96 HISTORY OF MECHANICS. 



performed a difficult integration, in which this un- 

 dertaking engaged him. His memoirs occupy a 

 very large portion of the Petropolitan Transactions 

 during his life, from 1728 to 1783 ; and he declared 

 that he should leave papers which might enrich 

 the publications of the Academy of Petersburg for 

 twenty years after his death ; a promise which has 

 been more than fulfilled; for, up to 1818, the vo- 

 lumes usually contain several memoirs of his. He 

 and his contemporaries may be said to have ex- 

 hausted the subject ; for there are few mechanical 

 problems which have been since treated, which they 

 have not in some manner touched upon. 



I do not dwell upon the details of such pro- 

 blems; for the next great step in Analytical Me- 

 chanics, the publication of D'Alembert's Principle 

 in 1743, in a great degree superseded their interest. 

 The Transactions of the Academies of Paris and 

 Berlin, as well as St. Petersburg, are filled, up to 

 this time, with various questions of this kind. They 

 require, for the most part, the determination of the 

 motions of several bodies, with or without weight, 

 which pull or push each other by means of threads, 

 or levers, to which they are fastened, or along 

 which they can slide ; and which, having a certain 

 impulse given them at first, are then left to them- 

 selves, or are compelled to move in given lines and 

 surfaces. The postulate of Huyghens, respecting 

 the motion of the center of gravity, was generally 

 one of the principles of the solution ; but other 



