Unfortunately, there is an element of doubt in the inquiry, of which no amount of care on the part of our observers and mathematicians will enable them to get rid. I refer to the behaviour of Venus herself. It is to the peculiarity we are now to consider that the quasi-failure of the observations made in 1769 must be attributed. It is true that Mr. Stone, the first-assistant at the Greenwich Observatory, has managed to remove the greater part of the doubts which clouded the results of those observations. But not even his skill and patience can serve to remove the blot which a century of doubt has seemed to throw upon the most exact of the sciences. We shall now show how much of the blame of that unfortunate century of doubt is to be ascribed to Venus.
At a transit, astronomers confine their attention to one particular phase—the moment, namely, when Venus just seems to lie wholly within the outline of the sun’s disc. This at least was what Halley and Delisle both suggested as desirable. Unfortunately, Venus had not been consulted, and when the time of the transit came she declined to enter upon or leave the sun’s face in the manner suggested by the astronomers. Consider, for example, her conduct when entering on the sun’s face:—
At first, as the black disc of the planet gradually notched the edge of the sun’s disc, all seemed going on well. But when somewhat more than half of the planet was on the sun’s face, it began to be noticed that Venus was losing her rotundity of figure. She became gradually more and more pear-shaped, until at last she looked very much like a peg-top touching with its point the edge of the sun’s disc. Then suddenly—‘as by a lightning flash,’ said one observer—the top lost its peg, and then gradually Venus recovered her figure, and the transit proceeded without further change on her part until the time came for her to leave the sun’s face, when similar peculiarities took place in a reversed order.
Here was a serious difficulty indeed. For when was the moment of true contact? Was it when the peg-top figure seemed just to touch the edge of the sun? This seemed unlikely, because a moment after the planet was seen well removed from the sun’s edge. Was it when the rotund part of the planet belonged to a figure which would have touched the sun’s edge if the rotundity had been perfect elsewhere? This, again, seemed unlikely, because at this moment the black band connecting Venus and the sun was quite wide. And, besides, if this were the true moment of contact, what eye could be trusted to determine the occurrence of a relation so peculiar? Yet the interval between this phase and the final or peg-top phase lasted several seconds—as many as twenty-two in one instance in 1769—and the whole success of the observation depended on exactness within three or four seconds at the outside.
We know that Venus will act in precisely the same manner in 1874. If we had been induced to hope that improvements in our telescopes would diminish the peculiarity, the observations of the transit of Mercury, in November 1868, would have sufficed to destroy that hope, for even with the all but perfect instruments of the Greenwich Observatory, Mercury assumed the peg-top disguise in the most unpleasing manner.
It may be asked, then, What do astronomers propose to do in 1874 to prevent Venus from misleading them again as she did in 1769? Much has already been done towards this end. Mr. Stone undertook a series of careful researches to determine the law according to which Venus may be expected to behave, or to misbehave herself; and the result is, that he has been able to tell the observers exactly what they will have to look for, and exactly what it is most important that they should record. In 1769, observers recorded their observations in such doubtful terms, owing to their ignorance of the real significance of the peculiarities they witnessed, that the mathematicians who had to make use of those observations were misled. Hinc illæ lacrymæ. Hence it is that an undeserved reproach has fallen upon the ‘exact science.’
The amount of the error resulting from the misinterpretation of the observations made in 1769 was, however, very small indeed, when its true character is considered. It is, indeed, easy to make the error seem enormous. The sun’s distance came out some four millions of miles too large, and that seems no trifling error. Then, again, the resulting estimate of the distance of Neptune came out more than a hundred million miles too great; while even this enormous error was as nothing when compared with that which resulted when the distances of the fixed stars were considered.
But this is an altogether erroneous mode of estimating the effect of the error. It would be as absurd to count up the number of hairs’ breadth by which the geographer’s estimates of the length and breadth of England may be in error. In all such matters it is relative and not absolute error we have to consider. A microscopist would have made a bad mistake who should over-estimate the length of a fly’s proboscis by a single hair’s breadth; but the astronomer had made a wonderfully successful measurement of the sun’s distance who deduced it within three or four millions of miles of the true value. For it is readily calculable that the error in the estimated relative bearing of the sun as seen from opposite sides of the earth corresponds to the angle which a hair’s breadth subtends when seen from a distance of 125 feet.
The error was first detected when other modes of determining the sun’s distance were applied by the skilful astronomers and physicists of our own day. We have no space to describe as fully as they deserve the ingenious processes by which the great problem has been attacked without aid from Venus. Indeed, we can but barely mention the principles on which those methods depend. But to the reader who takes interest in astronomy, we can recommend no subject as better worth studying than the masterly researches of Foucault, Leverrier, and Hansen upon the problem of the sun’s distance.
The problem has been attacked in four several ways. First, the tremendous velocity of light has been measured by an ingenious arrangement of revolving mirrors; the result combined with the known time occupied by light in travelling across the earth’s orbit immediately gives the sun’s distance. Secondly, a certain irregularity in the moon’s motion, due to the fact that she is most disturbed by the sun when traversing that half of her path which is nearest to him, was pressed into the service with similar results. Thirdly, an irregularity in the earth’s motion, due to the fact that she circles around the common centre of gravity of her own mass and the moon’s, was made a means of attacking the problem. Lastly, Mars, a planet which, as we have already mentioned, approaches us almost as nearly as Venus, was found an efficient ally.