[6] It may be necessary, perhaps, to explain to some why the western side is on the right in the little maps illustrating this paper, and not, as usual with maps, on the left. We are supposed to look down towards the earth in the case of a terrestrial map, and to look up from the earth in the case of a celestial map, and naturally right and left for the former attitude become respectively left and right for the latter.
[RESULTS OF THE BRITISH TRANSIT EXPEDITIONS.]
Another noteworthy attempt has been made to estimate the distance which separates our earth from the mighty central orb round which she travels with her fellow-worlds the planets. In other words, the solar system itself has been remeasured; for the measurement of any part of the system is in fact the measurement of the entire system, the proportions of which, as distinguished from its actual dimensions, have long been accurately known.
I propose briefly to describe the results which have been obtained (after some three years of careful examination) from the observations made by the British parties sent north, south, east, and west to observe the transit of Venus on December 9, 1874; and then to consider how these results compare with those which had before been obtained. First, however, it may be well to remind the reader of the unfavourable conditions under which the task of measuring our distance from the remote sun must of necessity be attacked.
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 91½ 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 286½ feet.