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omers for many years. It is the facility and success attending its recent application that has now aroused so much inter
undulatory theory of light expressed a great truth of nature, a certain deduction from that truth became almost obvious. It was, however, by no means certain that the practical application of this deduction to astronomical research would be feasi ble. That it has proved to be so in any degree is somewhat of a surprise, while it now appears susceptible of developments to an extent that could hardly have been dreamed of.
were determined, and if the investigation | principle has been a familiar one to astronwere repeated after a sufficient lapse of time, then the differences between the two distances would give an indication of the star's movement along the line of sightest. Once it became certain that the during the interval. But we may say at once that such a method of research is wholly impracticable. Our knowledge of the star-distances is far too imperfect for the successful application of this method. Nor is there the slightest prospect of any improvements in practical astronomy which could enable us to detect movements of stars in the line of sight in the way suggested. Certainly it offers no hope of a method which could compare for a moment in simplicity or precision with the beautiful spectroscopic process. Of course if a star were moving in the line of sight, there must be a certain change in its apparent lustre corresponding to the changes in its distance, and it might be supposed that by careful measurements of the brightness of a star conducted from time to time, conclusions could be drawn as to the speed with which it was moving. But the application of such a process is beyond the sphere of available methods. It would take at least a thousand years before even the most rapidly moving star would experience a change that would sensibly affect its lustre; and even if we had the means of measuring with precision the light emitted, our results would still be affected by the possible fluctuations in the star's intrinsic brightness. It is thus manifest that the resources of the older astronomy were quite incapable of meeting the demands of astronomers when it became necessary to learn the movements of the stars to us or from us as well as the movements perpendicular to the line of vision, which had always been the subject of much investigation. It is just here that the spectroscope comes in to fill the vacant place in the armory of the astronomer. It tells exactly what the older methods were unable to tell, and it does so with a certainty and a facility that suggest vast possibilities for the spectroscopic process in the future. The principle of the method is a beautiful illustration of the extent to which the different branches of physical science are interwoven. But the
The logic of the new method is simple enough. Our eyes are so constituted that when a certain number of ethereal vibrations per second are received by the nerves of the retina the brain interprets the effect to mean that a ray of, let us say, red light has entered the eye. A certain larger number of vibrations per second is similarly understood by the brain to imply the presence of blue light on the retina. Each particular hue of the spectrum-the red, orange, yellow, green, blue, indigo, violet — is associated with a corresponding number of vibrations per second. It will thus be seen that the interpretation we put on any ray of light depends solely, as far as its hue is concerned, on the number of vibrations per second produced on the retina. Increase that number of vibra tions in any way, then the hue shifts towards one nearer the blue end of the spectrum; decrease the number of vibrations per second and the hue shifts along the spectrum in the opposite direction.
From these considerations it is apparent that the hue of a light as interpreted by the eye will undergo modification if the source from which the light radiates is moving towards us or moving from us. In order to expound the matter simply I shall suppose a case of a rather simpler type than any which we actually find in nature. Let us suppose the existence of a star emitting light of a pure green color corresponding to a tint near the middle of the spectrum. This star pours forth each second a certain number of vibrations appropriate to its particular color, and if
the star be at rest relatively to the eye, then, we assume, the vibrations will be received on the retina at the same intervals as those with which the star emits them. Consequently we shall perceive the star to be green. But now suppose that the star is hurrying towards us, it follows that the number of vibrations received in a second by the eye will undergo an increase. For the relative movement 's the same as if the earth were rushing towards the star. In this case we advance, as it were, to meet the waves, and consequently receive them at less intervals than if we were to wait for their arrival. Many illustrations can be given of the simple principle here involved. Suppose that a number of soldiers are walking past in single file, and that while the observer stands still twenty soldiers a minute pass him. But now let him walk in the opposite direction to the soldiers, then, if his speed be as great as theirs, he will pass forty soldiers a minute instead of twenty. If his speed were half that of the soldiers, then he would pass thirty a minute, so that in fact the speed with which the observer is moving could be determined if he counts the number of soldiers that he passes per minute, and makes a simple calculation. On the other hand, suppose that the observer walks in the same direction as the soldiers; if he maintains the same pace that they do, then it is plain that no soldiers at all will pass him while he walks. If he moves at half their rate, then ten soldiers will pass him each minute. From these considerations it will be sufficiently apparent that if the earth and the star are approaching each other, more waves of light per second will be received on the retina than if their positions are relatively stationary. But the interpretation which the brain will put on this accession to the number of waves per second is that the hue of the light is altered to some shade nearer the blue end of the spectrum. In fact, if we could conceive the velocity with which the bodies approached to be sufficiently augmented, the color of the star would seem to change from green to blue, from blue to indigo, from indigo to violet; while, if the pace were still further increased, it is absolutely certain that the
waves would be poured upon the retina with such rapidity that no nerves there present would be competent to deal with them, and the star would actually disappear from vision. It may, however, be remarked that the velocity required to produce such a condition as we have sup posed is altogether in excess of any known velocities in the celestial movements. The actual changes in hue that the movements we meet with are competent to effect are much smaller than in the case given as an illustration.
