lUiiiarlis on Professor WalUicii's lleijli] to B. 29.,5 



m ichtbyoloii);y, as well as by his labours in various oiber de- 

 partments of natural scieoce, accompanies this description. 



The 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 

 Parss. 



New- York, Junr; 6, 1824. 



MATHEMATICS, MECHANICS, PHYSICS, AND 

 CHEMISTRY. 



Art. XIII. — Remarks on Professor Wallace^ s Reply to B. 



In Vol. VH. page 278, of this Journal, a paper was pub- 

 lished, under the title of " New Algebraical Series, by Pro- 

 fessor Wallace, Columbia, S. C' containing a demonstration 

 of the properties of a series of a pecuhar form, and showing 

 its uses in several cases. In some remarks on this, by B. in 

 Vol. VIII. 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, about fifty years since, in the Petersburgh 

 Transactions. 



There was nothing uncourteous in the manner or lan- 

 guage used by B. in mentioning this historical 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 pass- 

 ed over without comment, has also asserted, in page 100, 

 " 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 exainples of the simplest case of 



m m m—l 

 the binomial theorem, viz. (l^-^)"'=l -|-T"'~+"7. '~^ — 'z- 



-f-j &c.=/(7?i), where m is supposed a whole positive number,'''' 

 which case, as is well known, can be demonstrated in an ex- 



