SCT. VI. FORM OF THE EARTH. 45 



the poles dry. Beside, it is well known, that the con- 

 tinents at the equator are more elevated than they are 

 in higher latitudes. It is also necessary for the equili- 

 brium of the ocean, that its density 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 the- 

 ory, 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. 121). It is easy to show, in a spheroid whose 

 strata are elliptical, that the increase in the length of 

 the radii (N. 122), the decrease of gravitation, and the 

 increase in the length of the arcs of the meridian, cor- 

 responding to angles of one degree, from the poles to 

 the equator, are all proportional to the square of the co- 

 sine of the latitude (N. 123). These quantities are so 

 connected 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, multi- 

 plied 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 conse- 

 quently its figure, become known. This, indeed, is as- 

 suming 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 curva- 

 ture 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 contem- 



