Part 6

Not unfrequently we hear the measurement of the sun's distance, and the various errors which astronomers have had to correct during the progress of their efforts to deal with the problem, referred to in terms which would imply that astronomy had some reason to be ashamed of labours which are in reality among the most noteworthy achievements of their science. Because, some twenty years ago, the estimate of 95 million miles, which had for half a century held its ground in our books of astronomy as the true distance of the sun, was replaced for a while by an estimate of about 91-1/2 million miles, which has in turn been displaced for an estimate of about 92-1/3 million miles, it has been said that astronomy has very little claim to be called the exact science. It is even supposed by some that astronomy is altogether at sea respecting the sun's distance--which, if the estimates of astronomers thus vary in the course of three-quarters of a century, may in reality, it is thought, be very different from any of the values hitherto assigned. Others suppose that possibly the sun's distance may vary, and that the diminution of three or four million miles in the estimates adopted by astronomers may correspond to an approach of the earth towards the sun by that amount, an approach which, if continued at the same rate, would, before many centuries, bring the earth upon the surface of the sun, to be consumed as fuel perhaps for the warming of the outer planets, Mars, Jupiter, and the rest.

All these imaginings are mistaken, however. The exactness of astronomy, as a science, does not depend on the measurement of the sun's distance or size, any more than the accuracy of a clock as a timekeeper depends on the exactness with which the hands of the clock are limited to certain definite lengths. The skill with which astronomy has dealt with this particular problem of celestial surveying has been great indeed; and the results, when considered with due reference to the conditions of the problem, are excellent: but in reality, if astronomers had failed utterly to form any ideas whatever as to the sun's distance, if for aught they knew the sun might be less than one million, or more than a million millions of miles from us, the exactness of astronomy as a science would be no whit impaired. And, in the second place, no doubts whatever need be entertained as to the general inference from astronomical observations that the sun's distance is between 92 and 93 millions of miles. All the measurements made during the last quarter of a century lie between 90 and 95 millions of miles, and by far the greater number of those made by the best methods, and under the most favourable conditions, lie between 91 and 94 millions of miles. All the very best cluster closely around a distance of 92-1/3 millions of miles. We are not for the moment, however, concerned with the question of the exact distance, but with the question whether astronomy has obtained satisfactory evidence that the sun's distance lies in the neighbourhood of the distances deduced by the various methods lately employed. Putting the matter as one of probabilities, as all scientific statements must be, it may be said as confidently that the sun's distance lies between 85 millions and 100 millions of miles as that the sun will rise to-morrow; and the probability that the sun's distance is less than 90 millions, or greater than 95 millions of miles, is so small that it may in effect be counted almost as nothing. Thirdly, the possibility that the earth may be drawing nearer to the sun by three or four millions of miles in a century may be dismissed entirely from consideration. For, one of the inevitable consequences of such a change of distance would be a change in the length of the year by about three weeks; and so far from the year diminishing by twenty days or so in length during a century, it has not diminished ten seconds in length during the last two thousand years. If there has been any change year by year in the earth's distance from the sun, it is one to be measured by yards rather than by miles. Astronomers would be well content if their 'probable error' in estimating the sun's distance could be measured by thousands of miles; so that any possible approach of the earth towards the sun would go but a very little way towards accounting for the discrepancies between the different estimates of the distance, even if these estimates grew always smaller as time passed, which is assuredly not the case.

