11. On Elimination between an Indefinite Number of Unknown Quantities. 

 By the Rev. R. Muephy, M. A. Fellow of Cuius College, a?id of 

 the Cambridge Philosophical Society. 



[Read Nov. 26, 1832.] 



SECTION I. 



INTRODUCTION. 



Fourier, in his treatise, * Theorie de la Chaleur,' * has given an 

 example of the determination of an indefinite number of unknown 

 quantities, subject to the same immber of conditions. If n be the 

 number of those quantities, in order to discover their law by this 

 method, it will be necessary to eliminate successively the first (ni- 1) 

 and the last (« — »^) unknown quantities, thus determining the »^'^ by 

 a final equation containing that quantity only. 



This process is obviously too laborious, and the results too compli- 

 cated, to be practically useful, in most cases. 



The same objection applies to the elegant method of Laplace, which 

 makes the determination of one of the unknown quantities, depend 

 on the discovery of all the (w — 1) arbitrary multipliers introduced in 

 the process. It has besides the disadvantage of not seizing, in many 

 cases, the facilities offered by the peculiar forms of the proposed equa- 

 tions. 



• Vid. Fourier, p. 1 69 to 174- 

 Vol. V. Paet I. I 



