
 
 j-.i..r ::;;;::A*::::::rfr ^-• 
 
 ....♦ ■"-■•*••-*.::.'" ^-s**- ... .■^'"'y 
 
 A.pfiarctt« p<»tk of V«nn.s Irotn Kay 6lH to %*pt.Ut^ 
 ■|»O0 
 
 Fig. 7Sa. 
 
 wards, the apparent path of Venus amongst the stars is very 
 irregular as appears in the diagram. The planet appears to 
 make a loop, more or less like the one represented, every 
 580 days. 
 
 Quite similar descriptions apply to the planet Mercury. 
 
 81. Evening and Morning Star. 
 
 When Venus is situated in the arc C'AC it appears east of 
 the sun in the heavens, and after sunset it appears in the 
 
VENUS. 149 
 
 west as the evening star. If it be near the point A it will be 
 quite high in the western sky at sunset, and will be brighter 
 than any fixed star. 
 
 But when the planet is situated in the arc CBC, it appears 
 west of the sun, and rises in the morning before the sun, thus 
 forming a morning star. It is then to be seen in the eastern 
 horizon before sunrise. 
 
 Of course, any conspicuous starlike body which rises a 
 short time before the sun or sets a short time after the sun, 
 may appear as a morning and an evening star. But this 
 name is usually applied only to the planets. Thus, Mercury 
 is alternately morning and evening star, although it is rarely 
 visible in high latitudes, on account of its departing only 25° 
 from the sun, and on account of its small size. Jupiter and 
 Saturn are also spoken of as morning and evening stars 
 when in the proper positions, but Venus is the principal 
 planet appearing in this role. 
 
 82. Phases of Venus. 
 
 In inferior conjunction Venus is only about 26 millions of 
 miles from the earth, while in superior conjunction it is 
 
 "■"€).... 
 
 Fig. 76. 
 
 about 158 millions, so that its angular diameter varies from 
 about 1' when nearest the earth, to 10" when farthest away. 
 Also, the dark side of the planet faces the earth at inferior 
 conjunction, and the planet would be invisible even if it 
 
ISO ASTRONOMY. 
 
 were not obscured by the powerful rays of the sun. As it 
 leaves the inferior conjunction it gradually grows smaller 
 in appearance, and passes through the various phases of the 
 moon until the point of superior conjunction is reached, as 
 illustrated in the accompanying figure. 
 
 83. Transit of Venus. 
 
 It is obvious that if an inferior conjunction of Venus takes 
 place when the planet is sufficiently near one of the nodes 
 of its orbit, the planet will be seen to cross the sun's disc 
 as a small round black spot. This phenomenon, which we 
 now propose to study, is called a transit of Venus. 
 
 Conditions of a Transit. 
 
 Let EAC be a section of the plane of the ecliptic, 5" be the 
 sun, V the position of Venus when in inferior conjunction, 
 
 Fig. 77. 
 
 and E be the earth. Then by the application of continued 
 fractions we obtain that CA : CE^8 : 11 very nearly, so that 
 if we take CA as 8, EA becomes 3. 
 
 Now, in the position V, the planet, as seen from the earth, 
 just touches the limb of the sun and the angle SEC^16', 
 nearly. But lVCA=ysXJ'EC=6'. And this is the lati- 
 tude of the planet when, as seen from the earth, it appears 
 to graze the limb of the sun in passing the latter. 
 
 As the inclination of the orbit of Venus to the ecliptic is 
 3° 44', we readily find that the distance of the planet from 
 the node, when its latitude is 6', is 6'Xcosec3° 44', which 
 works out to 1 ° 42'. And if Venus is further from the node 
 than this, its latitude is more than 6', and it will not transit 
 the sun's disc in passing. But if it is nearer the node than 
 
TRANSIT OF VENUS. 
 
 151 
 
 1° 42', its latitude is less than 6' and it will be seen to cross 
 the sun in passing. And thus the whole transit limit is about 
 3° 24' at each node, or 1° 42' on each side of the node. 
 
 Fig. 78. 
 
 Let 5" be the sun, N a node of Venus' orbit, and E the 
 earth in line with the node, the ecliptic being in the plane of 
 the paper. The earth moves from E to E', through the angle 
 ESE'=59' in one day. And the angle by which it has passed 
 the node is A^E'S, which is Vs oi 59', very nearly, or 2° 37'. 
 So that the earth passes the node at the rate of 2° 37' per 
 day. 
 
 Again, 8 siderial years =2922.08 days, 
 
 and 13 revolutions of Venus=2921.10 days. 
 
 The difference is 0.98 days, during which time the earth 
 will move over 57' in regard to the sun, or over 2° 32' with 
 respect to the node. 
 
 Fig. 79. 
 
 Hence, if at any time Venus is in inferior conjunction at 
 the node, the conjunction 8 years afterwards will take place 
 with Venus 2° 32' past the same node. 
 
 From which it is readily seen that if a transit occurs as 
 at aa', there may be a second transit 8 years after, as at bb', 
 or vice versa, depending upon which node is concerned. 
 
152 
 
 ASTRONOMY. 
 
 But if the transit be central as cd , or nearly so, there can 
 be only a single transit, as the passages of Venus 8 years 
 before and 8 years after, both fall beyond the transit limit. 
 
 After two transits, 8 years apart, there cannot be another 
 transit for over a century. There were transits in 1874 and 
 1882, and the next two will be in 2004 and 2012. 
 
 Transits of Venus were looked upon, in the past, as astro- 
 nomical phenomena of singular importance, as furnishing the 
 means of finding the sun's horizontal parallax. Thus — Let 
 
 Fig. 80. 
 
 A, B be two observers upon the earth, and, for the sake of 
 simplicity of explanation, let them be at the end-points of 
 a diameter. 
 
 The observer at A sees Venus transiting the sun's disc 
 along aa', and the observer at B sees it passing along bb'. 
 Denote the angle AA'B by 2p, this angle being twice the sun's 
 horizontal parallax. The angle u, or A'BB' is determined by 
 the observation, which would be easily done if we could de- 
 termine exactly the points A' and B', or the paths aa' axidbV 
 on the sun's disc. 
 
 Let the angle A'VB' be denoted by p. Then all the angles 
 being very small, if E and V denote respectively the distances 
 of the Earth and Venus from the sun, 
 
 A'B'=Vp=Ea 
 .-. p=aE/V=c.+2p, .-. p=i(E/V—l)a. 
 
 Now Kepler's law III tells us that with any two planets, 
 the squares of their periodic times are proportional to the 
 cubes of their mean distances from the sun ; or 
 
MARS. 153 
 
 (224)= : (365y=V' : E\ 
 .-. E/V= {365/224)^^1.3847, 
 whence, p^0.1623a. 
 
 So that when a is known p is readily found, and this is the 
 sun's horizontal parallax. 
 
 Owing to the facts that transits of Venus occur so seldom 
 and that it is difficult to get good reliable observations when 
 they do occur, they are not considered of as much account 
 as formerly. And of course they are out of account for the 
 present century. 
 
 84. Mars. 
 
 As being our nearest superior neighbour of importance, 
 Mars is of considerable interest to us. It is smaller than the 
 earth, being only about 4210 miles in diameter, while that of 
 the earth is 7920 miles. It possesses an atmosphere which is, 
 however, much rarer than the terrestrial one. It revolves on 
 its own axis once in 24'' 37" 22« of our time, and thus has its 
 day and its night much the same in length as the earth has. 
 
 Its axis is inclined to the plane of its orbit at an angle of 
 25°, while that of the earth's axis is 23° 27', and Mars has 
 thus its seasons, spring, summer, autumn, and winter, much 
 the same in order and relative character as we have. 
 
 It has its year of 687 of our days or about 669 of its own 
 days. And it has its fields of ice and snow which gather 
 around either pole during its long wintry night of darkness, 
 and which gradually melt away, either in whole or in part, 
 when the pole comes to bask in the continuous rays of the 
 summer sun. 
 
 The orbits of earth and Mars are so situated relatively 
 that the perihelion of Mars is only about 60° distant from 
 the aphelion of earth, as is shown at P and A. The conse- 
 quence is that at a point between these as at E and M, the 
 two planets are separated by only about 36,000,000 miles, 
 while if each were in the opposite points of their orbits they 
 would be about 60,000,000 miles apart. 
 
154 ASTRONOMY. 
 
 When the earth is between the sun and Mars, the latter is 
 said to be in opposition, as at M ; and when the sun is be- 
 tween the earth and Mars, as at M', Mars is said to be in 
 conjunction. When Mars is in opposition it comes to the 
 meridian at midnight, and when in conjunction it is lost in 
 the glare of the sun. 
 
 Fig. 81. 
 
 With the earth at E and Mars at M' their distance apart 
 is from 225 to 250 millions of miles, so that the apparent 
 angular diameter of Mars will be from 5 to 7 times as great 
 when Mars is in opposition as it is when near conjunction. 
 As a consequence, when near conjunction Mars appears as 
 a very small star, while near opposition it almost rivals 
 Venus at its best. 
 
 When Mars is at m, dwellers on the earth at E cannot see 
 its whole enlightened face and it appears gibbous, or similar 
 to the moon when about 10 days old. But the planet cannot, 
 in any position, appear in a crescent form. 
 
 As the earth and Mars move in the same direction, as is 
 indicated by the arrows, and the earth moves in angle con- 
 siderably faster than Mars, in some part of the orbit, about 
 the opposition, Mars will appear to move backwards amongst 
 the stars. And thus, like Venus, Mars will appear to de- 
 scribe a loop in the heavens about the time of every opposi- 
 
MARS. 155 
 
 tion. The loop, however, is shorter than that described by 
 Venus. 
 
 By working out the value of (687x36Si)/(687— 365i) 
 we find the time elapsing between two consecutive opposi- 
 tions of Mars to be 780 days, very closely, and this is about 
 50 days greater than two years. 
 
 So that if an opposition took place at EM, January 1st, 
 1900, say, the next opposition would be about 50° further 
 on, at e'm', on February 20th, 1902, the next at e"m" on 
 April 11th, 1904, and so on. And thus all the oppositions 
 are not equally favorable for observations on the planet. 
 
 If, now, we form the convergents to the fraction 780/365, 
 we find that a near convergent is ^"/y, and then 7X780 
 =5460 days, while 15x365^=5479 days, nearly. So that 
 after 15 years, or 7 oppositions, the oppositions return to 
 within 19 days of their original place. And it can be readily 
 shown that after 126 years the oppositions will return to 
 within 2 days of their original places. 
 
 Mars, when in or about opposition, can be practically 
 employed in determining the sun's horizontal parallax. 
 
 AB is the diameter of the earth, and for the sake of sim- 
 plicity of explanation we will suppose observers to be placed 
 at A and at B. 
 
 Fig. 82. 
 
 As seen from A and B the projections of Mars upon the 
 surface of the heavens are a and b respectively. And if 6" 
 be a star, AS and BS are parallel. The observers measure 
 the angles SAa and SBb, and the difference of these is the 
 angle AMB, which is denoted by a. 
 
156 ASTRONOMY. 
 
 Then if ^ be the distance of the earth from the sun and 
 m be the distance of Mars, AM^m — e ; and if p be the sun's 
 horizontal parallax, 
 
 AB^2pe^=(m — e)a; and p^^(m/e — l)a. 
 
 And by Kepler's law III : m/e= (687/365)^/^=1.5246, 
 whence, p^0.2623a, 
 which gives the sun's horizontal parallax when a is known. 
 
 In carrying this out practically, the angle u. is small, being 
 only about 35", and is difficult to measure accurately, and 
 there are a number of small corrections to be made. But 
 the method has the advantage over transits of Venus in that 
 it can be repeated upon every favorable night for several 
 weeks, at every opposition of Mars. 
 
 85. Moons of Mars. 
 
 Dean Swift, in his story of the Laputans (about 1700), 
 described these people as having such good eyes and being 
 such observant astronomers that they had discovered two 
 moons to Mars, which they had called Deimos and Phobos. 
 
 And in 1877 Professor Hall actually discovered two 
 moons attendant upon Mars and called them, respectively, 
 Deimos and Phobos. 
 
 These moons are very small bodies, of some interest, no 
 doubt, to the inhabitants of Mars, if such there be; but being 
 invisible except through powerful telescopes, ' they are of 
 little interest to dwellers upon the earth. Nevertheless, they 
 offer the unique peculiarity that while the outer moon is an 
 orderly body following the order of procedure of all other 
 moons, the inner one has the time of its orbital revolution 
 less than that of the axial rotation of Mars, so that it rises 
 in the west and sets in the east. 
 
 86. Jupiter. 
 
 This is the giant planet of the solar system, being 86,000 
 miles in diameter. That is, about one-tenth of the sun's 
 diameter. So that in bulk Jupiter is about 1300 times 
 greater than the earth, and yet only one-thousandth part of 
 that of the sun. 
 
JUPITER. 157 
 
 Tn spite of its great size, this planet rotates on its axis in 
 something less than 10 hours. The result of this rapid rota- 
 tion is plainly discernible in the elliptic form of its disc, 
 which is manifestly due to the oblate-spheroidal form of the 
 planet. 
 
