NEWTON S PRINCIPIA. 165 



having differed from the rule which Torricelli had deduced 

 experimental ly, Xewton again investigated the question by 

 a different and an admirable process ; but even now the 

 subject remains in a very unsatisfactory state. Nor can it 

 be said that the science of hydrodynamics generally has 

 attained the perfection of the other branches of Mechanical 

 philosophy; while it is certain that the application to it of 

 the calculus by Euler and D Atembert*, and still more by 

 Clairaut, has greatly added to the theorems left by Sir 

 Isaac Newton ; and the researches of Laplace upon ca 

 pillary attraction form a department of science almost 

 unknown before the latter part of the eighteenth century. 

 The statement of these particulars was necessary in 

 order to place the relative merits of the different branches 

 of the Principia in their true light. That a great improve 

 ment was accomplished in natural knowledge by this por 

 tion of Sir Isaac Newton s discoveries, none can doubt. 

 That the Second Book displays at every step the profound 

 sagacity and matchless skill of its author, is undeniable. 

 That it would have conferred lasting renown upon any one 

 but himself, had it been the only work of another man, is 

 certain. Nor can we forget that in rating its importance 

 as we have ventured to do, we only undervalue this portion 

 of the Principia, by applying to it the severest of stand 

 ards, comparing it with the discovery of the laws which 

 govern the system of the universe, and placing it in con 

 trast with the other parts of that unrivalled effort of human 

 genius. 



* Their invention of the Calculus of Partial Differences \vas connected 

 with this subject. (See Life of D Alembert.) 



11 3 



