CALCULUS OF PARTIAL DIFFERENCES. 37 



instance to another purpose. Thoughtless and superficial 

 observers have charged this science with a tendency to render 

 the feelings obtuse. Any pursuit of a very engrossing or 

 absorbing kind may produce this temporary effect ; and it has 

 been supposed that men occasionally abstracted from other 

 contemplations, are particularly dull of temper. But no one 

 ever had more warm or kindly feelings than Euler, whose 

 chief delight was in the cheerful society of his grandchildren, 

 to his last hour ; and whose chief relaxation from his severer 

 studies was found in teaching these little ones. 



It has been alleged, and certainly has been somewhat found 

 by experience to be true, that the habit of contemplating 

 necessary truth, and the familiarity with the demonstrative 

 evidence on which it rests, has a tendency to unfit the mind 

 for accurately weighing the inferior kind of proof which we 

 can alone obtain in the other sciences. Once finding that 

 the certainty to which the geometrician is accustomed cannot 

 be attained, he is apt either to reject all testimony, or to become 

 credulous by confounding different degrees of evidence, re- 

 garding them all as nearly equal from their immeasurable 

 inferiority to his own species of proof much as great sove- 

 reigns confound together various ranks of common persons, 

 on whom they look down as all belonging to a different 

 species from their own. In this observation there is, no 

 doubt, much of truth ; but we must be careful not to extend its 

 scope too far, so as that it should admit of no exceptions. 

 D'Alembert affords one of the most remarkable of these ; as 

 far as physical science went, Laplace afforded another ; in 

 several other branches he was, perhaps, no exception to the 

 rule. 



Whatever of peace and comfort he enjoyed, D'Alembert 

 owed to geometry, and confessed his obligations. Whatever 

 he suffered from vexation of any sort, he could fairly charge 

 upon the temporary interruption of his mathematical pursuits. 

 Both portions of his history, therefore, enforce the doctrine 

 which I have laid down. 



His ' Traite de Dynamique ' at once placed him in the 



