NEWTON S PRINCIPIA. 125 



y ij lb 



millions of times swifter than that of light, or 147 thou 

 sand millions of miles in a second.* 



iii. The great system of most interesting truths which 

 we have now been contemplating is the work of those who 

 diligently studied the doctrines unfolded by Sir Isaac New 

 ton, respecting the motions of bodies which act upon each 

 other, while they are moving around common centres of 

 attraction. He laid down the principles upon which the 

 investigations were to be conducted ; he showed how they 

 must lead to a solution of the questions proposed, touching 

 the operation of disturbing forces ; and he exemplified the 

 application of his methods by giving solutions of these 

 questions in certain cases. Although his successors, tread 

 ing in his steps, have reaped the great rewards of their 

 learning and industry, and are well entitled to all praise 

 for the skill with which they both worked and improved 

 the machinery that he had put into their hands, at once 

 improving the calculus invented by him, and felicitously ap 

 plying it to advance and perfect his discoveries, yet the 

 distance at which his fame leaves theirs is at least equal to 

 that by which a Worcester and a Watt outstripped those 

 who, in later times, have used their mechanism as the means 

 of travelling on land and on water, in a way never foreseen 

 by those great inventors. Strict justice requires that we 

 should never lose sight of the truth repeatedly confessed by 

 Euler, Clairaut, Delambre, Lagrange, Laplace, that all 

 the advances made by them in the use of analysis, and in 

 its application to physical astronomy, are but the conse 

 quences of the Newtonian discoveries; so that we are guilty 

 of no exaggeration, if we regard the most brilliant achieve 

 ments of those great men only as corollaries from the pro 

 positions of their illustrious master. Let us briefly see 



* Mec. Cel. liv. vii. ch. 6 ; liv. x. ch. 7. 



