h, whose distance from a or b, is about 3950 miles.
What is to be inferred from this? We have said that the estimation of the semi-diameter of the earth, supposing it to be a sphere, would depend on the distance you have to go, in order that the direction of the vertical might be altered by one degree. We have to go further in the northern measure than in the equatorial measure. It would seem at first sight, as a consequence, that the earth was not turnip-shaped, but egg-shaped; and this was maintained by many respectable people at the time. On consideration, it appeared that this was not a correct inference. And the reasons were these: when we assume that the earth is spheroidal, not spherical, then, inasmuch as we mean by the direction of the vertical "the direction of a line perpendicular to the surface of the water," the direction of the vertical will not go to the earth's centre at all. It is necessary to consider something different, and that is, that the measures which we have obtained, give us information of the curvature of different points of the earth. They tell us that at AB the curvature is little, but that at a b the curvature is very sharp. Altogether, when properly considered, they lead us to the inference that the form of the earth is something like the oval in Figure 21; that it is flatter at the Poles, and sharper in its curvature at the Equator. The rule which theory gave was, that the earth would be spheroidal; that is, that its form would be that which is produced by the curve called the ellipse,[1] Figure 2la, revolving round its shorter axis BB′. Adopting then the
- ↑ The nature of this curve is more fully explained in the next Lecture.
