Star Spectroscopes--Cla.s.sification of Stellar Spectra--Type I., with very Few Absorption Lines--Type II., like the Sun--Type III., with Strongly Marked Dark Bands--Distribution of these Cla.s.ses over the Heavens--Motion in the Line of Sight--Orbital Motion Discovered with the Spectroscope: New Cla.s.s of Binaries--Spectra of Temporary Stars--Nature of these Bodies.

We have frequently in the previous chapters had occasion to refer to the revelations of the spectroscope, which form an important chapter in the history of modern science. By its aid a mighty stride has been taken in our attempt to comprehend the physical const.i.tution of the sun. In the present chapter we propose to give an account of what the spectroscope tells us about the physical const.i.tution of the fixed stars.

Quite a new phase of astronomy is here opened up. Every improvement in telescopes revealed fainter and fainter objects, but all the telescopes in the world could not answer the question as to whether iron and other elements are to be found in the stars. The ordinary star is a mighty glowing globe, hotter than a Bessemer converter or a Siemens furnace; if iron is in the star, it must be not only white-hot and molten, but actually converted into vapour. But the vapour of iron is not visible in the telescope. How would you recognise it? How would you know if it commingled with the vapour of many other metals or other substances? It is, in truth, a delicate piece of a.n.a.lysis to discriminate iron in the glowing atmosphere of a star. But the spectroscope is adequate to the task, and it renders its a.n.a.lysis with an amount of evidence that is absolutely convincing.

That the spectra of the moon and planets are practically nothing but faint reproductions of the spectrum of the sun was discovered by the great German optician Fraunhofer about the year 1816. By placing a prism in front of the object gla.s.s of a small theodolite (an instrument used for geodetic measurements) he was able to ascertain that Venus and Mars showed the same spectrum as the sun, while Sirius gave a very different one. This important observation encouraged him to procure better instrumental means with which to continue the work, and he succeeded in distinguishing the chief characteristics of the various types of stellar spectra. The form of instrument which Fraunhofer adopted for this work, in which the prism was placed outside the object gla.s.s of the telescope, has not been much used until within the last few years, owing to the difficulty of obtaining prisms of large dimensions (for it is obvious that the prism ought to be as large as the object gla.s.s if the full power of the latter is to be made use of), but this is the simplest form of spectroscope for observing spectra of objects of no sensible angular diameter, like the fixed stars. The parallel rays from the stars are dispersed by the prism into a spectrum, and this is viewed by means of the telescope. But as the image of the star in the telescope is nothing but a luminous point, its spectrum will be merely a line in which it would not be possible to distinguish any lines crossing it laterally such as those we see in the spectrum of the sun. A cylindrical lens is, therefore, placed before the eye-piece of the telescope, and as this has the effect of turning a point into a line and a line into a band, the narrow spectrum of the star is thereby broadened out into a luminous band in which we can distinguish any details that exist. In other forms of stellar spectroscope we require a slit which must be placed in the focus of the object gla.s.s, and the general arrangement is similar to that which we have described in the chapter on the sun, except that a cylindrical lens is required.

The study of the spectra of the fixed stars made hardly any progress until the principles of spectrum a.n.a.lysis had been established by Kirchhoff in 1859. When the dark lines in the solar spectrum had been properly interpreted, it was at once evident that science had opened wide the gates of a new territory for human exploration, of the very existence of which hardly anyone had been aware up to that time. We have seen to what splendid triumphs the study of the sun has led the investigators in this field, and we have seen how very valuable results have been obtained by the new method when applied to observations of comets and nebulae. We shall now give some account of what has been learned with regard to the const.i.tution of the fixed stars by the researches which were inaugurated by Sir William Huggins and continued and developed by him, as well as by Secchi, Vogel, Pickering, Lockyer, Duner, Scheiner and others. Here, as in the other modern branches of astronomy, photography has played a most important part, not only because photographed spectra of stars extend much farther at the violet end than the observer can follow them with his eye, but also because the positions of the lines can be very accurately measured on the photographs.

