130 



A letter was read from Professor Holmboe, accompany- 

 ing his memoir, " De Prised re Monetarid Norvegise,^'' &c., 

 and requesting to know from the Academy whether any of 

 the coins described in that work are found in Ireland.* 



July 12. 

 SIR Wm. R. HAMILTON, LL.D., President, in the Chair. 



Part I. of a " Memoir on the Dialytic Method of Elimi- 

 nation," by J. J. Sylvester, Esq. A. M., of Trinity College, 

 Dublin, and Professor of Natural Philosophy in University 

 College, London, was read. 



The Author confines himself in this part to the treatment 

 of two equations, the final and other derivees of which form 

 the subject of investigation. 



The Author was led to reconsider his former labours in 

 this department of the general theory by finding certain 

 results announced by M. Cauchy in L'lnstitut, March Num- 

 ber, of the present year, which flow as obvious and imme- 

 diate consequences from Mr. Sylvester's own previously pub- 

 lished principles and method. 



Let there be two equations in x, 



U= ax" + 6a;"-i -f- cx""-^ + ex""^ -f &c. = 0, 

 r = aa:™ -f j3a;''-i + \x"-'^ + kc. = 0, 



and let n = m + i, where i is zero or any positive value (as 

 may be). 



Let any such quantities as x'' U, x^V, be termed aug- 

 mentatives of ?7or V, 



To obtain the derivee of a degree s units lower than "V, 

 we must join s augmentatives of U with s -f- 1 of V. Then 

 out of 2* + t equations 



* The Committee of Antiquities, having been consulted on this point, reported 

 in the negative. 



