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.