The first observer who reduced the apparently chaotic diversity of stellar spectra to order was Secchi, who showed that they might all be grouped according to four types. Within the last thirty years, however, so many modifications of the various types have been found that it has become necessary to subdivide Secchi's types, and most observers now make use of Vogel's cla.s.sification, which we shall also for convenience adopt in this chapter.

_Type I._--In the spectra of stars of this cla.s.s the metallic lines, which are so very numerous and conspicuous in the sun's violet spectrum, are very faint and thin, or quite invisible, and the blue and white parts are very intensely bright. Vogel subdivides the cla.s.s into three groups. In the first (I.a) the hydrogen lines are present, and are remarkably broad and intense; Sirius, Vega, and Regulus are examples of this group. The great breadth of the lines probably indicates that these stars are surrounded by hydrogen atmospheres of great dimensions. It is generally acknowledged that stars of this group must be the hottest of all, and support is lent to this view by the appearance in their spectra of a certain magnesium line, which, as Sir Norman Lockyer showed many years ago, by laboratory experiments, does not appear in the ordinary spectrum of magnesium, but is indicative of the presence of the substance at a very high temperature. In the spectra of stars of Group I.b the hydrogen lines and the few metallic lines are of equal breadth, and the magnesium line just mentioned is the strongest of all. Rigel and several other bright stars in Orion belong to this group, and it is remarkable that helium is present at least in some of these stars, so that (as Professor Keeler remarks) the spectrum of Rigel may almost be regarded as the nebular spectrum reversed (lines dark instead of bright), except that the two chief nebular lines are not reversed in the star. This fact will doubtless eventually be of great importance to our understanding the successive development of a star from a nebula; and a star like Rigel is no doubt also of very high temperature. This is probably not the case with stars of the third subdivision of Type I.

(I.c), the spectra of which are distinguished by the presence of bright hydrogen lines and the bright helium line D3. Among the stars having this very remarkable kind of spectrum is a very interesting variable star in the constellation Lyra (b) and the star known as g Ca.s.siopeiae, both of which have been a.s.siduously observed, their spectra possessing numerous peculiarities which render an explanation of the physical const.i.tution of the stars of this subdivision a very difficult matter.

Pa.s.sing to _Type II._, we find spectra in which the metallic lines are strong. The more refrangible end of the spectrum is fainter than in the previous Cla.s.s, and absorption bands are sometimes found towards the red end. In its first subdivision (II.a) are contained spectra with a large number of strong and well-defined lines due to metals, the hydrogen lines being also well seen, though they are not specially conspicuous.

Among the very numerous stars of this group are Capella, Aldebaran, Arcturus, Pollux, etc. The spectra of these stars are in fact practically identical with the spectrum of our own sun, as shown, for instance, by Dr. Scheiner, of the Potsdam Astrophysical Observatory, who has measured several hundred lines on photographs of the spectrum of Capella, and found a very close agreement between these lines and corresponding ones in the solar spectrum. We can hardly doubt that the physical const.i.tution of these stars is very similar to that of our sun.

This cannot be the case with the stars of the second subdivision (II.b), the spectra of which are very complex, each consisting of a continuous spectrum crossed by numerous dark lines, on which is superposed a second spectrum of bright lines. Upwards of seventy stars are known to possess this extraordinary spectrum, the only bright one among them being a star of the third magnitude in the southern constellation Argus. Here again we have hydrogen and helium represented by bright lines, while the origin of the remaining bright lines is doubtful. With regard to the physical const.i.tution of the stars of this group it is very difficult to come to a definite conclusion, but it would seem not unlikely that we have here to do with stars which are not only surrounded by an atmosphere of lower temperature, causing the dark lines, but which, outside of that, have an enormous envelope of hydrogen and other gases.

In one star at least of this group Professor Campbell, of the Lick Observatory, has seen the F line as a long line extending a very appreciable distance on each side of the continuous spectrum, and with an open slit it was seen as a large circular disc about six seconds in diameter; two other princ.i.p.al hydrogen lines showed the same appearance.

As far as this observation goes, the existence of an extensive gaseous envelope surrounding the star seems to be indicated.

