SOLEDS on sriir \< SES. J2' 1 



and of figure art- supposed to coincide. This simplification 

 i< accordingly introduced, and. under the hypothesis of a fric- 

 tion proportional to the con-taut pressure, he finally obtains, 

 after a long ami complicated process, a solution of the prob- 

 lem, as far as the progressive motion ami the velocity about 

 the instantaneous axis arc concerned, but the determination 

 of the position of this axis in terms of the time is abandoned 

 .is absolutely unattainable 41 . 



The whole theory of simultaneous linear equations, so im- 

 portant in a large class of mechanical inquiries, was lefi by 

 Euler in a formed, hut by no means in a finished state. 

 I) Alemberl. in whose capacious and prolific intellect almost 

 every branch of mathematical and mechanical philosophy 



Das to have found place and to have borne abundant fruit, 

 invented, for the solution of these equations, the method of 

 indeterminate coefficients, a method remarkable for the faci- 

 lity of its application, and the fertile variety of its results 

 This method is not confined as Eider's is. to the case of con- 

 stant coefficients, bul brings to their least difficulties many 

 classes of equations which previously had been considered as 

 intractable. It was however not applied by D'Alembert to 

 the case of variable coefficients, until Lagrange and Lapl: 

 had considered (lie same subject in new and interesting lights. 

 In the memoirs of the Academy of Paris for 177 2. Laplace 

 gives with numerous developments Lagrange's process for in- 



^rating any number of simultaneous linear equations of the 

 first order with constant coefficients, and for determining tin 

 value of the arbitrary constants, which is by no means the 

 'least difficult part of the problem. JJoth the memoir of 

 Lagrange which discusses tin- variations of the nodes of the 



11 De motu globi circa axem obliquum quemcun per piano 



[i. 1782, P. ii. p. I"7. 



' a differentielles. Opuscu 



VI!. 178 !k it had employed the method of indeterminate mul 



. thirty-two yean before in the Berlin 

 telle methode de d'Alemberl [these are the word 

 Laplace) est sflrement une dea plus in . el dee plus (i condea de l'n 



llanea Taurinenria, Tom. IV, 1766, p. 273. 



