294 Remarks on Professor Wallace's reply to B. 
tremely short and simple | ceenie by the common operations 
of uate tion. 
Now it is a fact, Aolinighateadiay the posttive declaration of 
Professor Wallace to the contrary, that Euler’s demonstration 
is not restricted to this very simple and easy to be demon- 
strated case ; but is general for all values of the exponent, 
whether integer, fractional, positive, negative, or surd, and 
it is characterized by La Croix as being elegant and rigor- 
ous.* ‘Moreover, every thing that can pe obtained from the 
multiplication of these new series can be easily deduced 
from Euler’s method by a perfectly rigorous process. 
Professor Wallace complains that a wrong title was given 
to his paper. This could not have been known to B.; and if it 
had been known, it would in nowise have affected the justice 
of his remarks. The fact would still have been that Pro- 
fessor Wallace had republished as a late discovery what had 
been known by mathematicians for half a century. 
only difference, as it now appears, is, that Mr. Stainville 
ve it as new for the first time in 1818, and Professor Wal- 
lace for the second time in 1824—Euler’s having been pub- 
lished in 1775. When B. read the first communication of 
ih a Wallace, the thought never occurred that th 
was not claimed as a new process, particularly as the 
yords =a Algebraic Series” occur at the top of every page,* 
nd the of his obligation to Mr. 
Stanaeitte’ i vol. vii. p- 285, is so connected with the account 
of numerical faculties, integrations, derivations, and the no- 
tices of other series besides those denoted by fa, that it did 
not attract particular attention as referring exclusively to 
this last series. The whole notice of Mr. Stainville is compri- 
sed in this brief sentence, ‘‘M. de Stainville of the ore 
School has given the series in this communication in Volum 
IX. of ar ey Annals; and from the extensive rs 
plication of which they are “susceptible, the subject is de- 
serving of fartherjinvestigation.” This is not very definite 
because there are several series in that paper. Admitting 
it, however, to refer particularly to the series denoted by fa, 
the question will then occur—who discovered all its properties 
and made all the deductions from it? was it Mr. Stainville, 
_ démonstration précédente ne laisse rien 4 somali du cété de la ri- 
gueur et de Pélégance.—Comp. des. Elém 
rofessor Wallace it should be remarked Paint no part 
of this title can be attributed to him, as ther companying 
his ena The title mentioned was eoered at ee "tae of publie 
cat o 