_Type III._ contains comparatively few stars, and the spectra are characterised by numerous dark bands in addition to dark lines, while the more refrangible parts are very faint, for which reason the stars are more or less red in colour. This cla.s.s has two strongly marked subdivisions. In the first (III.a) the princ.i.p.al absorption lines coincide with similar ones in the solar spectrum, but with great differences as to intensity, many lines being much stronger in these stars than in the sun, while many new lines also appear. These dissimilarities are, however, of less importance than the peculiar absorption bands in the red, yellow, and green parts of the spectrum, overlying the metallic lines, and being sharply defined on the side towards the violet and shading off gradually towards the red end of the spectrum. Bands of this kind belong to chemical combinations, and this appears to show that somewhere in the atmospheres of these distant suns the temperature is low enough to allow stable chemical combinations to be formed. The most important star of this kind is Betelgeuze or a Orionis, the red star of the first magnitude in the shoulder of Orion; but it is of special importance to note that many variable stars of long period have spectra of Type III.a. Sir Norman Lockyer predicted in 1887 that bright lines, probably of hydrogen, would eventually be found to appear at the maximum of brightness, when the smaller swarm is supposed to pa.s.s through the larger one, and this was soon afterwards confirmed by the announcement that Professor Pickering had found a number of hydrogen lines bright on photographs, obtained at Harvard College Observatory, of the spectrum of the remarkable variable, Mira Ceti, at the time of maximum. Professor Pickering has since then reported that bright lines have been found on the plates of forty-one previously known variables of this cla.s.s, and that more than twenty other stars have been detected as variables by this peculiarity of their spectrum; that is, bright lines being seen in them suggested that the stars were variable, and further photometric investigations corroborated the fact.

The second subdivision (III.b) contains only comparatively faint stars, of which none exceed the fifth magnitude, and is limited to a small number of red stars. The strongly marked bands in their spectra are sharply defined and dark on the red side, while they fade away gradually towards the violet, exactly the reverse of what we see in the spectra of III.a. These bands appear to arise from the absorption due to hydrocarbon vapours present in the atmospheres of these stars; but there are also some lines visible which indicate the presence of metallic vapours, sodium being certainly among these. There can be little doubt that these stars represent the last stage in the life of a sun, when it has cooled down considerably and is not very far from actual extinction, owing to the increasing absorption of its remaining light in the atmosphere surrounding it.

The method employed for the spectroscopic determination of the motion of a star in the line of sight is the same as the method we have described in the chapter on the sun. The position of a certain line in the spectrum of a star is compared with the position of the corresponding bright line of an element in an artificially produced spectrum, and in this manner a displacement of the stellar line either towards the violet (indicating that the star is approaching us) or towards the red (indicating that it is receding) may be detected. The earliest attempt of this sort was made in 1867 by Sir William Huggins, who compared the F line in the spectrum of Sirius with the same line of the spectrum of hydrogen contained in a vacuum tube reflected into the field of his astronomical spectroscope, so that the two spectra appeared side by side. The work thus commenced and continued by him was afterwards taken up at the Greenwich Observatory; but the results obtained by these direct observations were never satisfactory, as remarkable discrepancies appeared between the values obtained by different observers, and even by the same observer on different nights. This is not to be wondered at when we bear in mind that the velocity of light is so enormous compared with any velocity with which a heavenly body may travel, that the change of wave length resulting from the latter motion can only be a very minute one, difficult to perceive, and still more difficult to measure.

But since photography was first made use of for these investigations by Dr. Vogel, of Potsdam, much more accordant and reliable results have been obtained, though even now extreme care is required to avoid systematic errors. To give some idea of the results obtainable, we present in the following table the values of the velocity per second of a number of stars observed in 1896 and 1897 by Mr. H.F. Newall with the Bruce spectrograph attached to the great 25-inch Newall refractor of the Cambridge Observatory, and we have added the values found at Potsdam by Vogel and Scheiner. The results are expressed in kilometres (1 km. = 062 English mile). The sign + means that the star is receding from us,-that it is approaching.

Newall. Vogel. Scheiner.