On the other hand, we may consider the original green star and the earth to be moving apart from each other. The effect of this is that the number of waves poured into the eye is lessened, and accordingly the brain interprets this to imply that the hue of the star has shifted from the green to the red end of the spectrum. If the speed with which the bodies increase their distance be sufficiently large, the green may transform into a yellow, the yellow into an orange, the orange into a red; while a still greater velocity is, at all events, conceivable which would cause the undulations to be received with such slowness that the nature of the light could no longer be interpreted by any nerves which the eye contains, and from the mere fact of its rapid motion away from us the star would become invisible. Here again we must add the remark that the actual velocities animating the heavenly bodies are not large enough to allow of the extreme results now indicated.
However, in the actual circumstances of the celestial bodies it seems impossible that any change of hue recognizable by the eye could be attributed to movement in the line of sight. Nor does this merely depend on the circumstance that the velocities are too small to produce such an effect. It must be remembered that the case of a star which dispenses light of perfect simplicity of composition is one that can hardly exist among the heavenly bodies, though it may be admitted that there is a certain approach to it in one or two remarkable cases. It is, however, much more usual for the light from a star to be of a highly composite type, includ. ing rays not only from all parts of the
visual spectrum, but also of rays belonging to the ultra-violet region, as well as others beyond the extreme red end. The effect of the retreat of a star, so far as its color is concerned, is that though the green is shifted a little towards the red, a bluish hue moves up to supply the place of the green, and as a similar effect takes place along the entire length of the spectrum, the total appearance is unaltered.
It is a fortunate circumstance that the lines in the spectrum afford a precise means of measuring the extent of the shift due to motion. If the movement of the star be towards us then the whole system of lines is shifted towards the blue end, whereas it moves towards the red end when the star is hastening from us. The amount of the shift is a measure of the speed of the movement. This is the consideration which brings the process within the compass of practical astronomy. We need not here discuss the appliances, optical, mechanical, and photographic, by which an unexpected degree of precision has been given to the measurements. It seems that in the skilful hands of Vogel and Keeler it is possible in favorable cases to obtain determinations of the velocities of objects in the line of sight with a degree of precision which leaves no greater margin for doubt than about five per cent. of the total amount. It is truly astounding that such a degree of accuracy should be attainable under conditions of such difficulty. It must also be remembered that the distance of the object is here immaterial, unless in so far as the reduction in the brilliancy of the star owing to its distance involves a difficulty in making the observations.
As the first illustration of the extraordinary results that are now being obtained by the application of the new process, I take the case of the celebrated variable Algol. This star is a well-known object to all star-gazers; it lies in the constellation of Perseus, and its vagaries attracted notice in early times. In ages when the stars were worshipped as divinities it was not unreasonable to suppose that a star whose light varied in any extraordinary manner should naturally be viewed with some degree of suspicion as contrasted with stars that dispense their beams with uniformity. It was doubtless a feeling of this kind which rendered Algol a star of questionable import to the ancient stu dents of the heavens. It was accordingly known as the Demon Star, for this is the equivalent of the name by which we now know it. As to the peculiarities of Algol
which have given it notoriety, these are very simply described. For two days and ten hours the star remains of uniform lustre, being ranked about the second magnitude; then a decline of brightness sets in, and the star in a few hours parts with three-fifths of its brightness. At the lowest point it remains for about twenty minutes, and then the brilliancy commences to increase, so that in a few hours more Algol has resumed its original character. The entire period required for the decline and the rise is about ten hours, and the whole cycle of the changes has been determined with much accuracy, and is at present two days, twenty hours, forty-eight minutes, fifty-two seconds. The length of the period seems to undergo some trifling fluctuations of a few seconds, but on the whole the permanence of the system is a striking part of the phenomenon. Considering that these changes can be observed without any telescope, it is not surprising that they have been known for centuries. Indeed, it fortunately happens that there is a smaller star near Algol which serves as a convenient standard of comparison. Under ordinary circumstances Algol is much brighter than its neighbor, but when it sinks to its lowest point it then happens that the two stars have almost equal lustre. It is only within the last year or two that the mystery of the variability of Algol has been at last revealed and the phenomenon of the Demon Star has received its true interpretation.
