Page:Popular Astronomy - Airy - 1881.djvu/170

156 14, and therefore it will be 18,000 miles, exactly the same as in Figure 43. Thus the interval between the two lines of the apparent path of Venus is the same, whether we suppose the earth's distance from the sun to be one hundred millions of miles, or fifty millions of miles.

But there is this cause of difference in their effects, that on one of these suppositions the whole diameter of the sun is one million of miles, but on the other it is only half-a-million of miles. Thus, as taken in absolute measures of miles, the parallel lines CD, EF, are just as far apart as the parallel lines C'D', E'F'; but they are drawn across a circle whose diameter in one case is double what it is in the other. But, as viewed from the earth, the apparent diameter of the sun is the same on the two suppositions, but the lines CD, EF, (if we could see them painted on the sun), would appear nearer together, on the supposition of Figure 43, than on that of Figure 44. Now, inasmuch as in the two Figures we make no difference of supposition as to the position of Venus as viewed from the earth's centre, the lines will cross the sun's disc in the same general position in both figures; and, therefore, they will meet the edge of the sun's disc at nearly the same angle ; and, therefore, as the interval between them is the same, the difference of length in miles between CD and EF is the same as the difference of length between C'D' and E'F'. But as the lines CD and EF are about double the length of C'D' and E'F', the proportion of the difference of lengths