— 82 — 



arranged. The last number piiblished is No. IV — there is no 

 subcription and I believe the Journal is only to be procured on 

 the Continent like other English books, through a bookseller, 

 bnt if you have any difficulty in doing this at Bern, I dare say 

 that I could manage to have the numbers sent to you through 

 my own booksellers here Mess'* Williams & Norgate. I have 

 been studying with renewed interest your memoir on elimination: 

 permit nie to express the pleasure it gave nie to see the enormuos 

 extension you have made in the niethod of Symmetrie functions. 

 The theorem in your memoir that if U = o, V = o t^Ce are any 

 equations and ^ = o their resultant then that dU, öY &c ai'e 

 respectively proportional to d(f was in some measure new to 

 nie, I had always imagined (what your proof shews was an 

 unnecessary restriction) that the theorem was only true wlien 

 U, V Sic were absolutely general functions. It is however assumed 

 in your form of the theorem that the Coefficients of eacli of the 

 functions U, V • • are independent of the Coefficients of the 

 other functions; the niost general form of the theorem seenis 

 to be as foUows, viz. R, r &c being quantities whicli may be 

 assumed at pleasure (but no generality would be lost by giving 

 them any particular values) then 



R, r . . 



dU.dU 



dx dy 



dx dy . 

 which of course represents a function of the form 



L^U -|- M(JV -f- ^*^c will be identically equal to Köip 

 — a theorem in which any relations whatever may exist between 

 the coefficients of the functions U, V &c a very slight alteration 

 of your proof will shew the truth of the theorem. I liope soon 

 have the pleasure of sending you a continuation of my memoir 

 on Quantics. I have the lionor to be, Sir, your obedient servant 



A. Cayley. 

 2. Stone Buildings 



Lincolns Inn London 

 22. sep. 1856. 



