Page:Popular Astronomy - Airy - 1881.djvu/71

Rh hang in the direction CGF, and that at B in the direction c g f. The place of the star, however, which I observe, is unaltered. The telescope is to be pointed in the same direction, whether we use it at Shanklin or Balta: or the line CD is parallel to c d. Suppose, therefore, I have gone through the observations in the way I have described, by observing what part of the limb of the Zenith Sector is crossed by the plumb-line; I get different parts of the limb in the observations at these two points. When I am observing the star at Balta, the plumb-line crosses at g; when I am observing it at Shanklin Down, the plumb-line crosses at G. Thus we obtain the difference of the direction of the vertical at the two places.

Now, then, I have arrived at something which I can use for taking the dimensions of the earth. In the way that I have described I have the inclination between the line, which is perpendicular to the surface at A, Figure 20, and the line which is perpendicular to the surface at B. If I continue these two lines downwards until they meet at a great distance below, as at H, I shall get a centre from which I may make a sweep to describe the curvature of this part; or, in other words, a centre, about which I may describe a circle passing through A and B, and such, that its arc AB, shall be exactly as much bent as the line AB on the earth's surface. If the earth be spherical or round, it is plain that these lines come to the earth's centre, and the distance AH, which I have found is the semi-diameter of the earth.