 The greatest distance of Jupiter from the earth is to its 
 least distance about as 3 is to 2, and as the brightness of the 
 planet varies inversely as the square of the distance, the 
 brightness at opposition is to that at conjunction as 9 is to 4. 
 Thus, unHke Mars, Jupiter never becomes a very faint object, 
 while, when at its best in favorable oppositions, it nearly 
 rivals Venus in brilliancy. 
 
 As it travels about the sun in 433.2 days, it is easy to cal- 
 culate that there will be an opposition every 398 days, or a 
 little over 1 year and 1 month. So that if there be an oppo- 
 sition in any year early in January there will be an opposition 
 the next year in February, the next year in March, and so 
 on in every month except some month near the end of the 
 list. 
 
 87. Jupiter's Satellites. 
 
 One of the first-fruits of the telescope in the hands of 
 Galileo was the discovery of four moons revolving around 
 Jupiter. In recent years several others have been discovered, 
 but as these latter are visible only in the largest telescopes, 
 while the four discovered by Galileo can be seen by an ordi- 
 nary field glass, all the interest in the satellites of Jupiter 
 centres about the four which were first seen, and which are, 
 of course, much the largest. 
 
 The accompanying table gives the principal facts connected 
 with these four small bodies : 
 
 Distance 
 Number. Name. Diam. from Jupiter. Period of rev. 
 
 I lo 23;S0m. 267000m. 1.77 days. 
 
 11 Europa 2090m. 42S0OOm. 3.SS days. 
 
 Ill Ganymede 3430m. 678000m. 7.15 days. 
 
 IV Calisto 2920m. 1 193000m. 16.69 days. 
 
158 ASTRONOMY. 
 
 It will be noticed that the only one of these smaller than 
 our moon is II, and that it is only 70 miles less in diameter ; 
 and yet, owing to the great distance of Jupiter from us, these 
 moons appear as stars of the 6th and 7th magnitude, that is, 
 scarcely visible to the sharpest normal eye. 
 
 Again, they are all farther from their central planet than 
 our moon is from the earth, the most distant one being nearly 
 five times as far. And yet the period of revolution of the 
 most distant is not much more than one-half of that of our 
 moon. This is due to the powerful attraction of the central 
 planet ; and we see that if Jupiter were to replace our earth, 
 our moon would have to complete its revolution in about 40 
 hours in order to avoid being drawn into the centre of attrac- 
 tion. From considerations of this kind it is not difficult to 
 compare the mass of any planet, which has a moon revolving 
 about it, with the mass of the earth. 
 
 88. Eclipses, &c., of Jupiter's Satellites. 
 
 Knowing the sizes of the sun and of Jupiter, and the dis- 
 tance between them, a little calculation shows that the length 
 of the umbra of Jupiter's shadow is about 54,000,000 miles, 
 and therefore extends far beyond the orbit of the most 
 distant moon. 
 
 As a consequence of this, and the fact that the inclinations 
 of the orbits of the first three moons to the orbit of Jupiter 
 are quite small, these moons pass through the shadow and 
 are eclipsed at every revolution. But the inclination of the 
 orbit of the fourth moon being greater, it is not eclipsed at 
 every revolution but only at some of them. These eclipses 
 are phenomena of some importance as observed from this 
 earth. 
 
 But we have other interesting phenomena, besides eclipses, 
 connected with the moons of Jupiter, namely, occultations of 
 the moons as they pass behind the planet, and transits of 
 both moon and shadow across the disc of the planet. The 
 accompanying figure, which is necessarily much exaggerated 
 in some of its dimensions, will help to explain the occurrence 
 of these phenomena. 
 
JUPITER'S MOONS. 
 
 159 
 
 5" is the sun, GEF the earth's orbit with the earth at pre- 
 sent at E, J the planet Jupiter casting its dark shadow far 
 out into space, and I and III the orbits of two of the moons, 
 sav the first and the third. 
 
 Fig. 83. 
 
 Considering moon III, when it reaches a it enters the 
 shadow and is ecHpsed, and at h it emerges from the shadow. 
 At c it is seen to pass behind Jupiter and be occulted, or 
 hidden, and at d it passes out of the occultation. 
 
 Thus from o to & there is an eclipse and from c to c^ an 
 occultation, and these are both visible from the earth at E. 
 
 At e, on the other side of its orbit, moon III casts its 
 shadow on the disc of the planet; and as the moon moves 
 from e to f the shadow, in the form of a dark spot, is seen 
 to traverse the face of Jupiter. At g the shadow has passed 
 off from the disc and the moon itself, as a light spot, is seen 
 to enter and to pass across the disc of the planet as the moon 
 moves from g to h. So on one side we witness an eclipse 
 and then an occultation, and on the other side a transit, first 
 of the shadow, and then of the moon, all being visible at E. 
 If the earth were at E', the phenomena would be the same 
 but in a reversed order. These appearances are represented 
 by A and D, where the shaded circle represents a section of 
 the planet's shadow where the moon III traverses it. 
 
 In the case of moon I, or even III, the satellite is so near 
 the planet that the eclipse passes into the occultation without 
 the moon becoming visible between, as represented at B, and 
 the transits of the shadow and of the moon may both be seen 
 upon the disc at the same time, as at C. 
 
160 ASTRONOMY. 
 
 If Jupiter were inhabited, every point traversed by the 
 shadow in its passage across the disc would witness an 
 eclipse of the sun. And astronomers on such a planet would 
 be kept busy predicting eclipses, if indeed their very com- 
 monness did not destroy the interest in them. 
 
 Eclipses and shadow transits are independent of the earth's 
 position in its orbit, and would be the same as seen from any 
 other planet; that is, as phenomena, they are absolute, and 
 their beginning and end mark absolute moments of time ; but 
 such is not the case with the occultations and the moon 
 transits. 
 
 89. Determination of Longitudes by Eclipses of Jupiter's Moons. 
 
 Given two places A and B, the difference in their mean 
 time clocks is their difference in longitude. But if A and B 
 could observe and record, in mean time, the occurrence of 
 an absolute event, they would have the difference in their 
 mean time clocks. And the eclipses of Jupiter's satellites are 
 such events. These are predicted to take place at certain 
 times at Greenwich, and if they are observed at B, then B 
 can compare its time with that of Greenwich and thus de- 
 termine its longitude. 
 
 This means of finding longitudes is quite correct in theory, 
 but in practice it is found to be very difficult to say just 
 when an eclipse begins or ends, as the obscuration of the 
 moon is not an instantaneous event but a gradual one. And 
 on this account results obtained by this method are only close 
 approximations, which can be made closer, however, by mul- 
 tiplying the number of observations. 
 
 90. Progressive Motion of Light. 
 
 Soon after the discovery of Jupiter's moons, tables were 
 constructed showing the times of eclipses for the purpose of 
 observing them. These were made for a mean position of 
 the earth, as at E, and it was soon noticed that when the 
 earth came into a position such as F, with Jupiter near oppo- 
 sition, the eclipses invariably happened about 7 or 8 minutes 
 before their calculated times; and that with the earth at G, 
 and Jupiter near conjunction, the eclipse happened 7 or 8 
 minutes too late. 
 
VELOCITY OF LIGHT. 
 
 161 
 
 Roemer, a celebrated Danish astronomer, in speculating 
 upon these facts, came to the conclusion that light is not pro- 
 pagated instantaneously but progressively, that is, that light 
 requires time to pass from one point in space to another. 
 And he computed that it would require nearly 17 minutes for 
 light to cross the orbit of the earth, or, more exactly, 8^ 
 minutes to come from the sun to the earth. So that if the 
 sun could be instantaneously blotted out we would continue 
 to receive its light and heat for 8^ minutes after. 
 Thus the velocity of light became a problem in astronomy. 
 
 Several classical and successful experiments have been 
 carried out for determining the velocity of light, but we shall 
 here consider only one of them, namely, Foucault's experi- 
 ment. 
 
 Fig. 84. 
 
 A ray of light from the sun, or any other source, passes 
 through a narrow slit, T, in a shutter or other contrivance, 
 and falls upon the mirror, R, which is so attached to a pulley 
 as to be revolved at any required speed. TV is a mirror at 
 any distance from 2 miles to 5 miles from R and so adjusted 
 that light coming to it from R will be reflected directly back 
 to R, and thence along the direction RT. 
 
 At P a plane unsilvered glass is placed so that it may inter- 
 cept a portion of the rays coming back from R, and reflect 
 them to p on the scale S. 
 
162 
 
 ASTRONOMY. 
 
 Things being thus arranged, the mirror R is made to re- 
 volve. Then a ray of Hght takes some time, how^ever small, 
 to go from R to A'^ and back again ; and during this time the 
 mirror R has turned somewhat, and instead of sending the 
 ray back to P it sends it to Q, whence it is reflected to q. 
 
 And thus if Pp, with R at rest, be brought to zero mark 
 on the micrometer at the eye-end of a telescope, and R then 
 be put in motion, Pp is displaced in the direction of Qq, and 
 the amount of displacement is proportional to the velocity 
 of i?. 
 
 Hence, knowing the distance RN, the rate of revolution of 
 R, and measuring the displacement of Pp, it is not difficult 
 to calculate the velocity of light. 
 
 Of course, there are always discrepancies in the results of 
 very delicate experiments, but the mean of a great number 
 of trials may be taken as 186,000 miles per second. 
 
 If, then, it takes 8A minutes for light to come from the 
 sun to the earth, the sun's distance must be 93,000,000 miles. 
 The time 8™ 20« is called the equation of light. 
 
 91. Aberration of the Stars. 
 
 For an explanation of this subject, the following illustra- 
 tion will probably be sufficient : 
 
 XcliptiC 
 
 Fig. 85. 
 
 F is a yacht at rest, headed to the north, say; m is the 
 masthead, and mp is the pennant pointing eastward from a 
 west wind wm. 
 
ABERRATION OF LIGHT. 163 
 
 As long as the yacht remains still and the wind is west the 
 pennant will be directed .eastwards. But as the yacht gets 
 in motion northwards the pennant will gradually shift to a 
 direction mp' as if the wind were coming from zv', and a 
 person ignorant of the cause would say that the wind had 
 shifted somewhat towards the north. The fact, however, is 
 that the apparent direction of the wind is the resultant of 
 the eastern direction of the wind and the northern movement 
 of the yacht. 
 
 Now let the yacht represent the earth, E, moving along the 
 ecliptic, the wind represent the light coming from a star, 5', 
 at the pole of the ecliptic, and the pennant represent a tele- 
 scope so directed as to point to the star. 
 
 If the earth were at rest, the direction of the telescope 
 would be FS, perpendicular to the plane of the ecliptic. But 
 as the earth is in motion, the telescope must necessarily be 
 deflected to the direction ES', and the star appears to be at 
 S'. The angle of displacement SES' is the star's aberration, 
 and it is readily seen that its radian measure is the ratio of 
 the velocity of the earth to the velocity of light. 
 
 Aberration throws a star forwards in the direction parallel 
 to that of the earth's motion, so that the star S' will appar- 
 ently describe a small curve similar to the earth's orbit, or 
 practically a circle, about the true place 5". There is no 
 aberration of a star when the earth is moving directly to- 
 wards it or away from it, and the aberration is a maximum 
 when the direction of the star is normal to the earth's direc- 
 tion of motion. Thus, stars in the plane of the ecliptic 
 oscillate backwards and forwards in a line once a year, and 
 stars between the plane of the ecliptic and the pole of the 
 ecliptic apparently describe ellipses, of which the major axes 
 are constant and parallel to the ecliptic, and the minor axes 
 vary from zero for stars in the ecliptic to equality with the 
 major axis for the star at the pole of the ecliptic. 
 
 The discovery of aberration was purely a matter of obser- 
 vation and was made by Bradley in 1725, on the star y Dra- 
 conis, when looking for something entirely different. And 
 repeated observations have established that the average value 
 
164 ASTRONOMY. 
 
 of the aberration, or of the angular value of the major axis 
 of the ellipse, is 20".49. This is called the constant of aber- 
 ration. 
 
 92. Finding Sun's distance from constant of aberration. 
 
 This is one of the reliable methods of finding the sun's 
 distance, and the necessary calculation is not difficult. 
 
 Let R be the mean radius of the earth's orbit in miles ; 5" 
 be the number of seconds in a year ; and A be the velocity of 
 light in miles per second. 
 
 Then 2-kR/S is the orbital velocity of the earth in miles 
 per second ; and 
 
 2irR/S\ is the radian value of the constant of aberration, 
 that is of 20".49. 
 
 But 5=365.25X24X3600; and 20".49 expressed in ra- 
 dians is 20.49X7r/180x3600. 
 
 Whence 
 
 ie=92,800,000 miles, nearly. 
 
 This is probably the most satisfactory method of finding 
 the sun's distance. Of course, its accuracy depends upon 
 that of our knowledge of the velocity of light, and the close- 
 ness with which the constant of aberration can be obtained. 
 The uncertain element is the velocity of light. For experi- 
 ments give us the velocity of light when passing through the 
 atmosphere, and this undoubtedly differs slightly from its 
 velocity when passing through the space which intervenes 
 between the earth and the sun. The difference, however, 
 must be exceedingly small. 
 
