the verticals to be 12 degrees, and therefore we should have to travel 69 miles to make the inclination of the plumb-lines one degree, and that is commonly expressed by saying a degree on the earth's surface is equal to 69 miles.
I then pointed out to you the principal lines which have been accurately measured. All these lead to the conclusion, that towards the Poles of the earth you have to travel 69½ miles in order to pass over the space where the direction of the vertical changes by one degree, but that near the equator you have to go only 68¾ miles, in order to pass over the space where the direction of the vertical changes one degree.
Now, I call your attention to the interpretation of this circumstance: it shows that the earth's dimension is greater in the direction of the equatoreal axis, as shown in Figure 21. It is necessary to consider that the direction of the vertical is not to the centre of the earth—it is perpendicular to the surface; and the intersection of the two verticals at H or h does not give the distance from the centre, and does not depend on the distance from the centre, but on the curvature at each place. And inasmuch as, when near the Pole, you have to travel the greater distance in order to go through the same change of the direction of the earth's surface, it proves this: that the earth is less curved at the Pole than near the equator, and that you come to a shape something like Figure 21. About AB the surface is comparatively flat; about ab the curvature is sharpened; and at the Cape of Good Hope, or about A′B′, it is flattened again. So that we come to the conclusion, so far as our measures go, that the form of the earth is somewhat turnip-shaped, or is what we call an oblate spheroid.
