xxv.] ACCORDANCE OF THEORIES. 565 



be regarded as the best possible proof of the approximate 

 correctness of the mean result, yet instances have occurred 

 to show that we can never take too much trouble in con- 

 firming results of great importance. When three or even 

 more distinct methods have given nearly coincident num- 

 bers, a new method has sometimes disclosed a discrepancy 

 which it is yet impossible to explain. 



The ellipticity of the earth is known with considerable 

 approach to certainty and accuracy, for it has been esti- 

 mated 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 trigonometrical surveys, 

 and then to compare the lengths of these arcs with their 

 curvature as determined by observations of the altitude 

 of certain stars at the terminal points. The most probable 

 ellipticity of the earth deduced from all measurements of 



this kind was estimated by Bessel at , though subse- 

 quent measurements might lead to a slightly different 

 estimate. The divergence from a globular form causes a 

 small variation in the force of gravity at different parts of 

 the earth's surface, so that exact pendulum observations 

 give the data for an 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 ellip- 

 ticity is ~t which lies between the two numbers previously 



given, and was considered by him the most satisfactory 

 determination. In this case the accordance is undisturbed 

 by subsequent results, so that we are obliged to accept 

 Laplace's result as a highly probable one. 



The mean density of the earth is a constant of high 

 importance, because it is necessary for the determination 

 of the masses of all the other heavenly bodies. Astrono- 

 mers and physicists accordingly have bestowed a great 

 deal of labour upon the exact estimation of this con- 

 stant. The method of procedure consists in comparing the 