 93. Saturn. 
 
 This planet is interesting through its uniqueness. It is a 
 large planet, having a diameter of over 73,000 miles, and 
 is next to Jupiter in size. Its distance from the sun is 
 upwards of 900 milHon miles, or nearly 10 times the distance 
 of the earth. It revolves on its axis in the short time of lOJ 
 hours, and it requires 29^ years to complete its journey about 
 the sun. 
 
SATURN. 
 
 16S 
 
 Saturn is supplied with 9 moons, at least, and probably- 
 more, so that it forms in itself a very good type of the whole 
 solar system. But the most distinguishing feature of the 
 planet, and the one which brings it into prominence as a 
 celestial object is the peculiar and unique system of rings 
 which surround the planet. 
 
 Fig. 86. 
 
 The rings consist principally of three parts or divisions, 
 an outer bright ring, an inner bright ring, and a still more 
 inner ring, generally known as the crepe or fluid ring. 
 
 The bright rings, and probably the crepe one also, are very 
 flat and thin. For, while the whole diameter of the largest 
 ring is about 165,000 miles, the thickness is probably not 
 above 200 or 250 miles, and may be less. 
 
 The plane of the rings is coincident with the plane of the 
 planet's equator, and this is inclined at the average angle of 
 about 25° to the ecliptic, so that as the planet passes around 
 in its orbit, the rings present different phases to the earth. 
 In this way we are enabled to see sometimes one face of the 
 rings and at other times the opposite face. During these 
 changes the rings come, about every 15 years, into such a 
 position that their plane passes through the earth, and we see 
 the rings " edge on." In this position they become barely 
 visible as a slender continuous or broken line crossing the 
 planet. We have here a practical proof that the rings must 
 be very thin as compared with their other dimensions, the 
 thickness not rising to probably above 200 or 250 miles. 
 
166 ASTRONOMY. 
 
 In the figure are three views of Saturn. The two upper 
 views show the rings more or less opened out, and the lower 
 one the appearance when the plane of the ring passes through 
 the earth and the ring is seen " edge on." 
 
 Naturally, these rings have been great subjects for the 
 speculative astronomer and physicist. And how they man- 
 aged to maintain their positions and not fall in upon the body 
 of the planet, or upon one another, if they were solid, as they 
 appear to be, was a standing puzzle. But the puzzle has 
 been solved by dropping the hypothesis of a solid ring, or of 
 a ring in which the constituent parts are held together by 
 any forces except the universal attraction of gravitation. 
 
 The only tenable hypothesis and the one now generally 
 held is that the rings consist of immense swarms of meteoric 
 bodies, each revolving about the central planet upon its own 
 account like a tiny moon, and, of course, each being subject 
 to disturbances arising from the attractions of the others. 
 
 That the bodies may not be very near together is shown 
 by the fact that a stretch of SO or 60 miles would be scarcely 
 distinguishable at the distance of Saturn, and that two bright 
 bodies that far apart would merge their light into one. And 
 when we consider that we are looking through great depths 
 of such bodies, it is readily seen that the individual me- 
 teoroids may be a number of miles apart and yet appear as a 
 luminous whole. 
 
 There must, in such a system, be a great amount of inter- 
 ference and numerous collisions, the general consequence of 
 which would be that great numbers of the bodies would be 
 deflected from their courses and be caused after a time to 
 fall upon the planet. This is possibly the meaning of the 
 faint crepe ring; and it is altogether probable that the sur- 
 face of Saturn is being continuously bombarded by meteor- 
 ites to an extent surpassing all human experience, and that 
 at some time in the distant future the rings may be com- 
 pletely precipitated upon the central body. 
 
 It is said that Sir Wm. Herschell, the foremost astronomi- 
 cal observer of his time (1738-1822), makes no mention of 
 the crepe ring in any of his writings ; and it is inferred that 
 
URANUS AND NEPTUNE. 167 
 
 it was not then a conspicuous object. If the inference be 
 correct, we must conclude that this ring is rapidly growing, 
 and that the rings of Saturn are probably comparatively re- 
 cent introductions into the solar system. 
 
 94. Uranus and Neptune. 
 
 These are both large planets, but from their great distance 
 they are both telescopic and therefore of much less interest 
 than the other planets. 
 
 Uranus is supplied with four moons, as far as is known, 
 and Neptune with one. Neptune is about 30 times as far 
 from the sun as the earth is, and nothing can be said to be 
 known about its individual character. 
 
 SURFACE CONDITIONS OF THE PLANETS. 
 
 One planet at least, the earth, is the home and abode of 
 life and organic beings, and we are accustomed to associate 
 with the presence of life the presence of certain conditions 
 prevailing upon the surface of this earth, and which are 
 thought to be necessary to the existence of life. 
 
 It is not at all certain that our estimate of the necessary 
 conditions is a correct one, and some recent discoveries in 
 this line have shown that former estimates would need some 
 material modification. 
 
 Nor is it certain that we can attain to anything like exact 
 knowledge as to the surface conditions of any planet except 
 our own. But we may, by careful reasoning from what we 
 know, arrive at certain results that are highly probable, and 
 we may rest quite surely in the assumption that wherever 
 the surface conditions of a planet are favorable to the devel- 
 opment of life, there life is present, whether we can obtain 
 any direct evidence of its presence or not. 
 
 95. General Conditions for an Atmosphere. 
 
 We have, in this earth, a planet surrounded by a well de- 
 fined atmosphere, and we shall try to determine some of the 
 
168 ASTRONOMY. 
 
 conditions necessary for the existence of a planetary at- 
 mosphere. 
 
 According to physical theory a gas consists of exceedingly 
 minute particles or molecules which are far apart as com- 
 pared with their size, and which are moving in straight lines 
 with very high velocities. 
 
 Thus, the average velocity for oxygen is believed to be 
 about 15 miles a minute, while the molecule of hydrogen 
 moves about four times as fast or practically a mile a second. 
 These flying molecules must frequently come into collision, 
 and as they are perfectly elastic, some of them will have 
 their velocity temporarily increased while others will have 
 it diminished ; and Clerk-Maxwell concluded that in this way 
 the highest obtainable velocity for any molecule might be 
 6 or 7 times the average velocity. 
 
 The accompanying table gives this highest velocity for 
 the gases of our own atmosphere at the temperature of zero 
 Centigrade : 
 
 Hydrogen 7.4 miles per second. 
 
 Water Vapor 2.5 " 
 
 Nitrogen 2.0 " 
 
 Oxygen 1.8 " 
 
 Carbon dioxide 1.6 " " " 
 
 Now, the temperature of a gas is but another idea for the 
 average velocity of its particles, so that when the tempera- 
 ture is reduced the average, velocity and therefore the maxi- 
 mum, must be reduced also. And as it is not possible, at 
 present, to say what the temperature of the air may be at a 
 height of 60 or 70 miles, we see that in the applications of 
 this principle to be made hereafter we must allow ourselves 
 considerable latitude. 
 
 Again, if on any planet a particle be projected outwards 
 with sufficient velocity, the particle would, by its momentum, 
 overcome the planet's attraction and pass away into space. 
 The minimum velocity sufficient for this is called the critical 
 velocity for the planet. 
 
CONDITIONS FOR AN ATMOSPHERE. 169 
 
 The critical velocities for the sun and all the principal 
 planets are easily found, and are given in the following table, 
 the only doubtful one being Mercury : 
 
 Moon 1.5 miles per sec. Jupiter . ... 37 miles per sec. 
 
 Mercury 2.2 miles per sec. Saturn 22 miles per sec. 
 
 Venus 6.6 miles per sec. Uranus 13 miles per sec. 
 
 Earth 6.9 miles per sec. Neptune . .. 14 miles per sec. 
 
 Mars 3.1 miles per sec. Sun 382 miles per sec. 
 
 By a comparison of the two preceding tables it would ap- 
 pear that hydrogen can be retained only by the sun and the 
 four' outer planets. In the atmosphere of these planets, then, 
 hydrogen in a free state might be present, although this is 
 not probably the actual case. For there can be no doubt that 
 oxygen would be present in large quantities, and unless the 
 amount of hydrogen exceeded that of the oxygen, all the 
 hydrogen would in a short time unite with the oxygen present 
 to form water vapor. But if we may judge from analogy 
 with the earth, oxygen is present in much larger quantities 
 than hydrogen. 
 
 Again, the moon is not capable of retaining any of the pre- 
 vious list of gases upon its surface, and it must be therefore 
 devoid of any atmosphere, provided this principle is rigor- 
 ously applied. It is well known that observations on the 
 moon have so far shown no trace of the existence of an 
 atmosphere. 
 
 Mercury, being a very small planet, would find difficulty 
 in retaining any atmosphere except a very rare one, and that 
 would probably contain a larger percentage of carbon dioxide 
 than is the case with the terrestrial atmosphere. 
 
 The atmosphere of Venus should be very similar to that 
 of the earth in both composition and density, while that of 
 Mars should be much the same in composition, but of much 
 less density, owing to the smaller size of the planet. 
 
 Again, the spectroscope shows that, with two exceptions, 
 coronium and nebulum which are found only under peculiar 
 unique circumstances, all the chemical elements discovered 
 in the sun and stars are common to this earth. So that we 
 
170 ASTRONOMY. 
 
 are justified in believing that all the bodies of the universe 
 have practically the same chemical constitution and contain 
 the same chemical elements, whether they have the same 
 physical constitution or not. In other words, terrestrial 
 chemistry is practically the chemistry of the universe, just 
 as terrestrial physics is a part of its common physics. Hence, 
 when two planets have atmospheres we must infer that these 
 atmospheres are closely akin to one another, if not identical, 
 in chemical composition, as also to a very great extent in 
 their physical qualities. 
 
 So that to hold that one planet may have a considerable 
 atmosphere mainly composed of carbon dioxide while in the 
 atmosphere of another planet this gas is present in only a 
 small percentage of the whole, is illogical. 
 
 Again, the surface condition of a planet will depend upon 
 the amount of heat which the planet receives from the sun, 
 or at least upon the proportion of this heat which it retains. 
 Thus, other things being the same, a planet with a dense at- 
 mosphere rich in water vapor will be warmer than a planet 
 with a thin atmosphere. 
 
 But a planet having a high internal temperature, as is the 
 case with the four large outer ones, might, by slow conduc- 
 tion of heat from within outwards, remain for long ages 
 quite independent of the heat of the sun. 
 
 In endeavoring to arrive at some knowledge of the surface 
 conditions of the several planets, the most rational way 
 seems to be to begin with the earth, the planet that we know 
 best, and then compare the conditions which probably exist 
 on the other planets with those known to be present on the 
 earth. 
 
 96. The Earth. 
 
 The earth's atmosphere consists principally of a mechani- 
 cal mixture of the two gases, nitrogen and oxygen, in the 
 proportions by weight of about 78 nitrogen to 22 oxygen. 
 These two gases, which undergo no change at any tempera- 
 ture foimd upon the earth, liquifying only when near abso- 
 lute zero, form the great bulk of the atmosphere, and are 
 
TERRESTRIAL ATMOSPHERE. 171 
 
 present in every locality in almost exactly the same propor- 
 tions. And these two gases would naturally be present as 
 the chief constituents of the atmosphere of every planet 
 which possesses an atmosphere of any density. 
 Carbon dioxide and water vapor, although present in small 
 and varying quantities, are yet essentials and play an im- 
 portant part in the economy of nature. The average amount 
 of carbon dioxide present is about 6 parts in 10,000 of air, 
 and the water vapor may vary from almost zero in the midst 
 of an extended dry and arid plain, to nearly 2 per cent, in a 
 warm and moist climate. 
 
 The nitrogen of the air may play some important part, but 
 its principal apparent function is as a diluent of the oxygen 
 in order to prevent too vigorous action of the latter element. 
 
 The oxygen is essential to combustion and therefore to 
 respiration and animal life, while the carbon dioxide, which 
 is produced amongst other ways by the breathing of animals, 
 is necessary to the life of plants, being, in fact, their prin- 
 cipal food. 
 
 And water vapor in the atmosphere is not only necessary 
 to both plant and animal life, but serves other numerous and 
 important purposes in the functions of the atmosphere in its 
 relation to climate. 
 
 97. Terrestrial Atmosphere. 
 
 Air is a mixture of elastic gases so that the lowest layer 
 is compressed by the weight of all that lies above it, and as 
 a consequence the tension is greatest at sea-level and de- 
 creases quite rapidly as we ascend. At some point of eleva- 
 tion the attraction of gravitation on the particles must be 
 equal to the repulsive force between the particles. This must 
 form a sort of upper limit to the atmosphere, although this 
 limit is somewhat illy defined and undoubtedly undergoing 
 constant changes in elevation, as it is acted upon by the 
 attractions of both the sun and the moon. 
 
 The whole height of the atmosphere is believed to be some- 
 where about 100 miles. 
 