Aldebaran + 492 + 476 + 494 Betelgeuze + 106 + 156 + 188 Procyon - 42 - 72 - 105 Pollux - 07 + 19 + 04 g Leonis - 399 - 365 - 405 Arcturus - 64 - 70 - 83

These results have been corrected for the earth's...o...b..tal motion round the sun, but not for the sun's motion through s.p.a.ce, as the amount of the latter is practically unknown, or at least very uncertain; so that the above figures really represent the velocity per second of the various stars relative to the sun. We may add that the direction and velocity of the sun's motion may eventually be ascertained from spectroscopic measures of a great number of stars, and it seems likely that the sun's velocity will be much more accurately found in this way than by the older method of combining proper motions of stars with speculations as to the average distances of the various cla.s.ses of stars. This has already been attempted by Dr. Kempf, who from the Potsdam spectrographic observations found the sun's velocity to be 186 kilometres, or 115 miles per second, a result which is probably not far from the truth.

But the spectra of the fixed stars can also tell us something about orbital motion in these extremely distant systems. If one star revolved round another in a plane pa.s.sing through the sun, it must on one side of the orbit move straight towards us and on the other side move straight away from us, while it will not alter its distance from us while it is pa.s.sing in front of, or behind, the central body. If we therefore find from the spectroscopic observations that a star is alternately moving towards and away from the earth in a certain period, there can be no doubt that this star is travelling round some unseen body (or, rather, round the centre of gravity of both) in the period indicated by the shifting of the spectral lines. In Chapter XIX. we mentioned the variable star Algol in the constellation Perseus, which is one of a cla.s.s of variable stars distinguished by the fact that for the greater part of the period they remain of unaltered brightness, while for a very short time they become considerably fainter. That this was caused by some sort of an eclipse--or, in other words, by the periodic pa.s.sage of a dark body in front of the star, hiding more or less of the latter from us--was the simplest possible hypothesis, and it had already years ago been generally accepted. But it was not possible to prove that this was the true explanation of the periodicity of stars like Algol until Professor Vogel, from the spectroscopic observations made at Potsdam, found that before every minimum Algol is receding from the sun, while it is approaching us after the minimum. a.s.suming the orbit to be circular, the velocity of Algol was found to be twenty-six miles per second. From this and the length of the period (2d. 22h. 48m. 55s.) and the time of obscuration it was easy to compute the size of the orbit and the actual dimensions of the two bodies. It was even possible to go a step further and to calculate from the orbital velocities the ma.s.ses of the two bodies,[41] a.s.suming them to be of equal density--an a.s.sumption which is no doubt very uncertain. The following are the approximate elements of the Algol system found by Vogel:--

Diameter of Algol 1,054,000 miles.

Diameter of companion 825,000 miles.

Distance between their centres 3,220,000 miles.

Orbital velocity of Algol 26 miles per sec.

Orbital velocity of companion 55 miles per sec.

Ma.s.s of Algol 4/9 of sun's ma.s.s.

Ma.s.s of companion 2/9 of sun's ma.s.s.

The period of Algol has been gradually decreasing during the last century (by six or seven seconds), but whether this is caused by the motion of the pair round a third and very much more distant body, as suggested by Mr. Chandler, has still to be found out.

We have already mentioned that in order to produce eclipses, and thereby variations of light, it is necessary that the line of sight should lie nearly in the plane of the orbit. It is also essential that there should be a considerable difference of brightness between the two bodies. These conditions must be fulfilled in the fifteen variable stars of the Algol cla.s.s now known; but according to the theory of probability, there must be many more binary systems like that of Algol where these conditions are not fulfilled, and in those cases no variations will occur in the stars' brightness. Of course, we know many cases of a luminous star travelling round another, but there must also be cases of a large companion travelling round another at so small a distance that our telescopes are unable to "divide" the double star. This has actually been discovered by means of the spectroscope. If we suppose an extremely close double star to be examined with the spectroscope, the spectra of the two components will be superposed, and we shall not be aware that we really see two different spectra. But during the revolution of the two bodies round their common centre of gravity there must periodically come a time when one body is moving towards us and the other moving from us, and consequently the lines in the spectrum of the former will be subject to a minute, relative shift towards the violet end of the spectrum, and those of the other to a minute shift towards the red. Those lines which are common to the two spectra will therefore periodically become double.

