ACCORDANCE OF QUANTITATIVE THEORIES, &c. 207 



coincident results, a new method has sometimes disclosed 

 a discrepancy which it is yet impossible to explain. 



The ellipticity of the earth is known with very con- 

 siderable approach to certainty and accuracy, for it has 

 been estimated in three independent ways. The most 

 direct mode is to measure long arcs extending north and 

 south upon the earth's surface, by means of trigonome- 

 trical surveys, and then to compare the lengths of these 

 arcs with the amount of their curvature as determined by 

 the observation of the altitude of certain stars at the ter- 

 minal points. The most probable ellipticity of the earth 

 deduced from all measurements of this kind was estimated 



by Bessel at , though subsequent measurements might 



lead to a slightly different estimate. The divergence from 

 a globular form causes a small variation in the force of 

 gravity in different parts of the earth's surface, so that 

 exact pendulum observations give the data for an entirely 

 independent estimate of the ellipticity, which is thus found 



to be . In the third place the spheroidal protuberance 



about the earth's equator leads to a certain inequality in 

 the moon's motion, as shown by Laplace ; and from the 

 amount of that inequality, as given by observations, Laplace 

 was enabled to calculate back to the amount of its cause. 



He thus inferred that the ellipticity is , which lies be- 



O^O 



tween the two numbers previously given, and was con- 

 sidered by him to be the most satisfactory conclusion. In 

 this case the accordance is both close and undisturbed by 

 any other or subsequent results, so that we are obliged to 

 accept Laplace's result as a highly probable and accurate 

 one. 



The mean density of the earth is another constant quan- 

 tity of the highest importance, because it forms the starting- 

 point for the determination of the masses of all the other 