172 ASTRONOMY. 
 
 The average weight or tension of the atmosphere at sea- 
 level is about 15 pounds per square inch, or equal to that of 
 a column of mercury 30 in. high. As we go upwards this 
 tension diminishes at a rapid rate, so that at about ^ miles 
 high the tension is only 7^ pounds per square inch, and you 
 have left one-half of the atmosphere below you. 
 
 By measuring the weight or tension of the air at any given 
 point of elevation it is possible to calculate the height of that 
 point above sea-level. In this way the height of stations on 
 the side of a mountain may be determined. 
 
 Sound. Air is the vehicle of sound, so that the surface of 
 a planet without an atmosphere would be noiseless and as 
 quiet as death. 
 
 Temperature. The whole air to some extent, and the 
 vapor of water especially, exercises a marked influence over 
 temperature. Upon the top of a mountain where there is a 
 minimum of water vapor the sun shines brilliantly and its 
 direct rays become inconveniently warm, while the shade is 
 disagreeably cool, and a chill settles over the place as the 
 night comes on. But in the valley near the sea-level, with 
 an atmosphere nearly saturated with water vapor, the whole 
 air gets warm and there is very little difference in tempera- 
 ture between the sunshine and the shade. 
 
 Water vapor, and hence cloud, acts as a sort of a trap 
 which allows the intense rays of the sun to pass inwards 
 without difficulty, but which resists the passage of the less 
 intense heat rays outwards. Thus the water vapor in the 
 general atmosphere acts much the same part as the glass in 
 the roof of the gardener's hot-house. 
 
 A planet with a dense atmosphere filled with water vapor 
 would have its day and night temperature more or less equal- 
 ized, while a world without an atmosphere would be subject 
 to great extremes of temperature between day and night. 
 
 We have illustrations of these things in the facts that, 
 other things beings equal, a cloudy night is warmer than a 
 clear one, and a warm day with a damp " muggy " atmo- 
 sphere is more disagreeable than if the atmosphere were dry. 
 
TERRESTRIAL ATMOSPHERE. 173 
 
 The temperature of the atmosphere decreases as one goes 
 upwards, although not at a uniform rate, and the law of de- 
 crease appears to be a somewhat irregular one. The tem- 
 perature at a height of IS or 20 miles is not known with any 
 certainty, but it is probably pretty low. 
 
 Wind. This is but air in motion. We could scarcely 
 imagine a great mass of gas, surrounding a rotating planet, 
 to be at rest. As the relation of the sun's rays to the surface 
 of the earth is continually changing from hour to hour of 
 the day, and from day to day of the year, the surface condi- 
 tions of temperature can never be the same for any length 
 of time throughout any extensive region. In a warm locality 
 the air expands and rises and other air from cooler sur- 
 roundings comes in to fill the void. If a large body of water 
 is near there will be a sea breeze. 
 
 The general character of the wind will depend upon the 
 density of the atmosphere, and the difference of temperature 
 between adjoining regions. When this difference becomes 
 very great the wind may rise to a storm or a cyclone, al- 
 though the most of the destructive storms are probably due 
 to special conditions. 
 
 Regular winds, as the trades, are partly determined by 
 the earth's axial rotation, and so also are the prevailing 
 northwest wind in the north temperate zone and the prevail- 
 ing southwest wind in the south temperate zone. 
 
 Where the atmosphere is of sufficient density to support 
 them, clouds will be formed, and hence there will be rain or 
 snow and hail according to circumstances of temperature. 
 
 Light and Color. To a person in a darkened room, a pencil 
 of sun-light coming through a small hole makes its path 
 distinctly visible by illuminating the dust particles and even, 
 to some extent, the molecules of atmosphere in its course. 
 So also the beam from a search-light on a dark and cloudy 
 night makes its presence known by the illuminated track 
 which it pencils out far up into the sky. 
 
 Thus the general brightness of the day and the blue color 
 of the sky are due to the presence of the atmosphere. With- 
 out an atmosphere the sky would probably appear black, or 
 
174 
 
 ASTRONOMY. 
 
 nearly so, and the stars would be brilliant even in the day 
 time. Everything receiving the direct rays of the sun would 
 be strongly lighted, but shadows would be generally dark, 
 and rapidly shading into blackness. There would be no twi- 
 light; but night would follow day so suddenly as to be be- 
 wildering, although the greater brilliancy of the stars at 
 night would render the darkness less dense than if an 
 atmosphere were present. 
 
 Refraction. It is a fundamental principle in optics that 
 when a ray of light passes obliquely from one medium into 
 another of different density, the ray suffers a bending or 
 refraction at the common surface of the media. 
 
 Fig. 87. 
 
 Now the atmosphere grows denser from above downwards, 
 and for the purpose of illustration we may suppose it to be 
 divided into layers /, m, n, etc., where / is more dense than m, 
 m more dense than n, etc. Then rays of light from the star 
 J are bent downwards as they pass from space into layer n, 
 again as they pass from n into m, and from m into I. So that 
 the light meets the eye of the observer, at c, as if it came di- 
 rectly from j'. 
 
 As the layers of atmosphere are made thinner, and cor- 
 respondingly increased in number, the path of the ray 
 through the atmosphere assumes the form of a curve, and 
 the apparent place of the star is above its true place. 
 
REFRACTION. 175 
 
 Thus the effect of refraction upon the heavenly bodies is 
 to increase their apparent altitudes, the increment being 
 greatest at the horizon, and vanishing at the zenith. 
 
 In getting the true altitude from an observation the re- 
 fraction is always subtractive, that is, it has to be subtracted 
 from the apparent altitude. 
 
 The amount of the refraction depends upon the tempera- 
 ture and also upon the height of the barometer, or the weight 
 of the atmosphere at the time of observation, and these must 
 be considered where accuracy is required. 
 
 The following table gives the refraction to the nearest 
 tenth of a minute, for every degree of altitude from 1° to 
 90°, for a mean value of the thermometer and barometer :, 
 
 Table of Refraction. 
 
 Alt. 
 
 Ref. 
 
 Alt. Ref. 
 
 Alt. 
 
 Ref. 
 
 Alt. Ref. 
 
 Alt. 
 
 Ref. 
 
 Alt. 
 
 Ref. 
 
 1 
 
 24.4 
 
 16 
 
 3.4 
 
 31 
 
 1.6 
 
 46 
 
 0.9 
 
 61 
 
 0.5 
 
 
 
 76 
 
 0.2 
 
 2 
 
 18.4 
 
 17 
 
 3.2 
 
 32 
 
 1.6 
 
 47 
 
 0.9 
 
 62 
 
 0.5 
 
 n 
 
 0.2 
 
 3 
 
 14.5 
 
 18 
 
 3.0 
 
 33 
 
 l.S 
 
 48 
 
 0.9 
 
 63 
 
 0.5 
 
 78 
 
 0.2 
 
 4 
 
 11.8 
 
 19 
 
 2.8 
 
 34 
 
 1.4 
 
 49 
 
 0.8 
 
 64 
 
 0.5 
 
 79 
 
 0.2 
 
 5 
 
 9.9 
 
 20 
 
 2.6 
 
 35 
 
 1.4 
 
 50 
 
 0.8 
 
 65 
 
 O.S 
 
 80 
 
 0.2 
 
 6 
 
 8.5 
 
 21 
 
 2.5 
 
 36 
 
 1.3 
 
 51 
 
 0.8 
 
 66 
 
 0.4 
 
 81 
 
 0.2 
 
 7 
 
 7.4 
 
 22 
 
 2.4 
 
 37 
 
 1.3 
 
 52 
 
 0.8 
 
 67 
 
 0.4 
 
 82 
 
 0.1 
 
 8 
 
 6.6 
 
 23 
 
 2.3 
 
 38 
 
 1.2 
 
 53 
 
 0.7 
 
 68 
 
 0.4 
 
 83 
 
 0.1 
 
 9 
 
 5.9 
 
 24 
 
 2.2 
 
 39 
 
 1.2 
 
 54 
 
 0.7 
 
 69 
 
 0.4 
 
 84 
 
 0.1 
 
 10 
 
 5.3 
 
 25 
 
 2.1 
 
 40 
 
 1.2 
 
 55 
 
 0.7 
 
 70 
 
 0.4 
 
 85 
 
 0.1 
 
 11 
 
 4.9 
 
 26 
 
 2.0 
 
 41 
 
 1.1 
 
 56 
 
 0.7 
 
 71 
 
 0.3 
 
 86 
 
 0.1 
 
 12 
 
 4.5 
 
 27 
 
 1.9 
 
 42 
 
 1.1 
 
 57 
 
 0.6 
 
 72 
 
 0.3 
 
 87 
 
 0.1 
 
 13 
 
 4.1 
 
 28 
 
 1.8 
 
 43 
 
 1.0 
 
 58 
 
 0.6 
 
 73 
 
 0.3 
 
 88 
 
 0.0 
 
 14 
 
 3.8 
 
 29 
 
 1.7 
 
 44 
 
 1.0 
 
 59 
 
 0.6 
 
 74 
 
 0.3 
 
 89 
 
 0.0 
 
 15 
 
 3.6 
 
 30 
 
 1.7 
 
 45 
 
 1.0 
 
 60 
 
 0.6 
 
 75 
 
 0.3 
 
 90 
 
 0.0 
 
 It will be noticed from the table how large the refraction 
 is for an altitude of 1 degree, and how rapidly it falls for 
 the first 5 or 6 degrees. Now, there is always some uncer- 
 tainty about the refraction when it is very large, so that it 
 is not well, if it can be avoided, to depend too much upon 
 observations made on the altitudes of heavenly bodies near 
 
176 ASTRONOMY. 
 
 the horizon. And in order to find latitude accurately it is 
 profitable to observe stars as near the zenith as possible, and 
 thus get rid of the uncertainty of refraction. 
 
 When light from the sun traverses great stretches of at- 
 mosphere, and especially when water vapor is present in 
 considerable quantity, the light loses some of its constituents 
 by absorption. But these constituents are not taken out in 
 equable proportions. The rays about the violet end of the 
 spectrum are removed in larger proportion than those in the 
 vicinity of the red end, and as a consequence the transmitted 
 light assumes a ruddy hue from having the red constituent 
 in excess. 
 
 This is the reason why the sun appears red when seen 
 through a mist or fog, and why it is more or less golden in 
 color at its rising and its setting. 
 
 Thus the beautiful tints of the evening clouds with their 
 rich sheen of red and gold, the rosy blush of the dawn, and 
 the general color effects so beautiful at times in the higher 
 atmosphere, are all due to the same cause, the presence of air 
 containing vapor of water. The visibility and color of the 
 moon when immersed in the depths of the earth's shadow are 
 due to a like cause. 
 
 Meteors and Falling Stars. Meteors, such as come under 
 our observation, are originally small pieces of mineral matter 
 scattered through space, and, of course, moving in some 
 kind of an orbit about the sun as a centre of attraction. 
 They exist in immense numbers and vary in size from that 
 of a mere dust particle to stony bodies of some considerable 
 bulk. Some of these naturally come very close to the earth 
 and many fall upon its surface. 
 
 If it were not for the atmosphere none of these which now 
 are precipitated upon the earth would be visible. But meet- 
 ing the atmosphere at a velocity of from 15 to 30 miles a 
 second, the heat generated is so great as to raise the moving 
 particle to incandescence and dissipate it into impalpable 
 dust, which after floating in the air for a longer or shorter 
 time finds its way to the earth. It is while incandescent and 
 
METEORS. 177 
 
 being gasified that the particle leaves a trail of light in its 
 path and resembles a falling star. 
 
 If the meteorite be of considerable size, it may not be 
 wholly dissipated, but may fall to the earth as a solid stony 
 or metallic mass, of which the surface only has been fused, 
 and bury itself deep in the soil. And from such a position 
 they have occassionally been resurrected while still quite hot. 
 
 Sometimes, again, the heat generates gases in the interior 
 of the meteorite, and the resulting pressure bursts the mass 
 with a loud report and scatters the fragments in various di- 
 rections, with an appearance very much like the explosion of 
 a rocket. 
 
 It has been estimated that about six million meteorites, of 
 all kinds, fall to the earth every 24 hours. As they are prob- 
 ably at less than 100 miles from the earth's surface when 
 first becoming visible, it is evident that only a very small pro- 
 portion of the whole is visible at any one locality. 
 
 November and August Meteors. There are two well- 
 recognized rings of meteoric matter surrounding the sun, and 
 circulating about it in their own plane, each meteorite, of 
 course, moving under the law of gravitation as a minute 
 independent planet. These rings are so situated that the 
 earth, in its annual revolution about the sun, comes into con- 
 tact with a ring and passes through it, the one on November 
 14th and the other on August 12th or thereabouts. As a 
 consequence, the earth is treated to a distinct shower of 
 meteors on or about these two dates. 
 
 Of course, the phenomenon, in both cases, is local and can 
 be seen only from that side of the earth which is advancing 
 upon the meteoric ring, and then only if it be night at the 
 locality. The phenomena show themselves as a distinct in- 
 crease in the number of " falling stars " to be seen. 
 
