404 D'ALEMBEKT. 



purest happiness; and he was fond of dwelling upon 

 all its details. Perfectly tranquil, without a thought 

 of wealth or power or distinction, his whole enjoy- 

 ments of an intellectual cast, his existence was as 

 entirely that of a philosopher as ever fell to the lot of 

 any one in ancient or in modern days. " I awoke," he 

 would say, " every morning to look back, with a feeling 

 of gladness in my heart, on the investigation which I had 

 begun over-night, and exulting in the prospect of con- 

 tinuing it to the result as soon as I rose. When I stopt 

 my operations for a few moments to rest myself, I used 

 to look forward to the evening when I should go to the 

 theatre and enjoy another kind of treat, but also aware 

 that between the acts I should be thinking on the greater 

 treat my next morning's work was to afford me." It was 

 at this period of his life, at once glorious and happy, 

 though still passed in obscurity, that the good old woman 

 whom he loved as a mother, and who doated on him as a 

 son, would say when any one told her of the great renown 

 he was preparing for his name, " Oh, you will never be 

 any thing better than a philosopher. And what's a phi- 

 losopher'? A foolish body who wearies his life out to be 

 spoken of after he's dead." 



His studies, however, as might well be expected, soon 

 proved eminently successful. In 1739 he presented to 

 the Academy of Sciences a paper containing some import- 

 ant corrections of errors into which Pere Reynau had 

 fallen in his treatise " Analyse Demontree ;" these errors 

 D'Alembert had discovered when studying the book in 

 order to learn the calculus, and they related to the 

 integrals of binomials. This memoir gave a most favour- 

 able impression of his capacity to the eminent men who 



