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D'ALEMBERT. 



THE pleasures of a purely scientific life have often 

 been described; and they have been celebrated with very 

 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 circum- 

 stances over which he has little control. He must often 

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

 quently 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 circumstances by which he would ex- 

 tort her secrets ; add to all this the necessarily imper- 

 fect nature of inductive evidence, which always leaves it 

 doubtful if one generalization of facts shall not be after- 

 wards superseded by another, as exceptions arise to the 

 rule first discovered. But the geometrician"" relies en- 



* It may be as well to adopt the expression always used on the 

 Continent, to denote the cultivation of mathematical science : "Ce 



