study. In fact, it may be doubted

astronomers are

ing than that of the sun's motion through the celestial spaces. Followed by his train of attendantsplanets, asteroids, comets, and meteoric systems-he is ever rushing onwards through space with a velocity of which the human imagination is unable to form adequate conceptions. Whether the vast orbit which he must in reality be pursuing is of any regular figure, or rather consists of myriads of interlacing loops; whether in the former case there is some vast central orb around which his motions are directed, or whether the orbit is simply regulated by the gravity of the scheme of fixed stars, without any preponderant mass at the centre; whether, in fine, the sun is an attendant star, or is himself one of the regulating orbs of the sidereal scheme on all these points astronomy is as yet silent. Speculation has, indeed, suggested many interesting surmises, grounded on more or less probable evidence; but as yet no theory founded on an exact examination of the results of systematic observation has been presented to the world. Nor is it likely that astronomers will quickly be able to systematise the motions of the stars. The Copernicus of the sidereal system is not to be expected for many generations, perhaps not for thousands of years. Nay, if it befitted us to doubt after the achievements of our Newtons and our Herschels, we might fear that the great problem of co-ordinating the motions of the fixed stars into a single scheme, is one which it will never be given to the human race to triumph over.

What has already been done, however, is well worthy of careful

problem which has been solved by our astronomers has been thoroughly appreciated. I wish to exhibit the nature of the results which have been obtained, and then to discuss some peculiarities which, without in any sense throwing doubt over the justice of the conclusions to which astronomers have arrived, yet serve (unless I mistake) to prove in the clearest manner that the assumptions on which the problem of the sun's motion has been solved require modification. The work of our astronomers resembles, in a sense, the famous work of Adams and Leverrier, when they spread forth the subtle webs of their analyses to capture the unseen planet whose influence had so long been felt upon the outskirts of the solar system. Just as their assumptions respecting the mass and distance of the great unseen were incorrect, yet led to a correct result, so the assumptions on which our astronomers have founded their determination of the sun's motion in space may be now shown, by means of that very determination, to have been wholly incorrect.

Let us first rightly grasp the nature of the problem which the elder Herschel set himself.

He argued that if our sun is moving through space, the effects of his motion must generally be on this wise: The stars in those regions of space towards which the sun is moving must seem to open out,' precisely as the trees of a forest seem to open out' as we approach them. The stars in the opposite region must seem to close in to a corresponding extent. But the most marked effect must appear in the stars which are on or near

the celestial circle midway between these two regions. All such stars must be affected by a 'backward drift,' corresponding precisely in degree to the rate of the sun's advance.

It will be observed that hitherto the question of the stars' distance has not been introduced. But it is clear that this question must affect to a most important extent the effects of any definite solar motion. For anything that Herschel knew when he began his inquiry, the stars might be so far off that the sun's motion, even though vast in itself, might produce absolutely no appreciable effect upon the position of the stars. Then again, supposing the first-magnitude stars, presumably the nearest, were affected in a certain degree by the sun's motion, then the second magnitude stars would be less affected, the third still less, and so on. Again, the stars looked upon as being suns, like our own central luminary, might be expected to have their own motions through space, and it was uncertain before inquiry whether these motions might not be quite sufficient to mask the effects of the sun's motion; or at any rate the balance of effects might be so small as to render it very doubtful whether accident or a real motion of the sun had been the cause of the slight apparent preponderance of motions in some definite direction.

I mention all these circumstances that the reader may be able to appreciate the boldness of Herschel's genius in venturing to search, amidst so many conflicting evidences as he might expect to meet with, for that small residuum of motion on which he hoped to found the doctrine of the sun's motion through the side

real spaces.