But in truth, if we consider the nature of the task undertaken by astronomers in this case, we can only too readily understand that their measurements should differ somewhat widely from each other. Let us picture to ourselves for a moment the central sun, the earth, and the earth's path, not as they really are, for the mind refuses altogether to picture the dimensions even of the earth, which is but an atom compared with the sun, whose own proportions, in turn, mighty though they are, sink into utter insignificance compared with the enormous scale of the orbit in which the earth travels around him. Let us reduce the scale of the entire system to one 500-millionth part of its real value: even then we have a tolerably large orbit to imagine. We must picture to ourselves a fiery globe 3 yards in diameter to represent the sun, and the earth as a one-inch ball circling round that globe at a distance of about 325 yards, or about 350 paces. The diameter of the earth's orbit would on this scale, therefore, be somewhat more than a third of a mile. If we imagine the one-inch ball moving round the fiery globe once in a year, while turning on its axis once in a day, we find ourselves under a difficulty arising from the slowness of the resulting motions. We should have found ourselves under a difficulty arising from the rapidity of the actual motions if we had considered them instead. The only resource is to reduce our time-scale, in the same way that we have reduced our space-scale: but not in the same degree; for if we did we should have the one-inch ball circling round its orbit, a third of a mile in diameter, sixteen times in a second, and turning on its axis five thousand times in a second. Say, instead, that for convenience we suppose days reduced to seconds. Then we have to picture a one-inch globe circling once in rather more than six minutes about a globe of fire 3 yards in diameter, one-sixth of a mile from it, and turning on its axis once in a second. We must further picture the one-inch globe as inhabited by some 1,500 millions of creatures far too small to be seen with the most powerful microscope--in fact, so small that the tallest would be in height but about the seven-millionth of an inch--and we must imagine that a few of these creatures undertake the task of determining from their tiny home swiftly rotating as it rushes in its orbit around a large globe of fire, 325 yards from them--the number of yards really intervening between that globe and their home. If we rightly picture these conditions, which fairly represent those under which the astronomer has to determine the distance of the sun from the earth, we shall perceive that the wonder rather is that any idea of the sun's distance should be obtained at all, than that the estimates obtained should differ from each other, and that the best of them should err in measurable degree from the true distance.

Anything like a full explanation of the way in which transits of Venus across the sun's face are utilised in the solution of the problem of determining the sun's distance would be out of place in these pages. But perhaps the following illustration may serve sufficiently, yet simply, to indicate the qualities of the two leading methods of using a transit. Imagine a bird flying in a circle round a distant globe in such a way that, as seen from a certain window (a circular window suppose), the bird will seem to cross the face of the globe once in each circuit. Suppose that though the distance of the globe is not known, the window is known to be exactly half as far again from the globe as the bird's path is, and that the window is exactly a yard in diameter. Now in the first place, suppose two observers watch the bird, one (A) from the extreme right side, and the other (B) from the extreme left side of the window, the bird flying across from right to left. A sees the bird begin to cross the face of the globe before B does,--say they find that A sees this exactly one second before B does. But A's eye and B's being 3 feet apart, and the bird two-thirds as far from the globe as the window is, the line traversed by the bird in this interval is of course only 2 feet in length. The bird then flies 2 feet in a second (this is rather slow for a bird, but the principle of the explanation is not affected on that account). Say it is further observed that he completes a circuit in exactly ten minutes or six hundred seconds. Thus the entire length of a circuit is 1,200 feet,--whence by the well-known relation between the circumference and the diameter of a circle, it follows that the diameter of the bird's path is about 382 feet, and his distance from the centre of the globe 191 feet. So that the distance of the globe from the window, known to be half as great again, is about 286-1/2 feet.

If we regard the globe as representing the sun; the window of known size as representing our earth of known dimensions; the bird travelling round in a known period and at a distance whose proportion to the window's distance is known, as representing Venus travelling in a known period round the sun and at a distance bearing a known proportion to the earth's; this way of determining the distance of a remote globe illustrates what is called Delisle's method of determining the sun's distance. It requires that the two observers, A and B, should each make exact note of the moment when the bird seemed to begin to cross the disc of the remote globe; and in like manner Delisle's method requires that two observers, widely separated on the earth in a direction nearly parallel to that in which Venus is travelling, should make the most exact note of the moment when Venus begins to cross the sun's face. Also, as all I have said about the bird's beginning to cross the face of the distant globe would apply equally well if said about the end of his seeming passage across that disc, so two observers, widely separated on the earth, can determine the sun's distance by noting the end of her transit instead of the beginning, if they are suitably placed for the purpose. The window of our illustration remains unchanged during the bird's imagined flight, but as the face of the earth turned sunwards (which corresponds to that window) is all the time changing with the earth's rotation, a different pair of stations would have to be selected for observing the end of transit, than would be suitable for observing the beginning.

