Both these methods have been successfully applied to the problem of determining the sun’s distance, and both have recently been applied afresh under circumstances affording exceptionally good prospects of success, though as yet the results are not known.
It is, however, when we leave the direct surveying method to which both the observations of Venus in transit and Mars in opposition belong (in all their varieties), that the most remarkable, and, one may say, unexpected methods of determining the sun’s distance present themselves. Were not my subject a wide one, I would willingly descant at length on the marvellous ingenuity with which astronomers have availed themselves of every point of vantage whence they might measure the solar system. But, as matters actually stand, I must be content to sketch these other methods very roughly, only indicating their characteristic features.
One of them is in some sense related to the method by actual survey, only it takes advantage, not of the earth’s dimensions, but of the dimensions of her orbit round the common centre of gravity of herself and the moon. This orbit has a diameter of about six thousand miles; and as the earth travels round it, speeding swiftly onwards all the time in her path round the sun, the effect is the same as though the sun, in his apparent circuit round the earth, were constantly circling once in a lunar month around a small subordinate orbit of precisely the same size and shape as that small orbit in which the earth circuits round the moon’s centre of gravity. He appears then sometimes displaced about 3000 miles on one side, sometimes about 3000 miles on the other side of the place which he would have if our earth were not thus perturbed by the moon. But astronomers can note each day where he is, and thus learn by how much he seems displaced from his mean position. Knowing that his greatest displacement corresponds to so many miles exactly, and noting what it seems to be, they learn, in fact, how large a span of so many miles (about 3000) looks at the sun’s distance. Thus they learn the sun’s distance precisely as a rifleman learns the distance of a line of soldiers when he has ascertained their apparent size—for only at a certain distance can an object of known size have a certain apparent size.