III. 



DYNAMICAL PRINCIPLE. CALCULUS OF PARTIAL 

 DIFFERENCES. PROBLEM OF THREE BODIES. 



THE pleasures of a purely scientific life have often been 

 described ; and tbey have been celebrated with veiy heartfelt 

 envy by those whose vocations precluded or interrupted such 

 enjoyments, as well as commended by those whose more 

 fortunate lot gave them the experience of what they praised ; 

 but it may be doubted, if such representations can ever apply 

 to any pursuits so justly as to the study of the mathematics. 

 In other branches of science the student is dependent upon 

 many circumstances over which he has little control. He 

 must often rely on the reports of others for his facts ; he must 

 frequently commit to their agency much of his inquiries ; his 

 research may lead him to depend upon climate, or weather, 

 or the qualities of matter, which he must take as he finds it ; 

 where all other things are auspicious, he may be without the 

 means of making experiments, of placing nature in circum- 

 stances by which he would extort her secrets ; add to all this 

 the necessarily imperfect nature of inductive evidence, which 

 always leaves it doubtful if one generalisation of facts shall 

 not be afterwards superseded by another, as exceptions arise 

 to the rule first discovered. But the geometrician relies 

 entirely on himself; he is absolute master of his materials; 

 his whole investigations are conducted at his own good 

 pleasure, and under his own absolute and undivided control. 

 He seeks the aid of no assistant, requires the use of no 

 apparatus, hardly wants any books ; and with the fullest 

 reliance on the perfect instruments of his operations, and on 

 the altogether certain nature of his resxilts, he is quite 

 assured that the truths which he has found out, though they 



D 