 Zodiacal light. This subject, although having no direct 
 connection with the atmosphere, is intimately related to that 
 of meteorites. 
 
 Besides the two rings of meteoric matter, through whose 
 substance the earth has to pass in November and August, 
 there may be, and probably are, numerous other rings, more 
 
178 ASTRONOMY. 
 
 or less diffused, which, from lying wholly outside the earth's 
 orbit, or wholly inside, are never met by the earth in its 
 course, and consequently never reveal their existence by a 
 display in the upper atmosphere. And it is generally held 
 by astronomers that the sun is surrounded by an extensive 
 expanse of meteoric matter of very low density and extend- 
 ing outwards as far as the earth's orbit or even beyond it. 
 
 This would account for the innumerable host of small 
 meteorites which are met by the earth throughout its annual 
 course, as well as for that peculiar phenomenon known as 
 the zodiacal light. 
 
 The zodiacal light appears as a faint triangular-shaped 
 halo of light rising from the western horizon after sunset. 
 It is most conspicuous in torrid climes ; and in northern 
 regions it is seen best in the spring as the ecliptic, along 
 which it lies, then cuts the horizon at the greatest angle. 
 
 Imagine the sun to be surrounded by a very diffuse lenti- 
 cular expansion of meteoric matter with the plane of the 
 lens nearly coincident with that of the ecliptic, and extending 
 outwards to the distance of the earth's orbit, or nearly so. 
 Such an expansion, by reflecting the light of the sun from 
 its innumerable particles, would give quite accurately the 
 appearance of the zodiacal light. 
 
 There are strong reasons for believing that this is the 
 cause of the phenomenon. And it is probable that this me- 
 teoric matter, as also the meteoric rings already referred to, 
 are merely refuse matter from the evolution of the solar 
 system, and from the disintegration of innumerable comets 
 which have wholly or partly lost their integrity by too close 
 proximity to the sun. 
 
 98. The Moon. 
 
 Theoretically the moon can have no atmosphere, as it can- 
 not retain any of the atmospheric gases upon its surface. 
 Hence, life cannot be present and the silence of death must 
 envelop it. 
 
 Its surface must be wholly rock or volcanic products, 
 where disintegration and the formation of soil are impossible 
 
THE MOON. 179 
 
 processes, as these are due to the " weathering " effects of 
 an atmosphere. 
 
 The face turned for 14 days to the Hght and heat of the 
 sun probably rises to a very high temperature, while that im- 
 mersed for a like time in the gloom of night sinks towards 
 the temperature of space, whatever that may be. But even 
 that does not necessarily mean that the temperature should 
 approach absolute zero, for the north pole of the earth re- 
 mains cut off from the rays of the sun for five months at 
 a time and yet, as far as is known, the thermometer scarcely 
 ever reaches 100° below zero Fahrenheit even under these 
 conditions. 
 
 The shadows should be very dark and the sky quite black, 
 while the stars should shine out with a brilliancy unknown 
 upon earth. 
 
 If an atmosphere were present on the moon, a star, when 
 being occulted or hidden behind the moon, should be some- 
 what displaced by refraction and should lose its light gradu- 
 ally. This, however, is not the case. The star comes to the 
 edge of the lunar disc without any displacement, and then 
 suddenly vanishes ; plainly showing that the moon has no 
 atmosphere. 
 
 Moreover, as long and as often as the moon has been 
 observed and mapped and photographed, not a single well 
 indicated change has appeared upon its surface. 
 
 The lunar disc is quite covered with ring mountains with 
 or without a central cone, and small cup-shaped cavities with 
 elevated edges are plentiful everywhere. These show the 
 great extent of volcanic action in past ages. 
 
 A few years ago some astronomers thought that present 
 volcanic action was to be seen in the crater Linne, but later 
 observations have not corroborated this, and it is now gen- 
 erally held that the surface of the moon is practically dead 
 in every sense. 
 
 The sharp and jagged peaks of the mountains cast their 
 black shadows into the valley of the crater or across the 
 adjacent plain, and lengthen out wonderfully as they are 
 approached by the terminator. By measuring the lengths of 
 
180 
 
 ASTRONOMY. 
 
 these shadows it is possible to calculate the heights of the 
 peaks above the surrounding regions. In this way Beer and 
 Madler estimated that some of the mountains are not less 
 than 20,000 feet high. 
 
 The moon does not appear uniformly bright, but is more 
 or less mottled with darker spots. These, which were form- 
 erly supposed to be seas, are seen in the telescope to have 
 small craters scattered through them, thus showing that they 
 are not now seas, whatever they may once have been. The 
 disposition of these darker parts gives rise to the fanciful 
 figure of the " man in the moon " and other like things. 
 
 The accompanying plates will serve to give some general 
 idea of the character of the lunar surface. 
 
 IK!! 
 
 ^- ^^^^^B 
 
 
 
 ^^^H(^'.>?-:!% 
 
 ^'K. ^H 
 
 ^^^^^^^^^HBiV>aH 
 
 0W» . -a.) ^ ^^11 
 
 Hb 
 
 ^1 
 
 ^^^^^Hil 
 
 SsSrT^M 
 
 ^^^^^IKu[ 
 
 mSt "' : '"'■'mt 
 
 H 
 
 U 
 
 Fig. 
 
 Fig. 89. 
 
 Fig. 88 is a selenographic map of the moon, showing the 
 general positions of the mountains on its surface. The most 
 mountainous region is around the moon's south pole, which 
 here appears at the top of the figure, on account of the in- 
 version produced by the astronomical telescope. 
 
 Fig. 89 shows the moon a little past the first quarter, and 
 the irregularity of the terminator gives a very good idea of 
 the character of the surface. The conspicuous ring moun- 
 tain just on the terminator is Copernicus. 
 
THE MOON. 
 
 181 
 
 Fig. 90 is an enlarged view of Copernicus, showing the 
 roughness of the ring and generally of the surrounding 
 region. The great number of small craters, adjacent to the 
 main one, is well brought out. 
 
 E 
 
 ^M 
 
 ^^Pn 
 
 ^^R^^t^fl 
 
 ■ 
 
 ^^ 
 
 Fig. 90. 
 
 m^ ''f 'i^^^^is 
 
 iil^^^^^wt' 
 
 K^l 
 
 
 
 pj 
 
 
 lft->nSw9i 
 
 
 ■ ^ ^^aL 
 
 
 fcCf^BJ 
 
 ^^^^M 
 
 ^ 
 
 Fig. 91. 
 
 
 Fig. 92. Pig. 93. 
 
 Fig. 91 is the ring mountain Triesnecker, with top of the 
 central cone lighted by the sun, and the height of the ringed 
 wall may be judged of by the extent of the shadows. The 
 adjacent smoother part of the surface is traversed by several 
 very prominent cracks. 
 
182 ASTRONOMY. 
 
 Fig. 92 shows the mountains Theophilus, Cyrillus, and 
 Catharina. The whole structure is peculiar, showing how 
 one ring sometimes invades the possessions of another. 
 
 Fig. 93 shows a range of mountains, towards the moon's 
 rtlx ^'^''^stmthcrn limb, which do not appear to be volcanic, but more 
 after the character of the Alps. These are the lunar Ape- 
 nines, and the ruggedness of their character is shown by the 
 long pointed shadows cast by their peaks. 
 
 Various superstitions and fanciful notions have been con- 
 nected with the moon, in times past, such as its influence 
 over people and over the weather, and in regard to its power 
 as an oracle or a charm. The most of these are gradually 
 disappearing with the diffusion of correct astronomical in- 
 formation, but many of them die hard. 
 
 The moon is many times larger than the largest known 
 asteroid, so that it would be idle to expect the presence of 
 life or even an atmosphere upon any of the asteroids. 
 
 99. Venus. 
 
 In a transit of Venus, the outline of the dark body of the 
 planet is plainly seen for some time before the planet has 
 fully advanced upon the solar disc, thus showing that Venus 
 is surrounded with a well-defined atmosphere; and some 
 astronomers have held that the atmosphere of Venus is even 
 more dense than the terrestrial one. And from previous 
 considerations we infer that the two atmospheres, that of 
 Venus and that of the Earth, are much alike in their general 
 composition and character. 
 
 But as Venus exposes continually the same hemisphere to 
 the sun, the surface conditions must be somewhat different 
 from what they are with us. 
 
 The temperature of the bright side must be very high, 
 especially about the central parts, unless very dense clouds 
 prevail, and the temperature of the dark regions must be 
 correspondingly low. 
 
 As we know nothing absolutely about the water supply of 
 Venus, we may reasonably assume that water is present in 
 considerable quantity, as there is no reason for believing 
 
VENUS. 183 
 
 that, in this respect, Venus differs very much from the earth. 
 Then reasonable speculation will lead us to something like 
 the following: 
 
 Strong winds prevail throughout all the regions bordering 
 on the line separating darkness from light, the surface cur- 
 rent coming out of the darkness and being cool, while the 
 upper current is the very reverse. These winds, originating 
 as they do in the sun's heat, would be a perpetual source of 
 power. They also tend to equaKze the temperature of the 
 two hemispheres by carrying hot air from the light into the 
 dark, and cold air from the dark into the light. And in pass- 
 ing from the middle of the lighter half to the middle of the 
 other it is probable that the temperature, which would be 
 high at the start, would gradually fall to a very low point at 
 the finish. So that throughout a belt many degrees wide, 
 lying along the border line, the temperature would be as 
 varied as that prevailing upon the earth, the principal differ- 
 ence being that on Venus there is no change of season and 
 no alteration of day and night. But each different region, in 
 relation to the border line, has its own unchangeable climate 
 and the sun perpetually fixed above or below its horizon. 
 
 The water carried by the upper winds is precipitated as 
 lain or snow upon the border land, and the middle of the 
 dark hemisphere is possibly covered by a large ice cap, while 
 the surrounding regions are cool and moist, so that winds 
 blowing from the dark portion of the planet are not only 
 cool but well supplied with moisture. 
 
 Such a condition as that prevailing in the border land may 
 be a very agreeable and acceptable one, and there is no reason 
 why this belt may not be the abode of life. And when we 
 remember that scarcely one- fourth of the surface of the earth 
 is inhabitable land, it is quite possible that there may be 
 even a larger portion of life on Venus than on the earth. 
 
 100. Mars. 
 
 This planet is considerably smaller than the earth, its dia- 
 meter being about 4200 miles. But, owing to its axial 
 rotation and the inclination of its equator to the plane of its 
 
184 ASTRONOMY. 
 
 orbit, it has a regular return of day and night in a little over 
 24 hours, and an orderly rotation of seasons, and in these 
 respects it offers conditions remarkably like those prevailing 
 on the earth. 
 
 Its south hemisphere is best suited for observation because 
 the south pole leans towards the earth v^fhen Mars is at its 
 least distance from us. 
 
 But when either pole comes out from its long dark winter 
 into the light and heat of the sun, it is seen to be surrounded 
 by a large white polar cap, which gradually dwindles away to 
 a comparatively small spot, or occasionally vanishes alto- 
 gether, as the advancing Martian spring and summer warm 
 up the polar regions. 
 
 These caps are now generally admitted to be snow, 
 although the deposit is probably not as thick as is found 
 about the terrestrial poles. The melting of this polar snow, 
 at the advent of the Martian summer, shows that the tem- 
 perature of Mars cannot be much different from that pre- 
 vailing on the earth, and some astronomers have thought 
 that the mean temperature of Mars may be even higher than 
 that of the earth. We would expect the opposite on account 
 of the greater distance of Mars from the sun, but it seems 
 that temperature may be affected by other causes than mere 
 distance. 
 
 The planet has an atmosphere which is probably not one- 
 half as dense as the terrestrial one, but yet sufficiently so to 
 give rise to twilight, and to support light dust clouds in its 
 lower strata. 
 
 Water appears to be scarce on Mars, as there are no visible 
 seas or lakes or rivers. And yet the atmosphere must con- 
 tain a large amount to form the snows which cover over all 
 the polar and a part of the temperate zones every year. This 
 scarcity of water is probably due to the fact that. Mars 
 being a small planet and older than the earth, the surface 
 rocks have cooled so deeply that the former seas have pene- 
 trated into the interior. 
 
 The rocks of the earth a few miles below the surface are 
 sufficiently hot to absolutely prevent water from penetrating 
 
MARS. 18S 
 
 them. But when, in some milHons of years, the earth, by 
 the convection and radiation of its internal heat, becomes 
 sufificiently cool to allow the seas to sink inwards, water will 
 undoubtedly become as scarce upon the earth as it is now 
 on Mars. 
 
 Fig. 94. 
 
 The figure is from a drawing by Lowell showing a view 
 of Mars with some darker portions which are supposed to 
 be ancient sea bottoms. As there are no high elevations on 
 the planet it is likely that these sea bottoms are only shallow 
 depressions, and that they no longer contain water. 
 
