40. THERE is a third effect, which the water has on the earth by changing its figure, that is taken notice of by our author; for the explaining of which we shall first prove, that bodies descend perpendicularly to the surface of the earth in all places. The manner of collecting this from observation, is as follows. The surfaces of all fluids rest parallel to that part of the surface of the sea, which is in the same place with them, to the figure of which, as has been particularly shewn, the figure of the whole earth is formed. For if any hollow vessel, open at the bottom, be immersed into the sea; it is evident, that the surface of the sea within the vessel will retain the same figure it had, before the vessel inclosed it; since its communication with the external water is not cut off by the vessel. But all the parts of the water being at rest, it is as clear, that if the bottom of the vessel were closed, the figure of the water could receive no change thereby, even though the vessel were raised out of the sea; any more than from the insensible alteration of the power of gravity, consequent upon the augmentation of the distance from the center. But now it is clear, that bodies descend in lines perpendicular to the surfaces of quiescent fluids; for if the power of gravity did not act perpendicularly to the surface of fluids, bodies which swim on them could not rest, as they are seen to do; because, if the power of gravity drew such bodies in a direction oblique to the surface whereon they lay, they would certainly be put in motion, and be carried to the side of the vessel, in which the fluid was contained, that way the action of gravity inclined.
41. HENCE it follows, that as we stand, our bodies are perpendicular to the surface of the earth. Therefore in going from north to south our bodies do not keep in a parallel direction. Now in all distances from the pole the same length gone on the earth will not make the same change in the position of our bodies, but the nearer we are to the poles, we must go greater length to cause the same variation herein. Let M I L K (in fig. 117) represent the figure of the earth, M, L the poles, I, K two opposite points in the middle between these poles. Let T V and P O be two arches, T V being most remote from the pole L; draw T W, V X, P Q, O R, each perpendicular to the surface of the earth, and let T W, V X meet in Y, and P Q, O R in S. Here it is evident, that in passing from V to T the position of a man’s body would be changed by the angle under T Y V, for at V he would stand in the line Y V continued upward, and at T in the line Y T; but in passing from O to P the position of his body would be changed by the angle under O S P. Now I say, if these two angles are equal the arch O P is longer than T V: for the figure M I L K being oblong, and I K longer than M L, the figure will be more incurvated toward I than toward L; so that the lines T W and V X will meet in Y before they are drawn out to so great a length as the lines P Q and O R must be continued to, before they will meet in S. Since therefore Y T and Y V are shorter than P S and S V, T V must be less than O P. If these angles under T Y V and O S P are each 1/90 part of the angle made by a perpendicular line, they are said each to contain one degree. And the unequal length of these arches O P and V T gives occasion to the assertion, that in passing from north to south the degrees on the earth’s surface are not of an equal length, but those near the pole longer than those toward the equator. For the length of the arch on the earth lying between the two perpendiculars, which make an angle of a degree with each other, is called the length of a degree on the earth’s surface.