But yet more startling is it to find how slender was the stock of materials which Herschel had at his command. When we know that modern astronomers have examined

VOL. LXXX.-NO. CCCCLXXVII.

the motions of hundreds of stars in dealing with the same problem, it is amazing to think that Herschel should have hoped to deduce from the motions of only seven stars a result of so much importance as that he was in search of. It is yet more amazing to find that he achieved a perfect success. He announced in 1783 that the sun is advancing towards a point in the constellation Hercules. Even at the present day astronomers have not been able to say more, so far at least as the direction of the sun's motion is concerned. Every subsequent inquiry has exhibited the constellation Hercules, or its immediate neighbourhood, as including the point which astronomers call the apex of the sun's motion.'

But this result-I mean the successful determination of the direction of the sun's motion from the consideration of only seven stars—is not only amazing; it is highly significant. Let us at once accept it in its full importance. It proves, not merely that the sun has such a motion as Herschel had suspected, but that the sun's motion must bear a very considerable proportion to the motions of the other stars in space. Had the sun been one of those stars which move very slowly compared with their fellow-orbs, there can be no doubt whatever that so rough and inexact a mode of inquiry could have revealed nothing respecting the direction in which the sun is travelling. It is only by looking upon the sun's motion as far from being the least rapid of the stellar journeyings, that we can understand or appreciate Herschel's

success.

We shall presently see that this fact is of the greatest significance in reference to the results which have rewarded later researches.

Herschel's conclusions were not left unnoticed or unchallenged. So small, however, has been the number of those who have disputed the

A A

justice of Herschel's views, and so thorough has been the vindication which those views have received at the hands of the ablest astronomers, that we need not be at the pains to discuss the arguments by which a few mathematicians (I believe only two) have attempted to impugn the accuracy of Herschel's conclusions. At an early stage in the inquiry it was felt that the relative distances of the stars must have an important bearing on the determination of the actual nature of the sun's proper motion. The general drift of the stars in a certain direction may be very significant evidence of the sun's motion in the contrary direction. But if we wish to estimate the actual velocity with which the sun is travelling, we must have clear conceptions on two very important points. We must determine the relation between the distances of the brighter and fainter stars, ranging them in definite gradations of magnitude; and, moreover, we must know the actual distance of several stars.

On the last point astronomers have obtained satisfactory results. There are, indeed, very few stars whose distances are known; but several of these distances have been ascertained in a manner there is no disputing. Over and over again, for instance, has the distance of the leading brilliant in the Centaur (a famous double star) been determined; and the results have always been closely accordant. Then there is the small star (No. 61) in the Swan, whose rapid apparent motions long since suggested to astronomers the idea of its proximity to our system. This star's distance has been measured by Bessel and Peters (by independent processes), and with satisfactorily accordant results. And several other stars might be named respecting whose distances very little doubt remains in the minds of our astronomers.

But on the other point there has been a considerable variety of opinion. All agree that the fainter stars must be assumed to lie much farther away than Sirius, or Capella, or Arcturus, or Vega. But whether the relative distance is satisfactorily indicated by the diffe rence of brilliancy, or whether it would not be better, so far as the particular problem we are dealing with is concerned, to take the relative apparent motions of the stars as affording the best criterion of their relative distances, is an important point on which astronomers have long been at issue. It is a singular circumstance that they have never (to the best of my knowledge) thought of instituting a direct comparison between the evidence of the two criteria of distance. All that has been done is this. One class of astronomers have arranged the stars into sets according to their apparent brilliancy, and, assigning a suitable mean distance to the stars of each set, have determined the sun's motion on the strength of the evidence thus deduced. Another class of astronomers have arranged the stars into sets according to the magnitude of their apparent motions, and have determined the sun's motion accordingly. Now it has happened that the results of both processes have been coincident.