 The fine lines running in all directions and intersecting 
 in well-defined points, or oases, through most of which 
 several lines pass, are the celebrated canals of Mars. These 
 were first seen by Schiaparelli, in 1877, from whom they 
 
186 ASTRONOMY. 
 
 received the name canali. They are geodetic in form, or 
 pursue the most direct route from point to point on the 
 sphere, which seems to indicate that they are not accidental, 
 but rather the results of intelligent action. 
 
 The canals are not always visible, but come into visibility 
 soon after the polar snow cap begins to melt. They are very 
 faint at first, but gradually grow darker and more distinct 
 and new ones come into view farther away from the water 
 supply. But whether faint or distinct they always occupy 
 the same positions and have in them an element of per- 
 manency. 
 
 The theory of the canals, as it was proposed by W. H. 
 Pickering and is generally accepted, is that what we see as 
 a canal is a tract of irrigated country from 15 to 30 miles 
 wide, along the middle of which runs an irrigation canal 
 or ditch. That the water is supplied to this from the melting 
 snow fields in the vicinity of the pole. And the various 
 changes which a so-called canal is seen to undergo are due 
 to changes in the vegetation of the irrigated district during 
 the passing of the Martian spring and summer. 
 
 This explanation, of course, requires the existence of in- 
 telligent beings upon Mars, and if this is granted the theory 
 amply accounts for the appearances as well as any theory 
 can be expected to. But it may be here said that although a 
 considerable number of astronomers believe in the canals 
 and claim to have seen them, and have made drawings of 
 them, yet there are some astronomers who, although supplied 
 with large instruments, have never seen the canals and who 
 doubt their existence. 
 
 But it is difficult to prove a negative. Those who desire 
 fuller information on this subject are advised to read Per- 
 cival Lowell's book " Mars," in which is set forth about all 
 that has been done. 
 
 I 
 101. The Major Planets. 
 
 When we consider the great size and the low density of 
 the major planets, we are forced to the conclusion that a 
 
JUPITER. 
 
 187 
 
 large part of their apparent bulk consists of gaseous matter, 
 and that they must consequently be surrounded by very dense 
 and extended atmospheres. The only feasible explanation 
 of such a state of matters seems to be that the solid or liquid 
 body of the planet is at a very high temperature — so high, in 
 fact, that many more things exist in these atmospheres than 
 in the atmospheres of the minor planets — or, in other words, 
 that the major planets on account of their great size have 
 not yet lost their primitive heat, and that their surfaces may 
 still be red hot, or nearly so. 
 
 Of course, life cannot be existent under these circum- 
 stances. But when some hundreds of millions of years have 
 passed away and all the minor planets have become cold and 
 dead, then these giants may have their day of importance, 
 and one after another may swarm with living creatures. 
 
 Fig. 95. 
 
 The accompanying figure shows the planet Jupiter as seen 
 through the telescope. The disc is crossed by numerous dark 
 bands parallel to the planet's equator, and known as the belts 
 of Jupiter. These are most cUstenf near the equator and are 
 undoubtedly great cloud masses drawn out in the banded 
 form by the rapid axial rotation of the planet. 
 
188 ASTRONOMY. 
 
 102. THE STARS. 
 
 The formal and systematic study of the stars constitutes 
 a special department called stellar astronomy, and is of suffi- 
 cient magnitude and importance to require a large treatise 
 for its exposition. All that can be done in this work is to 
 give the briefest outline of the subject. 
 
 Our sun is a star, the star that is nearest to us, and the 
 one that we know best. And yet our knowledge of the sun, 
 although more satisfactory than it was a hundred years ago, 
 is far from being complete. 
 
 If we wish to know what a star is, the reasonable way is 
 to study the sun, which, although only a third or fourth rate 
 star, is yet typical of all the stars, as far as is known. 
 
 But the study of the sun is not easy. The sun is 93 mil- 
 lions of miles away and the smallest visible spot on its 
 surface is not less than 100 miles across. 
 
 Besides, the condition of matters in the sun is so different 
 from any thing on earth as to transcend all human experi- 
 ence if not human imagination. 
 
 Fancy, if you can, a globe so large that it would fill the 
 moon's orbit twice over, and that this whole immense globe 
 is one seething, boiling steaming mass, whose temperature is 
 so high as to greatly transcend any temperature available on 
 earth — so high that chemical compounds can not exist and all 
 matter is resolved into its most elemental principles — where 
 carbon and platinum and the most refractory substances are 
 kept in a gasified state — ^where every thing is gaseous or 
 ultra-gaseous and fluids and solids are non-existent — if you 
 can fancy all this you may get some idea of the nature of 
 the sun. 
 
 The most acceptable theory of the condition of the sun is 
 about as follows: 
 
 The whole sun is gaseous, and therefore, in its exterior 
 parts, at least, more mobile than a body of water. The in- 
 terior is intensely hot, so that chemical combination is 
 impossible. From this interior violent upward currents carry 
 the glowing materials into the cooler atmosphere far above 
 the photosphere, or principal light-giving layer of the sun. 
 
THE SUN. 189 
 
 Here they are sufficiently cooled to allow some forms of 
 chemical combination to take place, and clouds are formed, 
 somewhat after the manner in which terrestrial clouds are 
 formed from water vapor being chilled in the upper air ; but 
 the solar clouds are not aqueous but vapors of iron, carbon, 
 platinum, etc. 
 
 Then, as in the welshback burner, the solid mantle is in- 
 tensely bright while its temperature is only that of the faintly 
 luminous gas which surrounds it, so the solar clouds give off 
 many times more light than the gases from which they were 
 formed, although having a somewhat lower temperatitre. 
 
 These great cloud-patches form the bright spots which so 
 thickly strew the sun's photosphere, while the uncombined 
 gases form the darker background ; for as seen through a 
 proper telescope the sun presents a mottled appearance which 
 Prof. Langley described as appearing like snow flakes upon 
 a background of grey cloth. 
 
 The principal part of the sun's light comes from these spots, 
 and from the faculae which appear like the intensely lumi- 
 nous crests of enormous waves. 
 
 Faculae are most numerous near sun spots, and both the 
 spots and the faculae indicate violent commotion in that part 
 of the photosphere. Thus the spectroscope has shown that 
 movements as high as 320 miles a second often take place in 
 the regions of a sun spot. 
 
 The solar clouds are heavier than the surrounding gases 
 and quickly sink into the interior to be there dissipated and 
 resolved anew into their gaseous constituents, and so to run 
 the same course over again. 
 
 In the sun spot the uprush of matter from the interior is 
 so violent that the surface of the photosphere is broken and 
 forced apart, producing mountainous waves and sending 
 spray to a height of some thousands of miles, forming the 
 faculae and leaving in the light-giving surface a great de- 
 pression anywhere from 1000 to 3000 miles deep, and in rare 
 cases upwards of 100,000 miles across. 
 
 Into this depression the overlying and cooler gases rush 
 with great velocity, and the depth of these in the cavity ab- 
 
190 ASTRONOMY. 
 
 sorbs so much of the light from the brilliant mass beneath as 
 to appear relatively dark against the intense brightness of 
 the general surface. For it must be borne in mind that the 
 darkest sun spot is brighter than the arc light. 
 
 In the midst of a total solar eclipse, when the dark body 
 of the moon completely hides the body of the sun, the moon 
 appears to be fringed here and there with fiery red projec- 
 tions which undergo rather rapid changes. This is the 
 chromosphere, which is an outer gaseous envelope of the 
 sun, too large to be completely covered by the moon, and 
 having much less light-giving power than the photosphere. 
 The chromosphere, which is probably 10,000 miles high or 
 more, contains in its lower parts the vapors of all the ele- 
 ments, and in its higher parts the vapors of the lighter 
 elements and especially hydrogen and helium in excess. The 
 brilliant red color is due to incandescent hydrogen which 
 gives a strong red line in the spectrum. 
 
 The upper layer of the chromosphere is singularly agitated 
 by the upward rush of hot gases from below, and is occa- 
 sionally projected outwards in great jets which attain a 
 height of 15 or 20 thousand miles in a few hours. 
 
 Professor Young, who gave a great part of his life to 
 studying the sun, says that " the appearance, which probably 
 indicates a fact, is as if countless jets of heated gas were 
 issuing through vents and spiracles over the whole surface, 
 thus clothing it with flame which heaves and tosses like the 
 blaze of a conflagration." 
 
 Lockyer saw at times the bright lines of the spectrum dis- 
 placed and broken and distorted, plainly showing the pres- 
 ence of tremendous cyclonic storms in their passage along 
 the solar surface. These storms had velocities as high, at 
 times, as 250 miles per second. Comparing these with our 
 greatest tornadoes, which scarcely ever exceed 100 miles an 
 hour, we can form some faint idea of the state of matters in 
 the sun. Hurricanes like these " coming down from the 
 north would reach the Gulf of Mexico in about 30 seconds, 
 carrying with them the whole surface of the continent in a 
 mass, not simply of ruin, but of glowing vapor." This will 
 
THE SUN. 191 
 
 possibly give some faint idea of the fierceness of the action 
 going on in the sun. 
 
 Young saw a vast hydrogen rosy-colored cloud 100,000 
 miles long floating above the photosphere at a height of 
 15,000 miles, and supported by upright columns or streamers 
 by which it was supplied from below. In about 25 minutes 
 after, this immense cloud had broken into a mass of debris 
 consisting of violently agitated filaments. These rose to a 
 height of 200,000 miles and gradually faded away. 
 
 Lockyer has seen a prominence fully 40,000 miles high 
 shattered into confusion in ten minutes, while Respighi cal- 
 culated that the initial velocities of some eruptions which he 
 witnessed must have been over 400 miles per second, or 
 greater than the critical velocity for the sun. 
 
 And the logical conclusion from such observations is that 
 great quantities of hydrogen and other light material is con- 
 tinually escaping from the attraction of the sun and expand- 
 ing itself in the boundless interstellar space. 
 
 The outermost appendage of the sun, if indeed it can be 
 called an appendage, is the Corona. This is a faint halo of 
 glory which surrounds the place of the sun when totally 
 eclipsed, and it can be seen at no other times. Hence the 
 interest which attaches to a total eclipse of the sun. 
 
 The corona is not an atmosphere, as it seems to be devoid 
 of weight. It is unsymmetrical and variable in form, extend- 
 ing outwards at some times and in some directions to millions 
 of miles. Its density is probably not one ten-thousandth part 
 of the best vacuum that we can produce, for comets have 
 been known to traverse parts of it at velocities as high as 
 200 miles per second or over without being sensibly checked 
 in their courses. 
 
 The corona is probably matter, mostly in a corpuscular 
 state, carried outwards from the sun by the repellant force 
 of its fierce radiation. For it is now known that light rays 
 exert a slightly repulsive force upon any object upon which 
 they fall. And as this repulsion varies as the square of the 
 diameter of a particle, while the weight or gravitation of the 
 particle varies as the cube of the diamteer, in very finely 
 
192 ASTRONOMY. 
 
 divided matter the repulsive force would overcome the gravi- 
 tation of the particle and it would be driven outward into 
 space. 
 
 But the sun is a third rate star ; and every star is a sun in 
 which the same forces are at play as in our sun, and in some 
 cases with much greater activity, so that every star sends 
 forth continually streams of radiant matter into surrounding 
 regions, and thus the whole of interstellar space must be, 
 figuratively speaking, " thronged with corpuscular traffic." 
 
 103. Distances and Comparative Sizes of the Stars. 
 
 By taking the diameter of the earth's orbit, 186 million 
 miles, as a base, the parallaxes of a few stars have been deter- 
 mined, with a more or less degree of accuracy. 
 
 The star having the largest known parallax is a. Centauri, 
 its parallax being about 0".67, which means that the star is 
 at a distance of about 25 trillions of miles. Instead of deal- 
 ing with these large numbers, astronomers have agreed to 
 express stellar distances in light-years, in which the unit is 
 the distance traversed by light in a year, at the velocity of 
 186,000 miles per second. 
 
 The following table gives the distances of some prominent 
 stars in light-years : 
 
 a Centuari, the nearest star 4.2 It.-yrs. 
 
 Sirius, the brightest star in the sky. .. . 8.5 
 
 Procyon, the little dog star 10 
 
 Altair, the first star in the eagle 14 
 
 Aldebaran, the bull's eye 30 
 
 Pollux, one of the twins 60 
 
 Arcturus, mentioned in Job 100 
 
 Regulus, the lion's heart 140 
 
 This list includes only prominent stars, and not all the 
 stars whose distances have been measured. 
 
 In their first attempts at finding the distances of the stars, 
 astronomers made the natural mistake of supposing that the 
 larger and brighter stars were the nearer. But that this is 
 not so is shown by the fact that Regulus and Arcturus are 
 
THE STARS. 193 
 
 very much brighter than a Centauri and yet many times 
 farther away. 
 
 The star known as 61 Cygni is barely visible to the eye, 
 but has a large proper motion, that is, it changes its place 
 in the heavens to a considerable extent in each year. And 
 yet its distance is determined to be about 7 It. -years. So we 
 see that the stars with the largest proper motion are not 
 necessarily the nearest. 
 
