98 Professor Wallace in Reply to the Remarks of B. 



Art. XVIIL — Pt'ofessor Wallace,in reply to the Remarks 

 of B, upon his paper on Algebraic Series, contained in 

 Vol, VII. of this Journal, page 278. 



Columbia, S. C. Sept. 10, 1824. 

 Mr. Editor. 



Your correspondent Mr. B. in Art. XI. of your Journal 

 for May 1824 has, it appears, made some prof ound discov- 

 eries relative to a communication of mine, inserted in the 

 Journal for Feb. 1824. Permit me to rectify some of Mr. 

 B's. mistakes, and place the subject in its proper light. I 

 am very unwilling to subject Mr. B. to the imputation of 

 mala fides, or of a want of knowledge ; and I am still more 

 unwilling to revive, in any degree, the polemical spirit of 

 ancient writers who scarcely communicated with each oth- 

 er, except in the way of attack or reproach, and in a man- 

 ner too little creditable to their candour or impartiality. 



Mr. B. commences his observations on the " new alge- 

 hraical series^'' given by me, and endeavours to shew that 

 these series can hardly be called new, &;c. In my com- 

 munication, Mr. Editor, I no where called them new. My 

 introduction was omitted in the Journal* and the one which 

 Mr. B. criticises inserted. If Mr. B. however had read 

 the whole of the communication, he would find p. 285 of 

 the Journal, that the series in question, were given by M. 

 De Stainvilleof the Polytechnic School, in Vol. IX. of the 

 Annales de Mathematiques for 1818 and 1819, by Gergonne, 

 and therefore not mine. Where then is Mr. B's. candour ? 

 The series themselves are of little consequence, for many 

 others might be substituted for the same purpose. It is 

 the results produced by their multiplication, as Stainville 

 has shown, that is interesting. For this simple operation 



* As the Editor was, on account of ill health, absent at the Springs of 

 Ballston, when Professor Wallace's communication was printed, he neces- 

 sarily left the papers for the Journal in the hands of another person, and 

 therefore knew nothing of the suppression of the introductory remarks, or of 

 the title which was adopted. Authors should always furnish titles for their 

 own pieces, and then they will incur no risk of having their views misap- 

 prehended. That Professor Wallace may have no cause for complaint, in 

 the present instance, not a word of his MS. has been suppressed or altered, 

 ' ithough there are a few expressions, which we could have wisljed had 

 been omitted or modified. Editor. 



