Page:Popular Astronomy - Airy - 1881.djvu/171

Rh to the whole length in Figure 43 is only half what it is in Figure 44. Thus, suppose the position of the lines to be such that CD is longer than EF by one-thirtieth part: then C'D' is longer than E'F' by one-fifteenth part. And if the earth's distance from the sun is one hundred-millions of miles, and if Venus be seen to cross the sun's disc in the direction which we have supposed, the difference of the times occupied by the passage of Venus over the sun, as viewed from A and from B, will be only one-thirtieth part of the whole time; but if the distance of the earth from the sun is only fifty millions of miles, the difference of times will be one-fifteenth part of the whole time.

Now we have come to something that can be compared immediately with observation. We can observe at the two stations A and B, the whole time that is occupied in the passage of Venus across the sun's face. And having ascertained the whole time of transit at each of these stations, we can take the difference between the two times, and find what proportion it bears to the whole time. If, (supposing the lines to cross the sun's disc in the direction supposed above,) the difference is found to be one-thirtieth of the whole, then we conclude that the sun's distance is one hundred millions of miles; if it is one-fifteenth of the whole, we conclude that the distance is fifty millions of miles; and so from any result of observation as to the difference of times occupied in the passage, we draw an inference as to the sun's distance.

It is now proper to remark that the observations cannot be made strictly as we have supposed, at two stations, A and B, which preserve the same relative position during the whole transit, because the earth is during all this time revolving on its axis. And it will be worth while to remark how advantage may