Remarks on Professor Wallace’s Repiy to B. = 293 
in ichthyology, as well as by his tahowiics in various other de- 
- partments of natural science, accompanies this description. 
he fish itself, after having been well preserved in muriate 
of soda, by dry salting, was forwarded, through the minister 
of the marine and colonies, by the way of Havre-de-Grace, 
to the administration of the royal garden and museum at 
- Paris. 
New-York, June 6, 1824. 
J 
MATHEMATICS, MECHANICS, PHYSICS, AND 
CHEMISTRY. 
* 
Ant. XII1.—Remarks on Professor Wallace's Reply to B. 
In Vol. VII. page 278, of this Journal, a paper was pub- 
lished, under the title of New Algebraical Series, by Pro- 
fessor "Wallace, Columbia, 8. C.” containing a demonstration 
of the properties of a series of a peculiar form, and showing 
its uses in several cases. In some remarks on this, by B. in 
Vol. VIIL. page 131, it was stated that this series was nothing 
more than the usual ‘development of the Binomial Theorem, 
and that the same method of demonstration had been pub- 
lished by Euler, a fifty years since, in the Petersburgh 
Transactions. Ae 
There was whan uncourteous in the manner or lan- 
guage used by B. in mentioning this Atstorical fact. It 
has however excited the displeasure of Professor Wallace, 
who, in his reply, in Vol. IX. pages 98—103, ‘besides 
making several improper insinuations, which will be on. 
ed over without comment, has also asserted, in 
“ that Euler presupposes the knowledge of the expansion 
of a binomial function, and the results which he-has given 
do not include a single case of a transcendent function, 
and were only given as examples of the re case of 
al 
the binomial theorem, viz. (1+: Jt=14+— 24, “92 
+, &c.=f/(m), where m is supposed a whole poste anomie 
which case, as is well known, can be demonstrated in an ex- 
