SEQUEL TO THE EPOCH OF NEWTON. 249 



that of the Peruvian and Swedish arcs gave 1-21 3th 

 for its value. 



Newton had deduced from his theory, by rea- 

 sonings of singular ingenuity, an ellipticity of 

 1 -230th ; but this result had been obtained by sup- 

 posing the earth homogeneous. If the earth be, as 

 we should most readily conjecture it to be, more 

 dense in its interior than at its exterior, its ellip- 

 ticity will be less than that of a homogeneous 

 spheroid revolving in the same time. It does not 

 appear that Newton was aware of this; but Clairaut, 

 in 1743, in his Figure of the Earth, proved this and 

 many other important results of the attraction of 

 the particles. Especially he established that, in 

 proportion as the fraction expressing the Ellipticity 

 becomes smaller, that expressing the Excess of the 

 polar over the equatorial gravity becomes larger; 

 and he thus connected the measures of the ellip- 

 ticity obtained by means of Degrees, with those 

 obtained by means of Pendulums in different lati- 

 tudes. 



The altered rate of a Pendulum, when carried 

 towards the equator, had been long ago observed 

 by Richer and Halley, and had been quoted by 

 Newton as confirmatory of his theory. Pendulums 

 were swung by the academicians who measured the 

 degrees, and confirmed the general character of the 

 results. 



But having reached this point of the verification 

 of the Newtonian theory, any additional step be- 