A discovery of this sort was first made in 1889 by Professor Pickering from photographs of the spectrum of Mizar, or z Ursa Majoris, the larger component of the well-known double star in the tail of the Great Bear. Certain of the lines were found to be double at intervals of fifty-two days. The maximum separation of the two components of each line corresponds to a relative velocity of one star as compared with the other of about a hundred miles per second, but subsequent observations have shown the case to be very complicated, either with a very eccentric elliptic orbit or possibly owing to the presence of a third body. The Harvard College photographs also showed periodic duplicity of lines in the star b Aurigae, the period being remarkably short, only three days and twenty-three hours and thirty-seven minutes. In 1891 Vogel found, from photographs of the spectrum of Spica, the first magnitude star in Virgo, that this star alternately recedes from and approaches to the solar system, the period being four days. Certain other "spectroscopic binaries" have since then been found, notably one component of Castor, with a period of three days, found by M.

Belopolsky, and a star in the constellation Scorpio, with a period of only thirty-four hours, detected on the Harvard spectrograms.

Quite recently Mr. H.F. Newall, at Cambridge, and Mr. Campbell, of the Lick Observatory, have shown that a Aurigae, or Capella, consists of a sun-like star and a Procyon-like star, revolving in 104 days.

At first sight there is something very startling in the idea of two suns circling round each other, separated by an interval which, in comparison with their diameters, is only a very small one. In the Algol system, for instance, we have two bodies, one the size of our own sun and the other slightly larger, moving round their common centre of gravity in less than three days, and at a distance between their surfaces equal to only twice the diameter of the larger one. Again, in the system of Spica we have two great suns swinging round each other in only four days, at a distance equal to that between Saturn and his sixth satellite. But although we have at present nothing a.n.a.logous to this in our solar system, it can be proved mathematically that it is perfectly possible for a system of this kind to preserve its stability, if not for ever, at any rate for ages, and we shall see in our last chapter that there was in all probability a time when the earth and the moon formed a peculiar system of two bodies revolving rapidly at a very small distance compared to the diameters of the bodies.

It is possible that we have a more complicated system in the star known as b Lyrae. This is a variable star of great interest, having a period of twelve days and twenty-two hours, in which time it rises from magnitude 4-1/2 to a little above 3-1/2, sinks nearly to the fourth magnitude, rises again to fully 3-1/2, and finally falls to magnitude 4-1/2. In 1891 Professor Pickering discovered that the bright lines in the spectrum of this star changed their position from time to time, appearing now on one side, now on the other side of corresponding dark lines. Obviously these bright lines change their wave length, the light-giving source alternately receding from and approaching to the earth, and the former appeared to be the case during one-half of the period of variation of the star's light, the latter during the other half. The spectrum of this star has been further examined by Belopolsky and others, who have found that the lines are apparently double, but that one of the components either disappears or becomes very narrow from time to time. On the a.s.sumption that these lines were really single (the apparent duplicity resulting from the superposition of a dark line), Belopolsky determined the amount of their displacement by measuring the distances from the two edges of a line of hydrogen (F) to the artificial hydrogen line produced by gas glowing in a tube and photographed along with the star-spectrum. a.s.suming the alternate approach and recession to be caused by orbital revolution, Belopolsky found that the body emitting the light of the bright lines moved with an orbital velocity of forty-one miles. He succeeded in 1897 in observing the displacement of a dark line due to magnesium, and found that the body emitting it was also moving in an orbit, but while the velocities given by the bright F line are positive after the princ.i.p.al minimum of the star's light, those given by the dark line are negative. Therefore, during the princ.i.p.al minimum it is a star giving the dark line which is eclipsed, and during the secondary minimum another star giving the bright line is eclipsed.

This wonderful variable will, however, require more observatioens before the problem of its const.i.tution is finally solved, and the same may be said of several variable stars, _e.g._ e Aquilae and d Cephei, in which a want of harmony has been found between the changes of velocity and the fluctuations of the light.

