46 FIGURE OF THE EARTH. SECT. VI. 



should be less than the mean density of the earth, otherwise the 

 continents would be perpetually liable to inundations from storms 

 and other causes. On the whole, it appears from theory, that a 

 horizontal line passing round the earth through both poles must 

 be nearly an ellipse, having its major axis in the plane of the 

 equator, and its minor axis coincident with the axis of the earth's 

 rotation (N. 122). It is easy to show, in a spheroid whose strata 

 are elliptical, that the increase in the length of the radii (N. 123), 

 the decrease of gravitation, and the increase in the lengtn of the 

 arcs of the meridian, corresponding to angles of one degree, from 

 the poles to the equator, are all proportional to the square of the 

 cosine of the latitude (N. 124). These quantities are so con- 

 nected with the ellipticity of the spheroid, that the total increase 

 in the length of the radii is equal to the compression or flattening, 

 and the total diminution in the length of the arcs is equal to the 

 compression, multiplied by three times the length of an arc of 

 one degree at the equator. Hence, by measuring the meridian 

 curvature of the earth, the compression, and consequently its 

 figure, become known. This, indeed, is assuming the earth to 

 be an ellipsoid of revolution ; but the actual measurement of the 

 globe will show how far it corresponds with that solid in figure 

 and constitution. 



The courses of the great rivers, which are in general navigable 

 to a considerable extent, prove that the curvature of the land 

 differs but little from that of the ocean ; and, as the heights of 

 the mountains and continents are inconsiderable when compared 

 with the magnitude of the earth, its figure is understood to be 

 determined by a surface at every point perpendicular to the 

 direction of gravitation, or of the plumb-line, and is the same 

 which the sea would have if it were continued all round the 

 earth beneath the continents. Such is the figure that has been 

 measured in the following manner : 



A terrestrial meridian is a line passing through both poles, all 

 the points of which have their noon contemporaneously. Were 

 the lengths and curvatures of different meridians known, the 

 figure of the earth might be determined. But the length of one 

 degree is sufficient to give the figure of the earth, if it be mea- 

 sured on different meridians, and in a variety of latitudes. For, 

 if the earth were a sphere, all degrees would be of the same 

 length ; but, if not, the lengths of the degrees would be greater, 



