52 ROTATION OF A FLUID MASS. [SECT. vi. 



compression or flattening would be less than in the case of 

 the homogeneous fluid. The compression is still less when 

 the mass is considered to be, as it actually is, a solid nucleus, 

 decreasing regularly in density from the centre to the surface, 

 and partially covered by the ocean, because the solid parts, 

 by their cohesion, nearly destroy that part of the centrifugal 

 force which gives the particles a tendency to accumulate at 

 the equator, though not altogether ; otherwise the sea, by the 

 superior mobility of its particles, would flow towards the 

 equator, and leave the poles dry. Besides, it is well known, 

 that the continents 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 theory, that a hori- 

 zontal 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 in- 

 crease in the length 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 

 (JST. 123). These quantities are so connected with the ellip- 

 ticity 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 com- 

 pression, 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. 



