the same instrument of which we have spoken so frequently, in reference to the determination of the elements of the earth's figure. By the use of the Zenith Sector, the difference of the directions of gravity at these two stations was found, exactly in the same manner as the difference of the directions of gravity in two stations of a meridional survey, Figure 18.
The direction of gravity at each station, you will observe, is the result of the gravity of the whole earth (as considered for a moment independently of the mountain), combined with the attraction of the mountain. And this is the consequence: supposing that at N, if there were no mountain, the direction of the gravity would be NE; then introducing the supposition of the mountain, the attraction of the mountain would pull the plumb-line sideways towards the centre of the mountain, and the direction of the gravity would be Ne. And in like manner, supposing that if there were no mountain, the direction of the gravity at S would be SF; then, introducing the mountain, the effect of its attraction is to pull the plumb-line towards the centre of the mountain, and the direction of gravity would be Sf.
Observe, then, the effect of the mountain; at N the direction of gravity is Ne instead of NE, and at S, the direction of gravity is Sf instead of SF; that is to say, the two directions which are taken by the plumb-line of the Zenith Sector, make a greater angle than they would if the mountain were not there.
Now, then, we come to the thing which we have to try. We know the general dimensions of the earth; we know what the inclination of the plumb-line at N and S would be if there were no mountain in the case. We know that this is a general rule:
