Remarks on Professor Wallace’s reply to B. 235 
or Professor Wallace? This is nowhere distinctly stated, 
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. ut the real fact i is 
that none of it is his. The whole of the first’ seven Pages, 
bid er PP. 278 —24, and a large portion of the tw 
maining pages of Professor Wallace’s first commen 
are etn literal lranslations from Stainville and Gergonne, 
and what is not copied from them is quite unimportant.’ 
From this statement a reader can judge whether te 
Wallace’s acknowledgment of his obligation to Mr. Stain- 
ville was sufficiently explicit to make himself, eet 
and to avoid the suspicion of appropriating to himself the 
labours of others 
It ought to be observed, asa 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 toa 
a 
Jinite form, represented by the binomial (1—4z) ete 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 sim e 
of an integer positjve exponent; but upon reflecting on some 
of the circumstances, } it appeared probable that mee had never 
seen the memoir of Euler, in vol. XIX. of the Nov. Co 
or thoroughly examined the account of it by La Ces 
volume of the .Vovi 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 some of our best libraries, even 
in those which contain most of the other volumes of that col- 
lection; probably there are not six copies of it in the United 
States. hen 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 
Cours de Mathématiques. This volume of La Croix’s work 
is enriched with numerous theorems, invented by Newton, 
Euler, La Grange, etc.; yet Prafeasot Wallace seems to be 
offended because B. referred him to it, and observes that he 
