478 Mr. Jerrnrd on the Transformation of Equations. 



of the heat emitted by the lamp pass immediately, while 

 those of the heat emitted by the boiling water are completely 

 absorbed. It is scarcely necessary to add that we should 

 have other transmissions if we took calorific sources of dif- 

 ferent temperatures from those I have just cited. There are, 

 then, several kinds of dark heat, as there undoubtedly exist 

 several kinds also of calorific rays in the heat which ordi- 

 narily accompanies light. 

 Paris, Nov. 15, 1835. Macedoine Mellon i. 



LXIV. On the Transformation of Equations, By G. B. 

 Jeruaiid, A.B. 



[Continued from page 203.] 



TN order to reduce the general equation of the mth degree 



x m + A# m - 1 + B.r w - 2 ... + J^-"" 1 + K^-"... + V = 0, 

 to the form 



y m + K'y»- n ... -f V = 0, 



in which A' = 0, B' = 0, ... J' = 0, 



I saw that it would be necessary when j/=P+Q.r+R.r* 



... + ~Lx\ to satisfy (it— 1) equations, which relatively to 

 P, Q, R, ... L were of 1,2, 3, ... (n— 1) dimensions, and 

 which in the notation of the Researches* would be expressed 



by /. (OP+ 1Q+ 2R... + XL) = 0, 



/.(OP+ I Q + 2 R ... + A L 2 ) = 0, 



/. (OP + 1Q + 2R... + xL s ) = 0. 



/. (OP+ 1Q+ 2R... + xL)»- 1 = o. 



No general method had as yet been discovered by mathema- 

 ticians for determining P, Q, R,... without the aid of an 

 equation of 1 , 2, 3,... (»— 1) dimensions, when the idea oc- 

 curred to me, that if, availing myself of the indefinite extent 

 of the series for y, I could detach some of the unknown 

 quantities P, Q, R,... from the rest so as to form a succes- 

 sion of groups, I might possibly be enabled to effect the de- 

 termination of these quantities by means of equations of 

 1,2,3,... (n — 1) dimensions only. But here a great diffi- 

 culty presented itself. For the purpose of detaching an un- 

 known quantity A from a function of n dimensions relatively 



* See Jerrard's Mathematical Researches, p. 41. 