 Again the star Canopiis or ^ Argus is next to Sirius in 
 brilliancy, although it has never shown any sensible parallax, 
 and its distance is consequently not less than 200 light-years, 
 and how much more we have no means of knowing. 
 
 We see, then, that the stars vary immensely not only in 
 distance but also in size ; for Canopus is brighter than Pro- 
 cyon and is not less than 20 times as far away; so that if 
 Canopus were in the position of Procyon it would be about 
 400 times as bright as Procyon is. And if the temperatures 
 of the two stars are about the same, it follows that Canopus 
 must be somewhere like 8000 times as large as Procyon. 
 
 Again, Elkins has shown that the average distance of the 
 10 brightest stars is 33 It. -years. 
 
 At this distance our sun would appear as a 5th magnitude 
 star, or a star just faintly visible. So that our glorious sun 
 does not hold a high rank among stars. If Sirius were at 
 the sun's distance it would be 360 times as bright as the sun. 
 But brightness varies as the square of the diameter and vol- 
 ume as the cube, so that if the sun and Sirius have the same 
 temperature, Sirius must be something like 7000 times as 
 large as the sun. 
 
 But Sirius is believed to be much hotter than the sun, so 
 that 7000 is probably considerably too large a number. Then 
 what shall we say of Canopus, which is nearly as brilliant as 
 Sirius, while being at least 20 times as far away. 
 
 104. Proper Motions of the Stars. 
 
 The name " fixed star '" is only a relative term. Every 
 star has its proper motion which, although apparently very 
 small, goes on unchanged from year to year and thus accu- 
 
194 ASTRONOMY. 
 
 mulates through the ages. ^\nd these accumulations will in 
 time, say 75 or 80 million years, change to a considerable 
 extent the features of the starry heavens. 
 
 Thus (t Centauri has a proper transverse motion of 3".7 
 per year. Now, knowing the distance of the star, we readily 
 find that this means about 15 miles per second. In like 
 manner it has been determined, approximately at least, that 
 61 Cygni travels across our line of vision at 38 miles per 
 second, which is about twice the velocity with which our sun 
 and solar system are moving through space ; and a star 
 known as 1830 Groombridge " scorches the way " at the rate 
 of 200 miles per second. We are accustomed to speak of the 
 great speed of a rifle ball, but the speed of Groombridge is 
 600 times as great. 
 
 By means of the spectroscope the astronomer is able to 
 measure with some accuracy the velocity of a star along the 
 line of sight. For when a star is approaching the earth or 
 sun its spectrum-lines are displaced towards the violet end 
 of the spectrum, and when going away from the sun the 
 spectrum-lines are displaced towards the red end of the 
 spectrum. 
 
 In this way are obtained the following: 
 
 Stars approaching, Arcturus 40 mil. per sec. 
 
 t'Herculis 44 " 
 
 y Leonis 24 " 
 
 Stars receding, Aldebaran ... .30 " 
 
 Sirius 25 " 
 
 eOrionis 15 " 
 
 105. Double Stars. 
 
 By this term is meant a system of two stars which revolve 
 about one another, or rather about their common mass cen- 
 tre. It is also called a binary system. 
 
 The first star shown to be double was 61 Cygni, but the 
 number now known rises into the hundreds or even the 
 thousands, so that they are no longer novelties in astronomy. 
 In a few cases the star can be seen to be double by the naked 
 eye, and in many cases by the telescope, but the majority of 
 
THE STARS. 195 
 
 the known doubles do not appear as such even under the 
 highest powers of the telescope. 
 
 The star 61 Cygni was known to consist of two stars as 
 far back as 1806, but it was left to Sir William Herschell to 
 show that it is a veritable double by showing that the stars 
 revolve about one another. 
 
 The star a Centauri is also a double, the constituents being 
 nearly equal, and about 17", or 1,900,000,000 miles apart. 
 And they complete a revolution in 81 years. From this it is 
 derived that the mass of a Centauri is about twice the mass 
 of the sun. 
 
 Sirius, also, is a double star. The diameter of the orbit 
 of the Sirian system is 3,500,000,000 miles, and the period 
 of revolution is 52 years. The comes is about Y^o as large 
 as Sirius itself, and the mass of the system is Sj times that 
 of the sun. So that the density of Sirius is less than the 
 sun's density, and Sirius is much larger and brighter and 
 hotter than the sun. 
 
 When a star cannot be seen to be double in the telescope, 
 its true character may be revealed by the doubling of the 
 lines in its spectrum. For if the earth lies anywhere near the 
 plane of their orbit, one star will be receding from us when 
 the other is approaching us, and the spectral lines of the 
 stars will both be displaced, but in opposite directions ; and 
 as a consequence the spectra when overlapped will show all 
 the lines doubled. The amount of displacement shows the 
 relative velocity of motion of the stars. 
 
 Thus Mizar, a star in the handle of the dipper, has been 
 shown, in this way, to be a remarkable double in which the 
 stars are 22,000,000 miles apart and complete their circuit 
 in 21 days. 
 
 P Aurigae is another spectroscopic double in which the 
 stars travel at the rate of 6S miles a second, and have a com- 
 bined mass 4.7 times that of the sun. 
 
 106. Variable Stars. 
 
 If one of the members of a binary system were much 
 darker than the other and in its revolution came between the 
 
196 ASTRONOMY. 
 
 bright member and the earth, the brightness of the system 
 would suffer a periodic diminution, and the star would be a 
 ■variable. 
 
 The most noted case of this kind is Algol, the "demon star 
 of the Arabs." Algol is a star about 1,000,000 miles in 
 diameter ; its dark attendant is 830,000 miles in diameter, or 
 about the size of our sun, and the time of revolution is 68.8 
 bour?. The star Algol loses and gains Y5 of its brilliancy in 
 a period of a few hours. 
 
 A number of other stars act in the same way as Algol, but 
 there are numerous other variable stars whose manner of 
 variation seems to be more or less arbitrary and irregular 
 and of which no reasonable explanation seems yet to be 
 forthcoming. 
 
 107. Star Clusters. 
 
 The group of stars known as the seven stars, or pleiades, 
 Is a coarse or open star cluster, as all the stars of the group 
 appear to be in some way connected together, and long ex- 
 posed photographs of the group show that the members are 
 more or less encompassed by a common nebulous mass. 
 
 A cluster called Praesepe, or the bee-hive, in the constel- 
 lation of Cancer, is smaller and more compact than the 
 pleiades, the whole group appearing as a faint hazy spot to 
 the unassisted sight. To the ancient Greeks, according to 
 Aratus, its becoming dim and disappearing was an indication 
 of coming rain ; a very natural weather sign, as the faint 
 light of the cluster is readily quenched in an atmosphere not 
 altogether clear. 
 
 A still more magnificent cluster, designated as 5 m librae 
 and appearing as a faint star, contains, according to Sir 
 Wm. Herschel, more than 200 stars. 
 
 But according to the same authority the most magnificent 
 cluster in the visible universe is the "star" known as <o Cen- 
 tauri, in which minute stars are too numerous to be counted, 
 and are so closely compressed towards the centre of the 
 cluster as to form a blaze of light. 
 
STAR CLUSTERS. 197 
 
 As to the nature of a star cluster of the closer kind, such 
 as 0) Centauri, or, in fact, of any kind, almost nothing can 
 be said to be known, except that it offers a field for unlimited 
 speculation. Whatever the cause may be, star clusters ap- 
 pear to be particularly rich in variable stars, but how these 
 variables are related to the' general stars of the cluster, or 
 in what way they depend upon the cluster for their varia- 
 bility, are questions as yet unanswered. 
 
 Fig. 96. 
 
 Are the stars of a cluster, like w Centauri, smaller than the 
 average stars of the universe, or is their faintness due to 
 immensity of distance? Are they comparatively close toge- 
 ther so that neighboring ones may influence each other, or 
 are they as far apart relatively to their size as stars in more 
 open parts of the skies? By what means have they become 
 compacted together and separated from the great body of 
 visible stars, or are they separate and distinct universes in 
 themselves? All of these questions press for answers, but 
 none of them, so far, have been answered. 
 
198 ASTRONOMY. 
 
 108. The Milky Way. 
 
 This is the name given to that faint and irregular band of 
 light which is seen to cross the skies from a northern point 
 to a southern one, and which of course, in a way, may be 
 said to rise and set every night. A volume might be written 
 upon the wonders of the milky way, and upon the various 
 speculations which have been indulged in and the theories 
 which have been advanced with regard to its nature and con- 
 stitution. And yet astronomers know very little more about 
 the real character of this enigma to-day than did some of the 
 ancient Greeks. Democritus and Pythagoras both,held that 
 the milky way was nothing more or less than a vast assem- 
 blage of stars, and Ovid speaks of it as a high road " whose 
 ground work is of stars." 
 
 Fig. 97. 
 
 The faint luminosity of the milky way is due to the com- 
 bined light of myriads of stars forming something like the 
 juxtaposition of thousands of star-clusters in which many of 
 the constituents are too faint and too close to be separated 
 even by the higher powers of the telescope. Where the milky 
 
THE MILKY WAY. 199 
 
 way is brightest, there the stars are thickest or most com- 
 pacted. Sir Wm. Herschel estimated that 116,000 stars 
 passed through the field of his telescope in 15 minutes; and 
 upon another occasion 258,000 stars passed in 41 minutes. 
 
 The groups of star-clusters which form the milky way are 
 in no places separate and distinct, but run into one another 
 with endless confusion, and apparently devoid of any ar- 
 rangement or system whateyer. 
 
 The accompanying photograph of a small portion of the 
 milky way, in the vicinity of Sagittarius, will give a better 
 idea of its general appearance than a volume of description. 
 The darkest parts are the general ground of the sky, and all 
 the various gradations of light are due to fields of stars. 
 
 It would be in vain to enter upon any speculations regard- 
 ing its internal constitution or its meaning in the universe, 
 for beyt)nd what is revealed through the telescope and photo- 
 graph, nothing whatever can be said to be known about this 
 mystery of the ages. 
 
 109. Nebulae. 
 
 The nebulae form another group of the mysterious and 
 unexplainable things in the heavens. 
 
 A nebula appears as a faint hazy spot, without definite 
 form., and illy defined even in the telescope. Two large ones, 
 the great nebula of Orion, and the nebula of Andromeda, are 
 barely visible to the naked eye, but the rest are telescopic. 
 With low powers of the telescope it is easy to confound a 
 faint star cluster with a nebula, while under high powers the 
 distinction is apparent in the fact that some seeming ne- 
 bulae have been resolved into stars, while others have not. 
 It was consequently thought, at once, that all nebulae might 
 be shown to be star clusters under sufficiently high powers 
 of the telescope. But the spectroscope has shown that such 
 an inference is untenable, as the spectra of the two things are 
 quite different, and that the spectrum of a nebula contains a 
 line which is found nowhere else, and which is attributed to 
 some substance called nebulum, which is totally unknown 
 anywhere except in a nebula. 
 
200 
 
 ASTRONOMY. 
 
 Nebulae exist by hundreds and are most thickly distributed 
 in those parts of the heavens which might be called the tem- 
 perate and polar regions of the milky way, that is, in those 
 regions which are quite removed from the milky way. No 
 explanation of such a distribution is forthcoming. 
 
 Within the boundaries of many of the nebulae numerous 
 stars may be seen. If the stars are between us and the nebulae 
 the distance of the latter must be exceedingly great, and their 
 size must surpass the powers of human imagination. And if 
 the stars lie beyond the nebula and are seen through its 
 depths, it is difficult to conceive of a substance so rare as to 
 be unable to quench the light of the faintest star and yet to 
 be itself visible. In fact, the great puzzle has been, and is 
 
 Fig. 98. 
 
 Still, as to how a substance so rare as a nebula must be, what- 
 ever may be its physical state, can be visible by its own inher- 
 ent light. The hypothesis of the " corpuscular traffic of the 
 universe," already spoken of, may be in the line of an ex- 
 planation. For the moving corpuscle meeting the particle of 
 
NEBULAE. 201 
 
 nebulous matter with a velocity comparable to that of light 
 may set up corpuscular vibration sufficient to make the par- 
 ticle visible, and thus the faint light of the nebula would 
 come from its superficial parts only, and not from its 
 interior. But this is mere hypothesis, and may or may not 
 be fact. 
 
 Many of the nebulae, if not the great majority of them, 
 have a distinctly spiral conformation, suggesting a rotation 
 about an axis. The photograph here shown is of the spiral 
 nebula of Ursa Major, and shows the conformation exceed- 
 ingly well. 
 
 The outlying portions show small tufts of nebulous matter 
 as if about to be thrown ofif by centrifugal force, and this has 
 strengthened the hypothesis that nebulae are in some way the 
 parents of stellar and planetary systems. But as a matter of 
 fact the origin, development, and final destiny of the nebulae 
 are among the profound secrets of the universe. 
 
 110. Comets. 
 
 A comet is a comparatively small mass of cosmic matter 
 which travels through space in some one of the curves 
 known as conic sections. If the comet is confined to the solar 
 system, as Halley's and several other comets, the orbit is an 
 ellipse, and however far away the body may go in its journey 
 outwards from the sun, it will invariably return in time to its 
 perihelion passage. Thus Halley's comet goes outward to 
 bej'ond the orbit of Neptune, and passes its perihelion within 
 the orbit of Venus. 
 