There are some striking a.n.a.logies between the complicated spectrum of b Lyrae and the spectra of temporary stars. The first "new star"

which could be spectroscopically examined was that which appeared in Corona Borealis in 1866, and which was studied by Sir W. Huggins. It showed a continuous spectrum with dark absorption lines, and also the bright lines of hydrogen; practically the same spectrum as the stars of Type II.b. This was also the case with Schmidt's star of 1876, which showed the helium line (D3) and the princ.i.p.al nebula line in addition to the lines of hydrogen; but in the autumn of 1877, when the star had fallen to the tenth magnitude, Dr. Copeland was surprised to find that only one line was visible, the princ.i.p.al nebula line, in which almost the whole light of the star was concentrated, the continuous spectrum being hardly traceable. It seemed, in fact, that the star had been transformed into a planetary nebula, but later the spectrum seems to have lost this peculiar monochromatic character, the nebula line having disappeared and a faint continuous spectrum alone being visible, which is also the case with the star of 1866 since it sank down to the tenth magnitude. A continuous spectrum was all that could be seen of the new star which broke out in the nebula of Andromeda in 1885, much the same as the spectrum of the nebula itself.

When the new star in Auriga was announced, in February, 1892, astronomers were better prepared to observe it spectroscopically, as it was now possible by means of photography to study the ultra-violet part of the spectrum which to the eye is invisible. The visible spectrum was very like that of Nova Cygni of 1876, but when the wave-lengths of all the bright lines seen and photographed at the Lick Observatory and at Potsdam were measured, a strong resemblance to the bright line spectrum of the chromosphere of the sun became very evident. The hydrogen lines were very conspicuous, while the iron lines were very numerous, and calcium and magnesium were also represented. The most remarkable revelation made by the photographs was, however, that the bright lines were in many cases accompanied, on the side next the violet, by broad dark bands, while both bright and dark lines were of a composite character. Many of the dark lines had a thin bright line superposed in the middle, while on the other hand many of the bright lines had two or three points maxima of brightness. The results of the measures of motion in the line of sight were of special importance. They showed that the source of light, whence came the thin bright lines within the dark ones, was travelling towards the sun at the enormous rate of 400 miles per second, and if the bright lines were actual "reversals" of the dark ones, then the source of the absorption spectrum must have been endowed with much the same velocity. On the other hand, if the two or three maxima of brightness in the bright lines really represent two or three separate bodies giving bright lines, the measures indicate that the princ.i.p.al one was almost at rest as regards the sun, while the others were receding from us at the extraordinary rates of 300 and 600 miles per second. And as if this were not sufficiently puzzling, the star on its revival in August, 1892, as a tenth magnitude star had a totally different spectrum, showing nothing but a number of the bright lines belonging to planetary nebulae! It is possible that the princ.i.p.al ones of these were really present in the spectrum from the first, but that their wave lengths had been different owing to change of the motion in the line of sight, so that the nebula lines seen in the autumn were identical with others seen in the spring at slightly different places.

Subsequent observations of these nebula lines seemed to point to a motion of the Nova towards the solar system (of about 150 miles per second) which gradually diminished.

But although we are obliged to confess our inability to say for certain why a temporary star blazes up so suddenly, we have every cause to think that these strange bodies will by degrees tell us a great deal about the const.i.tution of the fixed stars. The great variety of spectra which we see in the starry universe, nebula spectra with bright lines, stellar spectra of the same general character, others with broad absorption bands, or numerous dark lines like our sun, or a few absorption lines only--all this shows us the universe as teeming with bodies in various stages of evolution. We shall have a few more words to say on this matter when we come to consider the astronomical significance of heat; but we have reached a point where man's intellect can hardly keep pace with the development of our instrumental resources, and where our imagination stands bewildered when we endeavour to systematise the knowledge we have gained. That great caution will have to be exercised in the interpretation of the observed phenomena is evident from the recent experience of Professor Rowland, of Baltimore, from which we learn that spectral lines are not only widened by increased pressure of the light-giving vapour, but that they may be bodily shifted thereby.