It had been suggested long ago that the loss of light might be due to an eclipse of the brilliant star by some dark companion; indeed, this theory seemed to hold the field, inasmuch as its only rival was one which supposed Algol to be a revolving body darker on one side than the other. This, however, was easily shown to be incompatible with the observed facts as to the manner in which the light waxed and waned in a single cycle of charge. It was, however, impossible to subject the eclipse theory to any decisive test until astronomers were provided with the means of measuring the velocity of approach or retreat along the line of sight. The exist ence of the dark companion was therefore almost destitute of support from observations until Vogel made his wonderful discovery.
Applying the improved spectrographic process to Algol, he determined on one night that Algol was retreating at a speed of twenty-six miles a second. This in itself is a striking fact, but of course the
distance equal to the diameter of the circle from the position which it has when moving most rapidly towards us. This is true, but the extent of the shift of place is far too small to be visible to our instruments. In fact, it can be shown that the size of the circle in which Algol revolves could hardly be larger than is that which the rim of a three-penny bit would appear to have if viewed from a situation five hundred miles away. It is one of the extraordinary characteristics of the spectroscopic method that it renders such an orbital movement perceptible.
The fact that Algol revolves in an orbit having been thus demonstrated, we can again call in the assistance of the laws of dynamics to carry us a step further. Such a movement is possible on one condition and only one, and that is that there is an attracting body in the neighborhood around which Algol revolves. Of course the student of mechanics knows that in such a case each of the bodies revolves around the other. The essential point to be noticed is that the spectroscopic evidence admits of no other interpretation save that there must be another mighty body in the immediate vicinity of Algol. We had already seen reason to believe in the pos
velocity is not an exceptionally large one | for celestial movements. We know of one star at least which moves half-a-dozen times as fast. When, however, Vogel came to repeat his observations he found that Algol was again moving with the same velocity, but this time the movement was towards the earth instead of from it. Here was indeed a singular circumstance demanding the careful examination which it speedily received. It appeared that the movements of Algol to and fro were strictly periodic; that is to say, for one day and ten hours the star is moving towards us, and then for a like time it moves from us, the maximum speed in each advance or retreat being that we have mentioned, namely, twenty-six miles a second. The interest awakened by this discovery culminates when it appears that this movement to and fro is directly associated in a remarkable manner with the variation of Algol's lustre. It is invariably found that every time the movement of retreat is completed, the star loses its brilliance, and regains it again at the commencement of the return movement. It is thus plain that the changes in brilliance of the star bear an important relation to the periodic movement. Here was an important step taken. For the next advance in this re-sibility of the presence of such a companmarkable investigation we have to depend, not on our instruments, but on the laws of mechanics. We have spoken of Algol as moving to and fro, but it is necessary to observe that it is impossible for a star to run along a straight line for a certain distance, stop, turn back, again retrace its movement, stop, and again return. Such movement is simply forbidden by the laws of motion. We can, however, easily ascertain that there is a type of motion possible for Algol which shall be compatible with the results of the spectroscopic research and also be permitted by the laws of motion. There is no objection to the supposition that Algol is moving in a path which is nearly, if not exactly, a circle. In this it would only be moving as does the moon, or the earth, or any of the other planets. It will be only necessary to suppose that the plane of the orbit of Algol is directed so that it passes near the earth. During the description of one semicircle Algol will be coming towards us, while during the other semicircle it will be going from us, and thus the observed facts of the movement are conciliated with the laws of motion. Of course, this involves a certain periodic shift in the position of Algol in the heavens. It must, for instance, when moving most rapidly from us be at a
ion for the Demon Star, simply from the fact of its variability. There cannot be any longer a doubt that the mystery has been solved. Algol must be attended by a companion star, which, if not absolutely as devoid of intrinsic light as the earth or the moon, is nevertheless dark relatively to Algol. Once in each period of revolution this obscure body intrudes between the earth and Algol, cutting off a portion of the direct light from the star and thus producing the well-known effect. Here we have such a remarkable concurrence between the facts of observation and the laws of dynamics that it is impossible to doubt the explanation they provide of the variability of this famous star.