So much for the method called Delisle's. The other is in principle equally simple. In the imaginary experiment just described we supposed the two observers at the right and left sides of the circular window. Imagine them now to watch the bird from the top and bottom of the window, 3 feet apart. Suppose they note that the two tracks along which, as seen from these two points, the bird seems to cross the face of the distant globe, lie at a distance from each other equal to one-third of the globe's apparent diameter. Now, the bird being twice as far from the globe as from the window, the two tracks on the globe necessarily lie twice as far apart as the two points from which they are seen--or they lie 6 feet apart. The globe's diameter therefore is 18 feet. Knowing thus how large it is, and knowing also how large it looks, the observers know how far from them it lies. So, in the Halleyan method of determining the sun's distance by observing Venus in transit, astronomers are stationed far north and far south on the sunlit half of the earth, corresponding to the window of the imaginary experiment. Venus corresponds to the bird. The observers note along what track she travels across the sun's face. (That they partially determine this by noting how long she is in crossing, in no sense affects the principle of the method.) They thus learn that such and such a portion of the sun's diameter equals the distance separating them,--some six or seven thousand miles perhaps,--whence the sun's diameter is known. And as we know how large he looks, his distance from the earth is determined.

A peculiarity distinguishing this method from the former is that the observers must have a station whence the whole transit can be seen; for practically the place of Venus's track can only be ascertained satisfactorily by timing her passage across the sun's disc, so that the beginning and end must be observed and very carefully timed. This is to some degree a disadvantage; for during a transit lasting several hours the earth turns considerably on her axis, and the face turned sunwards at the beginning is thus very different from the face turned sunwards at the end of transit. It is often exceedingly difficult to find suitable northern and southern stations belonging to both these faces of the earth. On the other hand, the other method has its peculiar disadvantage. To apply it effectively, the observer must know the exact Greenwich time (or any other selected standard time) at his station,--or in other words he must know exactly how far east or west his station is from Greenwich (or some other standard observatory). For all the observations made by this method must be compared together by some absolute time standard. In the Halleyan method the duration of transit only is wanted, and this can be as readily determined by a clock showing local time (or indeed by a clock set going a few minutes before transit began and showing wrong time altogether, so only that it goes at the right rate) as by a clock showing Greenwich, Paris, or Washington time. The clock must not gain or lose in the interval. But a clock which would gain or lose appreciably in four or five hours, would be worthless to the astronomer; and any clock employed for scientific observation might safely be trusted for an interval of that length; whereas a clock which could be trusted to retain true time for several days, is not so readily to be obtained.

We need not consider here the origin of the misapprehension (under which our principal Government astronomer lay for some time), that the Delislean method was alone available during the transit of 1874, the Halleyan method, to use his words, 'failing totally.' The British stations were selected while this misapprehension remained as yet uncorrected. Fortunately the southern stations were suitable for both methods. The northern were not: for this reason, simply, that one set were so situated that night began soon after the beginning of transit, which alone could be observed; while the other set were so situated that night only came to an end a short time before the transit ended, so that the end of transit only could be observed. No doubt when the mistake just mentioned had been clearly recognised,--as it was early in 1873,--measures would have been taken to rectify its effect by occupying some suitable northern stations for observing the whole transit, if Great Britain had been the only nation taking part in the work. Fortunately, however, other nations might be trusted to occupy the northern region, which had so long been overlooked. England simply strengthened the southern observing corps: this could be done without any change by which the Government astronomers would have seemed to admit that 'some one had blundered.' Thus the matter was arranged--America, Russia, and Germany occupying a large number of stations admirably suited for applying the method which had been supposed to 'fail totally.' The British Official astronomers, on whom of course responsibility for adequately observing the transit (or at least for properly applying money granted by the nation for the purpose) alone rested, did in reality all, or nearly all, that was necessary in doubling some of the southern observing parties, and strengthening all of them; for unquestionably other nations occupied suitable northern stations in sufficiently strong force.