Dr. Zeeman's discovery, that a line from a source placed in a strong magnetic field may be both widened, broadened, and doubled, will also increase our difficulties in the interpretation of these obscure phenomena.

CHAPTER XXIV.

THE PRECESSION AND NUTATION OF THE EARTH'S AXIS.

The Pole is not a Fixed Point--Its Effect on the Apparent Places of the Stars--The Ill.u.s.tration of the Peg-Top--The Disturbing Force which acts on the Earth--Attraction of the Sun on a Globe--The Protuberance at the Equator--The Attraction of the Protuberance by the Sun and by the Moon produces Precession--The Efficiency of the Precessional Agent varies inversely as the Cube of the Distance--The Relative Efficiency of the Sun and the Moon--How the Pole of the Earth's Axis revolves round the Pole of the Ecliptic--Variation of Lat.i.tude.

The position of the pole of the heavens is most conveniently indicated by the bright star known as the Pole Star, which lies in its immediate vicinity. Around this pole the whole heavens appear to rotate once in a sidereal day; and we have hitherto always referred to the pole as though it were a fixed point in the heavens. This language is sufficiently correct when we embrace only a moderate period of time in our review. It is no doubt true that the pole lies near the Pole Star at the present time. It did so during the lives of the last generation, and it will do so during the lives of the next generation. All this time, however, the pole is steadily moving in the heavens, so that the time will at length come when the pole will have departed a long way from the present Pole Star. This movement is incessant. It can be easily detected and measured by the instruments in our observatories, and astronomers are familiar with the fact that in all their calculations it is necessary to hold special account of this movement of the pole. It produces an apparent change in the position of a star, which is known by the term "precession."

[Ill.u.s.tration: Fig. 100.]

The movement of the pole is very clearly shown in the accompanying figure (Fig. 100), for which I am indebted to the kindness of the late Professor C. Piazzi Smyth. The circle shows the track along which the pole moves among the stars.

The centre of the circle in the constellation of Draco is the pole of the ecliptic. A complete journey of the pole occupies the considerable period of about 25,867 years. The drawing shows the position of the pole at the several dates from 4000 B.C. to 2000 A.D. A glance at this map brings prominently before us how casual is the proximity of the pole to the Pole Star. At present, indeed, the distance of the two is actually lessening, but afterwards the distance will increase until, when half of the revolution has been accomplished, the pole will be at a distance of twice the radius of the circle from the Pole Star. It will then happen that the pole will be near the bright star Vega or a Lyrae, so that our successors some 12,000 years hence may make use of Vega for many of the purposes for which the Pole Star is at present employed! Looking back into past ages, we see that some 2,000 or 3,000 years B.C. the star a Draconis was suitably placed to serve as the Pole Star, when b and d of the Great Bear served as pointers.

It need hardly be added, that since the birth of accurate astronomy the course of the pole has only been observed over a very small part of the mighty circle. We are not, however, ent.i.tled to doubt that the motion of the pole will continue to pursue the same path. This will be made abundantly clear when we proceed to render an explanation of this very interesting phenomenon.

The north pole of the heavens is the point of the celestial sphere towards which the northern end of the axis about which the earth rotates is directed. It therefore follows that this axis must be constantly changing its position. The character of the movement of the earth, so far as its rotation is concerned, may be ill.u.s.trated by a very common toy with which every boy is familiar. When a peg-top is set spinning, it has, of course, a very rapid rotation around its axis; but besides this rotation there is usually another motion, whereby the axis of the peg-top does not remain in a constant direction, but moves in a conical path around the vertical line. The adjoining figure (Fig. 101) gives a view of the peg-top. It is, of course, rotating with great rapidity around its axis, while the axis itself revolves around the vertical line with a very deliberate motion. If we could imagine a vast peg-top which rotated on its axis once a day, and if that axis were inclined at an angle of twenty-three and a half degrees to the vertical, and if the slow conical motion of the axis were such that the revolution of the axis were completed in about 26,000 years, then the movements would resemble those actually made by the earth. The ill.u.s.tration of the peg-top comes, indeed, very close to the actual phenomenon of precession. In each case the rotation about the axis is far more rapid than that of the revolution of the axis itself; in each case also the slow movement is due to an external interference. Looking at the figure of the peg-top (Fig. 101) we may ask the question, Why does it not fall down? The obvious effect of gravity would seem to say that it is impossible for the peg-top to be in the position shown in the figure.

