Remarks on Professor Wallact's reply to B. 2f)3 



or Professor Wallace ? This is nowhere distinctly staled, 

 and it is believed that most persons, after reading what Pro- 

 fessor Wallace has written, would suppose he claimed some, 

 if not a very large portion, for his own. But the real fact is 

 that none of it is his. The whole of the first seven pages, 

 Vol. VII. pp. 278 — 284, and a large portion of the two re- 

 maining pages of Professor Wallace's first communication 

 are merely literal translaUons from Stainville and Gergonne, 

 and what is not copied from them is quite unimportant. 

 From this statement the reader can judge whether Professor 

 Wallace's acknowledgment of his obligation to Mr. Stain- 

 ville was sufficiently explicit to make himself understood, 

 and to avoid the suspicion of appropriating to himself the 

 labours of others. 



It ought to be observed, as n point which has an important 

 bearing on the question under discussion, that Mr. Stainville 

 and Professor Wallace have nowhere intimated that the 

 general expression of their new series can be reduced to a 



a 



jlnite form, represented by the binomial {\—kz) *, as B. 



first showed ; and it would seem from some circumstances 

 that they supposed the proposed series to be of a more gene- 

 ral nature than the binomial series, and to include it as a 

 particular case. 



At first it was a matter of surprise to find Professor Wal- 

 lace had made the assertion that Euler's demonstration of 

 the binomial theorem was restricted to the very simple case 

 of an integer positive exponent ; but upon reflecting on some 

 of the circumstances, it appeared probable that he had never 

 seen the memoir of Euler, in vol. XIX. of the Nov. Comm.^ 

 or thoroughly examined the account of it by La Croix. The 

 volume of the Novi Comm. in which it was originally pub- 

 lished, is now out of print and difficult to be procured, so 

 that it is not to be found in sonie of our best libraries, even 

 in those which contain most of the other volumes of that col- 

 lection j probably there are not six copies of it in the United 

 States. When B. wrote his former remarks, he had never 

 seen Euler's publication, but referred to the account of it 

 given by La Croix in one of the volumes of his complete 

 Cour* de Mathematiques. This volume of La Croix's work 

 is enriched with numerous theorems, invented by Newton, 

 Euler, La Grange, etc.; yet Professor Wallace seems to be 

 offended because B. referred him to it, and observes that he 



