Figure of the Earth. 143 



The investigations of Newton and Huygens into the laws that 

 regulate the action of central forces, furnish us with means, by 

 which the relation between the whole gravitating force of the 

 earth, and its diminution at the Equator, under the action of a 

 centrifugal force, may be determined : supposing the earth to be 

 a sphere, this ratio is that of 2S9 to 1 ; but in consequence of the 

 flattening of the earth at the poles and its increased diameter at 

 the Equator, of which we are about to speak, this relation is 

 c -hanged, and the centrifugal force bears a somewhat higher pro- 

 portion to that of gravitation. A great part of the surface of 

 the globe is covered with water, and many of the hypotheses of 

 geologists suppose that the earth was originally in a liquid state. 

 The figure of the earth, and the curvature of its surface, is that 

 which the surface of the great mass of water spontaneously as- 

 sumes ; and hence grew the belief that the shape of our globe 

 cannot be that of a perfect sphere ; for were the solid nucleus of 

 the earth perfectly spherical, the waters of the ocean must have 

 accumulated themselves, by virtue of the centrifugal force, in a 

 zone on each side of the Equator. 



In order that a mass of fluid acted upon by its own gravi- 

 tation, and the centrifugal force arising from its rotation 

 around an axis, should be at rest, and have no tendency to 

 move towards either its Poles, or its Equator, it is necessary, 

 that the pressure of all the columns of fluids, extending from 

 the centre to the surface, should be equal to each other. These 

 several columns, if enclosed in tubes, communicating with each 

 other at the centre, would therefore be in equilibrio; but a 

 column beneath the Equator, being formed of matter whose 

 gravity is diminished by the centrifugal force, must be longer 

 than one terminating at the Pole, and the lengths of the inter- 

 mediate columns must vary according to their latitude. The 

 figure that would result from such a state of equilibrium, was 

 investigated by both Newton and Huygens, but upon two different 

 hypotheses. Newton conceived the force of gravity to arise from 

 the mutual attraction of all the particles that compose the earth, 

 acting upon each other with forces inversely proportioned to the 

 squares of their respective distances ; he thence inferred, that 

 this force was not a constant one, and that if the figure of the 

 earth was due to the attraction of gravitation, the intensity of 

 this force at different points was affected by the earth's figure. 

 The earth being once flattened by the centrifugal force, this very 

 change of figure would render the force of gravity at the Equator 

 the least intense : applying this theory to a homogeneous spheri- 

 cal mass, and assuming, most happily, that an ellipsoid of revo- 

 lution would fulfil the conditions of equilibrium, he inferred that 

 the proportion between the polar and equatorial diameters was as 

 229 to 230, and the compression -j-j^th part of the greater axis. 