Yet everybody knows that this is possible so long as the top is spinning. If the top were not spinning, it would, of course, fall. It therefore follows that the effect of the rapid rotation of the top so modifies the effect of gravitation that the latter, instead of producing its apparently obvious consequence, causes the slow conical motion of the axis of rotation. This is, no doubt, a dynamical question of some difficulty, but it is easy to verify experimentally that it is the case.

If a top be constructed so that the point about which it is spinning shall coincide with the centre of gravity, then there is no effect of gravitation on the top, and there is no conical motion perceived.

[Ill.u.s.tration: Fig. 101.--Ill.u.s.tration of the Motion of Precession.]

If the earth were subject to no external interference, then the direction of the axis about which it rotates must remain for ever constant; but as the direction of the axis does not remain constant, it is necessary to seek for a disturbing force adequate to the production of the phenomena which are observed. We have invariably found that the dynamical phenomena of astronomy can be accounted for by the law of universal gravitation. It is therefore natural to enquire how far gravitation will render an account of the phenomenon of precession; and to put the matter in its simplest form, let us consider the effect which a distant attracting body can have upon the rotation of the earth.

To answer this question, it becomes necessary to define precisely what we mean by the earth; and as for most purposes of astronomy we regard the earth as a spherical globe, we shall commence with this a.s.sumption.

It seems also certain that the interior of the earth is, on the whole, heavier than the outer portions. It is therefore reasonable to a.s.sume that the density increases as we descend; nor is there any sufficient ground for thinking that the earth is much heavier in one part than at any other part equally remote from the centre. It is therefore usual in such calculations to a.s.sume that the earth is formed of concentric spherical sh.e.l.ls, each one of which is of uniform density; while the density decreases from each sh.e.l.l to the one exterior thereto.

A globe of this const.i.tution being submitted to the attraction of some external body, let us examine the effects which that external body can produce. Suppose, for instance, the sun attracts a globe of this character, what movements will be the result? The first and most obvious result is that which we have already so frequently discussed, and which is expressed by Kepler's laws: the attraction will compel the earth to revolve around the sun in an elliptic path, of which the sun is in the focus. With this movement we are, however, not at this moment concerned.

We must enquire how far the sun's attraction can modify the earth's rotation around its axis. It can be demonstrated that the attraction of the sun would be powerless to derange the rotation of the earth so const.i.tuted. This is a result which can be formally proved by mathematical calculation. It is, however, sufficiently obvious that the force of attraction of any distant point on a symmetrical globe must pa.s.s through the centre of that globe: and as the sun is only an enormous aggregate of attracting points, it can only produce a corresponding mult.i.tude of attractive forces; each of these forces pa.s.ses through the centre of the earth, and consequently the resultant force which expresses the joint result of all the individual forces must also be directed through the centre of the earth. A force of this character, whatever other potent influence it may have, will be powerless to affect the rotation of the earth. If the earth be rotating on an axis, the direction of that axis would be invariably preserved; so that as the earth revolves around the sun, it would still continue to rotate around an axis which always remained parallel to itself. Nor would the attraction of the earth by any other body prove more efficacious than that of the sun. If the earth really were the symmetrical globe we have supposed, then the attraction of the sun and moon, and even the influence of all the planets as well, would never be competent to make the earth's axis of rotation swerve for a single second from its original direction.

We have thus narrowed very closely the search for the cause of the "precession." If the earth were a perfect sphere, precession would be inexplicable. We are therefore forced to seek for an explanation of precession in the fact that the earth is not a perfect sphere. This we have already demonstrated to be the case. We have shown that the equatorial axis of the earth is longer than the polar axis, so that there is a protuberant zone girdling the equator. The attraction of external bodies is able to grasp this protuberance, and thereby force the earth's axis of rotation to change its direction.