solids iin -i nr \i es. ; 2 I 



Society** for 1 7 "><>. had been composed after a perusal of 

 D'Alembert's Treatise of 1749. The simplifications intro- 

 duced by the discovery of the properties of the oatural axes 

 of rotation by Segner* 3 in 1755 contributed materially to im- 

 prove the form and manageableness of the equations of rota- 

 tory motion, and in L758, Euler had made such advances in 

 this theory, thai the problem of the general motion of a fi 

 rigid body animated by no accelerating forces, or in other 

 words agitated only by the inertia of its particles — a problem 

 of some celebrity in the history of mathematics, — at last 

 yielded to the power of the calculus and to the penetrating 

 uius of its accomplished master**. Two years afterwards, 

 Euler resumed the consideration of this subject, in an inter- 

 esting paper in which he applied to a variety of curious prob- 

 lems the theory of the Segnerian axes"; and finally in 1761, 

 John Albert Euler. in a prize dissertation on the stowage and 

 ballasting of vessels, solved by a method evidently imitated 

 from his father's, the problem of a rigid body not solicited by 

 accelerating forces- 3 . The analysis employed in these solu- 

 tions though subtle and profound is certainly deficient in that 

 directness and precision so difficult to attain in a new and 

 complicated subject. To remedy Ibis imperfection. I)' \lem- 

 bert, in a paper written in 1762, though not published until 

 six years afterwards* 7 , derives the results of Euler from the 

 principles laid down in the firsl volume of his Opuscules**, by 

 a process so remarkable for it> simplicity and beauty, thai La- 

 grange has adopted and inserted it with an improved nota- 



,s Avertissemenl au sujel i i Equinoxes. 



Mem. d ; lead, de me VI. I 



Specimen Theorire Turbinum. 1 i 



- i riable 



I. Berl. Tome XIV. : 



ttion d'un corps Bolide quclconque, lorsqu'il tourne 

 autour d'un axe mobile. Mem Lead. Berl. Tome XVI. i 



'* Histoire de rAcadlmie des Sciences de Paris. Prix. I7G1. 



1T Du mouvemenl d'un Corps de figure quelconque. Opuscules, Tomi l\ 

 1768. p. 



** Opuscules, Tome I. 17':!. p. 71— 103 



VOL. in. 1 N 