There is, however, a further point in which the facts can be made to yield information of even a more striking character, inasmuch as it is unique of its kind. It is, of course, well known that stars in general show no appreciabie disks even in our best telescopes. In fact the better the instrument the smaller does the stellar point appear. This is, of course, due to the distance at which the stars are situated. It would be easy to show that if the sun were to be viewed by an observer placed on the nearest of the stars the apparent magnitude of its disk would be no
greater than an eagle would seem if soaring overhead at an altitude three times as great as the distance of New Zealand beneath our feet. Of course, no instrument whatever would render the dimensions of such an object perceptible, though such is the delicacy of the sense of perception of light that the eye may be able to detect the radiation from a self-luminous object which is itself too small to form an image of recognizable dimensions on the retina. The stars, of course, are suns often comparable with, and often far exceeding, our own sun in lustre and dimensions, but their distance is far too large to enable us to measure their diameters by the ordinary processes of the observatory. Even if the stars were brought towards the earth so that their distances were reduced to a tenth of what they are at this moment, it does not seem at all likely that any one of them would be even then seen clearly enough to enable us to perceive its diam eter. This statement becomes the more significant when it is borne in mind that there are several cases in which, though we are not able to measure the dimensions of stars, yet we are able to weigh them. If the period of revolution of a binary star has been determined, and if the distance of the pair from the sun is also known, we then have sufficient data to enable us to compare the mass of the binary system with that of the sun. It will therefore be understood that the first observations which declare the actual dimensions of a star merit the utmost attention. They constitute a distinct and important departure in our knowledge of the universe. It is surely a noteworthy epoch in the history of astronomy when, for the first time, we are able to apply the celestial callipers to gauge the diameter of a star. So far as surveying and measuring goes, this is the most significant piece of work in sidereal astronomy since the epoch, half a century ago, when the determination of a stellar distance first emerged from the mistiness of mere guess work and took a respectable position among the solved problems of astronomy. Nor is our gratification at the result of Vogel's striking work lessened by the fact of its unexpectedness. Who would have predicted some few years ago that the spectroscope was to be the instrument to which we should be indebted for the means of putting a measuring tape round the girth of a star? The process and the results are alike full of interest and are of happy augury for the future.
To explain exactly how it is possible to
deduce the diameter of Algol from the known facts of its movement would lead into some technicalities that need not be here mentioned. But the principle of the method is so plain that it would be unfitting to leave it without some attempt at exposition. We are first to notice that Algol, at the moment of its greatest eclipse, has lost about three-fifths of its light; it therefore follows that the dark satellite must have covered three-fifths of the bright surface. It is also to be noticed that the period of maximum obscuration is about twenty minutes, and that we know the velocity of the bright star. These facts, added to our knowledge that ten hours is required for the brilliancy to sink from and regain its original lustre, enable the sizes of the two globes to be found. There is only one element of uncertainty in the matter. We have assumed that the densities of the two bodies are the same. Of course, this may not be the case, and if it should prove to be unfounded, then some modification will have to be made in the numerical elements now provisionally assigned. There can, however, be little doubt that so far as the substantial features of the Algol system are concerned, the elements given by Vogel may be accepted. Let us endeavor to form a conception of what Algol and its companion are like. It is worth making the attempt, because, as we have already said, Algol is the first star among "yonder hundred mil lion spheres " of which the dimensions are approximately known. First we are to think of Algol itself. It is indeed a vast object, a glowing globe, a veritable sun, much larger than our own. of the sun would have to be increased by almost two hundred thousand miles to make it as great as that of Algol. But we may exhibit the relative proportions of the two bodies in a somewhat different manner. Imagine two globes, each as large as our sun; let those two be rolled into one, and we have a globe of the splendid proportions of Algol. But now for a singular circumstance which indicates the variety of types of sun which the heavens offer to our study. Though Algol is twice as big as the sun it is not twice as heavy. It is indeed an extraordinary circumstance that, notwithstanding the vast bulk of Algol, its weight is only about half that of the sun. The sun itself has a density about a fourth that of the earth, or but little more than the density of water, yet Algol has a density which is much less than that of water, in fact, this globe is apparently not much heavier than if it were made of cork. We