It is to be remembered, however, in estimating the probable value of the result which has been deduced from the British observations, that as yet only a portion of these observations has been effectively dealt with. The British observations of the beginning of transit at northern and southern stations give, when combined together, a value of the sun's distance. The British observations of the end of transit at other northern and southern stations give also, when combined together, a value of the sun's distance. And both sets combined give of course a mean value of the sun's distance, more likely on the whole to be correct than either value taken separately. But the British observations of the duration of transit as observed from southern stations do not of themselves give any means of determining the sun's distance. They must be combined with observations of the duration of transit as observed from northern stations; and no British party was stationed where such observations could be obtained. The value, then, of these particular British southern observations can only be educed when comparison is made between them and the northern observations by American, German, and Russian astronomers.

We must not, then, be disheartened if the results of the British operations _alone_ should not seem to be altogether satisfactory. For it may still happen that that portion of the British operations which only has value when combined with the work of other countries may be found to possess extreme value. We had good reason for doubting beforehand whether results of any great value could be obtained by Delisle's method. It was only because Halley's was supposed to fail totally that the Government astronomers ever thought of employing that method, which the experience of former transits had taught us to regard as of very little value.

It may be asked, however, how we are to form an opinion from the result of calculations based on the Delislean operations during the last transit, whether the method in satisfactory or not. If as yet the sun's distance is not exactly determined, a result differing from former results may be better than any of them, many will think; and therefore the method employed to obtain it may be more satisfactory than others. If, they may reason, we place reliance on a certain method to measure for us a certain unknown distance, how can we possibly tell from the distance so determined whether the method is trustworthy or not?

Perhaps the readiest way of removing this difficulty, and also of illustrating generally the principles on which the determination of the most probable mean value of many different estimates depends, is by considering a familiar experience of many, a case in which the point to be determined is the most probable time of day. Suppose that we are walking along a route where there are several clocks, the time shown by our own watch being, for whatever reason, open to question. We find, say, that as compared with our watch time, one clock is two minutes fast, the next three minutes fast, the next one minute slow, and so on, two or three perhaps being as much as six or seven minutes fast, and two or three being as much as three or four minutes slow as compared with the watch. We note, however, that these wider ranges of difference occur only in the case of clocks presumably inferior--cheap clocks in small shops, old clocks in buildings where manifestly the flight of time is not much noted, and so forth. Rejecting these from consideration, we find other clocks ranging from one minute or so before our watch time to four minutes or so after it. Before striking a rough average, however, we consider that some among these clocks are placed where it is on the whole better to be a minute or two before the time than a second late,--as, for instance, at banks, where there may be occasion to send out clerks so as to make sure of reaching certain places (Clearing-House, General Post-office, and so forth) within specified time limits. On the other hand, we note that others of these clocks are placed where it is better to be a minute or two after time than a second before it,--as at railway stations, post-offices, and so on, where it is essential that the public should be allowed time fully up to a specified hour, for some particular service. Taking fair account of such considerations, we might find that most probably the true time lay between half a minute _before_ and two minutes and a half _after_ our watch time. And thus we might infer that in reality the true time was one minute or so later than that shown by our watch. But if we were well acquainted with the characteristics of different clocks along our route, we might infer the time (nay, we might to all intents and purposes _know_ the time) far more accurately than this. We might, for instance, pass six or seven shop-windows where first-class specimens of horological work were shown,--in each window, perhaps, several excellent clocks, with compensated pendulums and other contrivances for securing perfect working. We might find at one of these shops all such clocks showing the same time within two or three seconds; at the next all such clocks also agreeing _inter se_ within two or three seconds, but perhaps their mean differing from the mean at the last shop of the kind by seven or eight seconds; and all six or seven shops, while showing similar agreement as regards the clocks severally displayed at each, agreeing also with each other so closely that ten or twelve seconds would cover the entire range between their several mean times. If this were observed, we should not hesitate to place entire reliance on these special sets of clocks; and we should feel certain that if we took the mean of all their means as the true time (perhaps slightly modifying this mean in order to give due weight to the known superiority of one or other of these clock-shops), we should not be in error by more than five or six seconds, while most probably we should have the time true within two or three seconds.