NEWTON S PRINCIPIA. 159 



Newton at last concluded, nor even that of 289 to 288, 

 according to his first approximation, but only that of 336 

 to 335 *, being an excess of little more than 23J miles. 

 The calculation of Newton was formed on the supposition 

 of the Earth being homogeneous ; and it is worthy of 

 remark, that although the later observations, by proving 

 the flattening at the poles to be less than he, on this 

 hypothesis, assigned it, have shown the Earth not to be 

 homogeneous, no correction or improvement whatever 

 has been made on his theory in this respect. We find 

 Laplace, on the contrary, in the very passage to which 

 we are now referring, assuming his precise fraction ^^ 

 as the one given by the theory upon the supposition of 

 the globe being homogeneous, and reasoning upon that 

 fraction.f 



Now it is fit that we here pause to contemplate perhaps 

 the most wonderful thing in the whole of the Newtonian 

 discoveries. The subject of curvilinear motion, or mo 

 tion produced by centripetal forces, was certainly in a 

 great measure new, and Sir Isaac Newton s treatment of 

 it was in the highest degree original and successful. But 

 the laws of attraction, the principles which govern the 

 mutual actions of the planets, and generally of the masses 

 of matter, on each other, was still more eminently a 

 field not merely unexplored, but the very existence of 

 which was unknown. Not only did he first discover this 

 field, not only did he invent the calculus by means of 

 which alone it could be explored, and without which 

 hardly a step could be made across any portion of it (for 

 the utmost resources of geometrical skill in the hands of 

 the Simsons and the Stewarts themselves, who in other 

 inquiries had performed such wonders by ancient ana- 



* Mec. Cel. liv. iii. ch. 5. t Il &amp;gt; id liv - & ch - 5 s - 4L 