Hence it has been assumed to be a matter of indifference what view is adopted, or rather it has been supposed that the relative motion of the stars must correspond pretty closely with their relative brilliancy; otherwise there would be (it has been thought) no such accordance as has resulted from the use of either indication to deter mine the sun's motion through space. I speak under correction, but I believe that no one has ever yet expressed any doubts on this point. As I have said, it does not seem to have occurred to any one to inquire whether the proper motions

of the stars corresponded with the distances which astronomers had deduced from the brightness of the stars of different magnitudes. To illustrate the nature of the case, I may compare it to a trial carried on simultaneously in two different courts and leading to the same decision. In such a case (the trial being carried on with closed doora) no one would be led to suspect that the evidence given in one court might possibly be wholly different from that given in the other, or even that there might be absolute incongruity between the two lines of evidence. Yet this might well be the case; and the decision, however just in itself, might thus be founded on false evidence in one or other, or even in both courts. I think I shall be able to show that the case certainly corresponds with this view in regard to the determination of the sun's motion through space.

Theastronomers who have adopted the rule of estimating star-distances by brilliancy have assigned the following relative distances to stars of the first seven magnitudes :

Now it is perfectly clear that the greater the distance of an object in motion, the more slowly the object will appear to move. Just as the apparent dimensions of a man, for instance, are diminished by distance, so also, if he is walking, will the apparent length of his steps be diminished.

This being understood, it is clear that if we take the average proper motions of the stars of different magnitudes, we ought to find a close correspondence between the result and the above list of distances, if the brilliancy of a star

Clearly this result is unsatis. factory. It is not merely that it differs altogether from the former, but that it is absurd in itself. We cannot suppose stars of the second magnitude to be farther away than stars of the third, fourth, fifth, or sixth. Before proceeding, we must master this difficulty, if possible. I think we can trace it to its source. The first orders of stars contain but few representatives, compared with the orders of the less brilliant stars. Thus the above list deals with only nine stars of the first magnitude, and only fifty-five of the second. It is clear that numbers such as these are insufficient for our purpose, when once it is found that the old law of distance has to be aban

is very easy to recognise the proper mode of treating the difficulty. The question really is whether the faint stars are proportionately far off. Let us then divide the stars into two classes, the first including all those which are visible in moderately bright moonlight-that is, stars of the first three magnitudes; the second including the remaining stars,1 visible to the naked eye on a clear night when there is no moon. Such a test as this must result in exhibiting the relative average proximity of the brighter stars, if brightness is indeed any criterion of proximity.

Here is the result:

So that, judged in this way, the stars of the smaller magnitudes must be looked upon as actually nearer to us (though very slightly) than the brilliant orbs which form the most striking of our constellations.

One cannot mistake the meaning of this result. The near approach to equality observed between the numbers may be partly accidental. Had our first set included one more magnitude, indeed, there would have resulted no such close approach to equality; but the yet more striking result of a markedly greater proper motion in the fainter set would have been noticed. If our first set had included only the first two magnitudes, there would again have been no exact equality, while the preponderance of proper motion would have been (though but slightly) on the side of the brighter stars. About these niceties we need not concern ourselves. The great point is that it is esta

blished, on evidence which seems wholly irresistible, that the bril liancy of the stars is no satisfactory criterion of proximity.

This inquiry into the significance of stellar brilliancy may seem a digression from the subject of the sun's motion in space. But it will presently be seen that the investigation is an absolutely essential preliminary to our inquiry into the recent work of astronomers on the subject of the sun's motion.

I have mentioned that two methods had been made use of in determining the point in space towards which the sun is moving. But both these methods were applied to the stars' apparent motions on the celestial vault. Lately the Astronomer-Royal suggested a total change in the mode of treating the subject. He argued that the question should be looked at as having reference to the motions of the stars in space, not upon the surface of the imaginary celestial globe. And he showed, in his usual lucid and masterly manner, how the mathematical considerations involved in the change of view must be dealt with. He also calculated the formule for determining in this new way the nature of the sun's motion in space. These formulæ would, of course, be out of place in the pages of a popular magazine; nor would it be easy to present the new mode of treating the subject without introducing considerations scarcely less unsuited to these pages. The mathematical reader will find Mr. Airy's able dissertation on the subject in vol. xxiv. of the Memoirs of the Royal Astronomical Society. The non-mathematical reader may accept the opinion of our leading astronomical authorities