364 HISTOEY OF MECHANICS. 



me try which are now its pride, was also the person w no made Mechanics 

 analytical ; I mean Euler. He began his execution of this task in 

 various memoirs which appeared in the Transactions of the Academy 

 of Sciences at St. Petersburg, commencing with its earliest volumes ; 

 and in 1736, he published there his Mechanics, or the Science of Motion 

 analytically expounded ; in the way of a Supplement to the Trans- 

 actions of the Imperial Academy of Sciences. In the preface to this 

 work, he says, that though the solutions of problems by Newton and 

 Hermann were quite satisfactory, yet he found that he had a difficulty 

 in applying them to new problems, differing little from theirs ; and 

 that, therefore, he thought it would be useful to extract an analysis 

 out of their synthesis. 



3. Mechanical Problems. In reality, however, Euler has done much 

 more than merely give analytical methods, which may be applied to 

 mechanical problems : he has himself applied such methods to an 

 immense number of cases. His transcendent mathematical powers, 

 his long and studious life, and the interest with which he pursued the 

 subject, led him to solve an almost inconceivable number and variety 

 of mechanical problems. Such problems suggested themselves to him 

 on all occasions. One of his memoirs begins, by stating that, happen- 

 ing to think of the line of Virgil, 



Auchora de prora jacitur stant litorc puppes ; 

 The anchor drops, the rushing keel is staid ; 



he could not help inquiring what would be the nature of the ship's 

 motion under the circumstances here described. And in the last few 

 clays of his life, after his mortal illness had begun, having seen in the 

 newspapers some statements respecting balloons, he proceeded to cal- 

 culate their motions ; and performed a difficult integration, in which 

 this undertaking 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 en- 

 rich 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 volumes usually contain several Memoirs of his. He 

 and his contemporaries may be said to have exhausted 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 problems ; for the next great 

 step in Analytical Mechanics, the publication of D'Alembert's Prin- 



