156 TERRESTRIAL PHENOMENA. 



from theoretical grounds the compression of the Earth, aa 

 a homogeneous mass, at -^-o. By the aid of new and more 

 perfect analysis, actual measurements have since shewn the 

 ellipticity of the terrestrial spheroid, when the density of the 

 strata is regarded as increasing towards the centre, to be 

 more nearly ^ T . 



Three methods have been employed in investigating the 

 curvature of the Earth's surface : it has been inferred from 

 measurements of degrees, from the vibrations of a pen- 

 dulum, and from certain inequalities in the Moon's orbit. 

 The first method is a direct geometrical and astronomical 

 one; in the other two, we infer from movements accu- 

 rately observed, the measure of the forces which occasion 

 those movements ; and from the inequality of the forces 

 we infer the difference between the equatorial and polar 

 diameters. In this part of the sketch of nature, I have 

 introduced an exception to the general manner of its treat- 

 ment, by noticing methods, because in this case they 

 afford a striking exemplification of the intimate connec- 

 tion existing between forms and forces in natural phse- 

 nomena; and also, because their employment has happily 

 given occasion to the attainment of a high degree of accuracy 

 in optical instruments, and in those employed in the mea- 

 surements of space and time, as well as to fundamental im- 

 provements in the astronomical and mechanical sciences, 

 and even to new and special branches of analysis. Except 

 the investigations concerning the parallax of the fixed stars, 

 which led to the discovery of aberration and nutation, the 

 history of science presents no problem in which the object 

 obtained, the knowledge of the mean compression of the 

 Earth . and the certainty that its figure is not a regular one, 



