meridian of Greenwich to its present position, has passed the point where it has its greatest distance from the Chinese empire, and consequently the oscillation of the needle (by the, reverse of what was inferred for the case of London) would be slowest during the centuries occupied by this passage. In Jamaica and Australia the neighbouring magnetic pole lies nearly due north and due south respectively, and has lately passed the meridian of those places, so that here, as in England in the middle of the seventeenth century, the needle has for many years had a small declination.

287

THE STAR-DEPTHS.

DURING the last two years it chances that I have many times given lectures on the stars, and, accordingly, it will not be wondered at that many suggestive questions have been addressed to me by thoughtful persons to whom the wonderful teachings of modern astronomy respecting the stardepths have been submitted. In particular-and this is one circumstance in which, as I conceive, the lecturer has an advantage over the author—I have had an opportunity of ascertaining the difficulties which have occurred to those who have heard the narrative of what astronomy has done. I propose in the present essay to consider some of the points which have thus been brought under my notice, feeling assured that a large proportion of those who study astronomical subjects are likely to find an interest in the matters I am now to touch upon.

I may remark, in the first instance, that misapprehensions are somewhat widely prevalent as to the knowledge which astronomers have obtained respecting the distances and real magnitudes of the fixed stars. The announcement is received with astonishment, and some degree of disappointment, that astronomers have only estimated the distance of a single star in the whole heavens in a manner which can be regarded as satisfactory; while even that estimate is probably many hundreds of millions of miles in error. Many appear to imagine that it is in a sense discreditable to astronomy that no greater success has been achieved in this direction; others suppose that the statement has its

origin in doubts or objections peculiar to myself; while some recall the fact that in books of astronomy the estimated distances of ten or twelve stars are indicated, together with a variety of elaborate calculations as to the average distances of stars of the various orders of apparent brightness, or (as it is technically termed) magnitude.

It is well that it should be generally known how powerless astronomy at present is in this matter of the determination of stellar distances. The astronomer can deal only with the actual conditions of a problem of this sort; he cannot select the conditions for himself. The surveyor of a difficult region of the earth can determine heights and distances by a variety of methods; he can undertake and execute a variety of more or less difficult operations; and where one process of survey does not satisfy him, he can try another, or several others. But the astronomer who wishes to determine the distance of a star, has one means only for obtaining that change of standpoint on which all such measurements must, in the long run, depend. And that means does not depend upon himself. It is not he who is to undertake the journey by which the change of standpoint is to be obtained, but the earth carrying him and his telescope along with her in her yearly orbital motion round the sun, shifts his standpoint for him. The case is even less under his control than the problem of determining the sun's distance, now so engrossing the attention of astronomers; for there the astronomer may vary his standpoint more or less, according as he is more or less in earnest in seeking to inaster his difficulties. He may, on the one hand, seek the bleakest and most dismal northerly regions, as the Russians propose to do during the coming transit of Venus; or, on the other, he may be careless in pushing his way as far southwards as possible, even as (it is to be feared) this country is likely to be careless, on that important occasion. But the measurer of a star's distance has no choice in the matter. He must be content to wait until the earth has carried him from one side of her path to the other, a span

wide enough, it should seem, to measure almost infinite distances, since the base line thus given is more than 180 millions of miles in length. But it is all too narrow for measuring star-distances, and if the astronomer could choose he would require the orbital sweep of Saturn, Uranus, and more distant Neptune, to give him a really effective hold on the stupendous problem. Even then, however, he would be left powerless in the presence of all but a few hundred stars; beyond these, the millions on millions known to astronomers would lie at distances which would laugh to scorn all means of measurement. In fine, to measure effectually the distances of the stars, the astronomer should be able to voyage with an interstellar comet, and live millions of years for every hour of his present life.

To show how feeble is the actual hold of the astronomer on this great problem, let us consider what the base-line of 180 millions of miles really represents, in the case even of the nearest of all the fixed stars. To the observer, when stationed at one end of this vast line, a star is seen necessarily in a different direction than to the same observer when (six months later) he is at the other end of that line. But the two direction-lines are so nearly parallel, even in the case of the nearest star, that if two lines were drawn as nearly parallel from a point, they would have to be extended to a distance of nearly two miles from that point before they would be a single inch apart. Or the matter may be presented in this way. We know how little the minute hand of a watch or clock changes in direction in a single second of time. Now the direction of a line from the nearest star in the heavens to the earth shifts during the half-year by less than the change of direction of the minute-hand of a watch or clock in the two-hundredth part of a second. This is as much as to say that if that star be regarded as the centre of a monstrous clock-face, and a line from the star to the earth as the minute-hand, then the extremity of that hand would move over 180 millions of miles in the two-hundredth part of a second of time.

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Now if astronomers had merely to recognise this change of direction, the task must be a sufficiently arduous one. In fact, two centuries passed after the first use of telescopic measuring-means before the slightest signs of displacement could be recognised in any star in the heavens. The earth

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during all these years was circling on her orbit with its vast span of 180 millions of miles and yet the star-sphere within which this motion was taking place remained seemingly as unchanged as though the earth had been absolutely at rest-and this although the most powerful instrumental means invented by man were applied to detect even the minutest sign of motion. But, as a matter of fact, the astronomer has to accomplish a much more difficult task before the distance of a star can be ascertained. All that the mere recognition of displacement would imply would be that the star does not lie at a distance so vast as to reduce to absolute nothingness the effects of the earth's orbital motion. The displacement must not be recognised only, but measured, before a star's distance can be estimated. Thus I have spoken of the change of direction as nearly equal to the two-hundredth part of the motion of the minute-hand of a clock or watch in a single second of time. It is such a fact as this that has to be ascertained. The astronomer must be able to say that the change is, let us say, greater than the two-hundred-andtenth part and less than the two-hundredth part of such motion of a minute-hand, or to make some other definite statement indicating the limits of error in the result of his observations. Then, and then only, the star's distance can be said to be estimated; though even then, be it noticed, the amount of error in the determination of a star's distance remains necessarily enormous. In the imagined case the error is probably within the twentieth part of the star's actual distance, but the twentieth part of the distance of the nearest star is more than ten thousand times the sun's distance.

After this it will not be regarded as very surprising that I reiterate the statement made above to the effect that the