 But if the orbit be any of the other conic sections, as the 
 parabola or the hyperbola, the comet, after passing the sun, 
 will drift away into space, never to return to the solar system. 
 
 The distinctive feature of the majority of visible comets is 
 the presence of a tail, which may be straight or be slightly 
 curved, but which is always directed away from the sun. 
 But some comets never develop tails, and the tail is never a 
 very conspicuous appendage except when the comjlt is in / ^ 
 some proximity to the sun. And thus the existence of a tail 
 
202 ASTRONOMY. 
 
 is dependent partly on the nature of the comet itself, and 
 partly upon some effect produced on the comet by the sun. 
 
 The mass of even the largest comet is exceedingly small, 
 for when a comet, in its visit to the sun, passes near one of 
 the planets of the solar system, the comet is always much 
 disturbed and its course seriously interfered with, while the 
 planet suffers no appreciable disturbance whatever. And 
 from many considerations it appears doubtful if the mass of 
 the largest comet is as much as one-millionth part of that of 
 the moon. 
 
 And yet the nucleus of some comets, as that of 1845, was 
 larger than this earth, while the enveloping coma, or sur- 
 rounding layers, is sometimes more than a million miles 
 across. 
 
 The only reasonable idea, then, that we can form of the 
 constitution of a comet seems to be that its nucleus consists 
 of an immense extent of small mineral pieces varying from 
 mere dust particles upwards to a few larger ones scattered 
 here and there, the whole reaching over thousands of miles, 
 and having the particles exceedingly small as compared with 
 the distances between them. 
 
 These particles, large and small, become luminous under 
 the solar rays and give out light something after the manner 
 of the motes which float in a sunbeam. 
 
 The coma must consist of still smaller particles, or of par- 
 ticles much more widely separated, or possibly of large quan- 
 tities of exceedingly diffuse gaseous matter. 
 
 The constituent particles of a comet may contain any kind 
 of matter, solid or liquid, and in a large number of cases the 
 spectroscope has shown that the comet is rich in hydrocar- 
 bons. Out in the low temperatures of the farther reaches 
 of the orbit much of this hydrocarbonacious matter might be 
 liquid or even solid. But upon drawing near to the sun, the 
 heat would volatilize it, and possibly some other substances, 
 and the closer the proximity to the sun the greater would be 
 the amount of gaseous hydrocarbons in the comet's consti- 
 tution. 
 
COMETS. 203 
 
 The particles of these vapors, exposed continuously to the 
 fierce rays of the sun, are, in part at least, driven out into 
 space with practically the velocity of light, and are finally 
 dissipated and scattered to swell the amount of " corpuscular 
 traffic." 
 
 This forms the tail which grows as the comet approaches 
 the perihelion, which is essentially and necessarily opposite 
 the sun, and which is not a permanent appendage of the 
 comet, but which is being continually dissipated and as con- 
 tinually renewed from cometary resources. 
 
 Thus a comet loses something of its substance every time 
 it makes its perihelion passage, and it is generally recognized 
 that those comets which have returned to their perihelion a 
 number of times have gradually grown smaller and less im- 
 posing, while a few have been quite lost. 
 
 A comet containing no hydrocarbons, or other volatile sub- 
 stances, cannot develop a tail. 
 
 For long ages comets have been looked upon as harbingers 
 of evil and imminent sources of serious harm to the world 
 and its inhabitants. Even so late as the year 1910 several 
 persons committed suicide through fear of being destroyed 
 by Halley's comet. This fear was helped on by the senseless 
 statements of would-be sensational astronomers. And there 
 is no more arrant humbug in existence than the man who is 
 always threatening humanity with the disasters which are 
 coming to the world from celestial sources. 
 
 The probability of the earth coming into direct collision 
 with a comet is too remote to be worth considering, and even 
 if such a collision should take place, it is not likely that the 
 earth would be treated to anything more serious than a bril- 
 liant meteoric display, in which some harm might be done, 
 but not as much as in a disastrous hurricane. 
 
 And as for being poisoned broadcast by passing through 
 the tail of a comet, it is pretty certain that our globe has 
 passed through the tails of several comets without the fact 
 being recognized by the unobservant inhabitant. According 
 to Hind, the earth penetrated the tail of the comet of 1861, 
 producing nothing more serious than a faint glow in the 
 
204 ASTRONOMY. 
 
 upper atmosphere ; according to Klinkerfues, the earth 
 passed through a great part of Biela's comet in 1872, giving 
 to the people on the advancing side of the earth a brilliant 
 and pleasing display of celestial fireworks ; and it is quite 
 certain that it was swept by the tail of Halley's comet on the 
 18th of May last, while thousands of people slept on quietly 
 without knowing that anything out of the common was 
 taking place. 
 
 The heavens are replete with wonder and mystery, and the 
 few years of civilized man upon the earth are but as a 
 moment in the long ages required for any material change 
 to take place in the general character of the universe, or in 
 the aggregation of the stars, or in the conformation of a 
 nebula. 
 
 After pursuing his calling for ten thousand years or more, 
 the astronomer will be in a better position than he is now to 
 pronounce upon the validity and reasonableness of the 
 theories and hypotheses which are current to-day. But it is 
 not to be expected that an existence, even as long as the 
 future duration of the earth itself, would enable him to solve 
 in a manner completely satisfactory a moiety of the problems 
 which present themselves for solution. 
 
 So the astronomer need have no fear that he will exhaust 
 the wonders and masteries of the mighty expanse, or be left 
 without new things to be discovered and explained, for, how- 
 ever far his life may reach into the future, his work will be 
 only a beginning in the knowing and understanding of the 
 practically infinite. 
 
INDEX. 
 Numbers refer to pages. 
 
 Aberration of Stars 163 
 
 Albedo 107 
 
 Almucantur 16 
 
 Altitude 16 
 
 Angle of the Vertical 37 
 
 Annus magnus 90 
 
 Anomalistic year 100 
 
 Anomaly 100 
 
 Antarctic Circle 71 
 
 Aphelion 57 
 
 Apogee 49 
 
 Apsis line 49 
 
 Arctic Circle 71 
 
 Ascending Node 31 
 
 Autumnal equinox 62 
 
 Axis major 48 
 
 Axis minor 48 
 
 Azimuth 16 
 
 Bore 52 
 
 Canal, level of 8 
 
 Canals of Mars 185 
 
 Celestial latitude 74 
 
 " longitude 74 
 
 " points and lines.. 24 
 
 " sphere 5 
 
 Centre of gravity SO 
 
 Chromosphere 190 
 
 Circle of Perpet. App. .. .20,97 
 
 Circle of Perpet. Occult. .22,97 
 
 " of altitude 16 
 
 Climate 100 
 
 Comets 201 
 
 Comparison of © and Q . 55 
 
 Conditions for atmosphere. 167 
 
 Conjunction, inf. and sup.. 148 
 
 Constellation 3 
 
 Conventional Zodiac 93 
 
 Corona 191 
 
 Critical Velocity 168 
 
 Culmination 25 
 
 Declination 26 
 
 Direct and Retrograde .... 148 
 
 Dominical letter 140 
 
 Double stars 194 
 
 Dynamic sun 80 
 
 Earth 6 
 
 Earth's axial rotation 18 
 
 " dimensions 34 
 
 " rotundity 6 
 
 Easter 139 
 
 Eccentricity 48 
 
 " error 80 
 
 of orbit 100 
 
 Eclipses 115,158 
 
 " duration of 121 
 
 " lunar 119 
 
206 
 
 ASTRONOMY. 
 
 Eclipses in a year 135 
 
 " occurrence of .... 127 
 
 " periodicity of 134 
 
 Eclipse liimts 128 
 
 " periods 131 
 
 " maps 126,127 
 
 Ecliptic 59 
 
 Ellipse 47 
 
 Epact 104,140 
 
 Equation of light 162 
 
 of time 81 
 
 Equator 15 
 
 Equatorial 32 
 
 Equinoctial year 91 
 
 Equinox 31,62 
 
 Faculae 189 
 
 First meridian 31 
 
 " point of Aries 31 
 
 Foci 48 
 
 Formula s=rO 33 
 
 Foucault's pendulum 22 
 
 Full moon 106 
 
 Gibbous 106 
 
 Golden number 105, 139 
 
 Gravitation 9 
 
 Great circle 15 
 
 Gregorian calendar 142 
 
 Harvest moon 110 
 
 Horizon 12 
 
 Horizontal parallax 41 
 
 Hunter's moon 110 
 
 Julian calendar 141 
 
 Jupiter 156 
 
 Jupiter's moons 157 
 
 Kepler's law I 47 
 
 " n 57 
 
 " ni 146 
 
 Latitude 26,37,74 
 
 " correction of 37 
 
 Leap year 91 
 
 Level, the 11 
 
 Level line 7 
 
 Limb 39 
 
 Local meridian 25 
 
 Longitude 29, 74 
 
 finding of 160 
 
 Lunation 104 
 
 Major planets 186 
 
 Mass centre 50 
 
 Mars 153,183 
 
 " moons of 156 
 
 Mean day 80 
 
 sun 80 
 
 time 81 
 
 Meridian 16 
 
 local 25 
 
 Meteors 175 
 
 Metonic cycle 138 
 
 Milky way 197 
 
 Moon 39,102,178 
 
 diameter of 44 
 
 distance of 42 
 
 stereograph of 114 
 
 wet and dry 108 
 
 Moon's diurnal aug 45 
 
 diurnal parallax ... 41 
 
 horizontal parallax. 41 
 
 libration 112 
 
 motion 102 
 
 nodes 133 
 
 orbit 49,108 
 
INDEX. 
 
 207 
 
 Moon's parallax in altitude 42 
 
 " siderial period .... 103 
 
 " synodic period .... 104 
 
 Moon light and earth light 107 
 
 Movements of the stars 193 
 
 Nadir 13 
 
 Nebulae 199 
 
 Nebulum 199 
 
 New moon 106 
 
 Nodes 61 
 
 " motion of moon's... 133 
 
 Noon mark 83 
 
 North and south line 16 
 
 North star 19 
 
 Number of stars 3 
 
 Nutation 114 
 
 Old and new style 142 
 
 Old moon in new moon's 
 
 arms 108 
 
 Obliquity of ecliptic 59 
 
 Obliquity error 80 
 
 Opposition 1S4 
 
 Order of planets 143 
 
 Parallax 38 
 
 " of moon 39 
 
 of sun ....54,152,156 
 
 " of stars 192 
 
 Penumbra 116 
 
 Photosphere 188 
 
 Planets 143 
 
 Progression of light 161 
 
 Perigee 49 
 
 Perihelion 57 
 
 Plumb line 10 
 
 Polaris 19,95 
 
 Polaris on meridian 28 
 
 Pole star 19,95 
 
 Poles IS 
 
 Precession of equinoxes . . 90 
 
 Prime vertical 16 
 
 Radius vector 57 
 
 Refraction 174 
 
 Retrograde motion 148 
 
 Right ascension 30 
 
 Saros, the 136 
 
 Saturn 164 
 
 Sea-level 11 
 
 Sea Offing 7 
 
 Seasons 69 
 
 Shadows 117 
 
 Siderial clock 78 
 
 day 78 
 
 time n 
 
 " year 85 
 
 Solar day 81 
 
 " noon 81 
 
 " time 81 
 
 " system 142 
 
 Spheroidal earth 35 
 
 Star clusters 196 
 
 Stars 188 
 
 " number of 3 
 
 " fixed 5 
 
 Standard time 87 
 
 Summer stolstice 61 
 
 Sun 53,188 
 
 Sun's distance 54, 164 
 
 " volume 56 
 
 " hor. parallax. .54, 152, 156 
 
 " ang. diameter 57 
 
 " constitution 188 
 
208 
 
 ASTRONOMY. 
 
 Sunday letter 140 
 
 Surface conditions 167 
 
 Temperature 172 
 
 Terminator 106 
 
 Terrestrial atmosphere . . . 171 
 
 " sphere S 
 
 Tides 51 
 
 Tidal action on moon S3 
 
 Time 11 
 
 Transit 25 
 
 of Venus ISO 
 
 Tropic of Cancer 71 
 
 " of Capricorn 73 
 
 Tropical year 91 
 
 True horizon 12 
 
 Two latitudes 36 
 
 Umbra 
 
 lis 
 
 Variable Stars 195 
 
 Venus 147 
 
 Vernal equinox .31,62 
 
 Visible horizon 12 
 
 Wanderings of pole 32 
 
 Wet and dry moon 109 
 
 Winds 173 
 
 Zenith 13 
 
 Zenith distance 16 
 
 Zodiac 64 
 
 " signs of 65 
 
 " ancient 68 
 
 " conventional 67,93 
 
Cornell University Library 
 arV15578 
 
 The elements of astronomy principally on 
 
 3 1924 031 322 203 
 olln.anx