sect, iv.] DISSERTATION SECOND. 107 



by a very subtle process of reasoning, Newton found that 

 the longer of the two canals must be to the shorter as 

 230 to 229. This, therefore, is the ratio of the radius 

 of the equator to the polar semi-axis, their difference 

 amounting, according to the dimensions then assigned to 

 the earth, to about 17 T ^ English miles. In this investiga- 

 tion, the earth is understood to be homogeneous, or eve- 

 rywhere of the same density. 



It is very remarkable, that though the ingenious and 

 profound reasoning on which this conclusion rests is not 

 entirely above objection, and assumes some things without 

 sufficient proof, yet, when these defects were corrected 

 in the new investigations of Maclaurin and Clairaut, the 

 conclusion, supposing the eanh homogeneous, remained 

 exactly the same. The sagacity of Newton, like the 

 Genius of Socrates, seemed sometimes to inspire him with 

 wisdom from an invisible source. By a profound study 

 of nature, her laws, her analogies, and her resources, he 

 seems to have acquired the same sort of tact or feeling 

 in matters of science, that experienced engineers and other 

 artists sometimes acquire in matters of practice, by which 

 they are often directed right, when they can scarcely de- 

 scribe in words the principle on which they proceed. 



From the figure of the earth thus determined, he showed 

 that the intensity of gravity at any point of the surface, 

 is inversely as the distance of that point from the centre ; 

 and its increase, therefore, on going from the equator to 

 the poles, is as the square of the sine of the latitude, the 

 same ratio in which the degrees of the meridian increase. 1 

 As the intensity of gravity diminished on going from the 

 poles to the equator, or from the higher to the lower 

 latitudes, it followed, that a pendulum of a given length 



1 Princip. Lib. III. prop. 20. 



