Professor Itigaud's Account of James Stirling. J 95 



says " I shall now annex two problems with their solutions 

 in summation of series, which I hope will not displease our 

 readers, and, when room permits, shall further illustrate Mr 

 Stirling's book entitled Summation and Interpolation of Infi- 

 nite Series."" The translation of the whole work was original- 

 ]y intended for occasional insertion,* by parts, in the same pe- 

 riodical miscellany, but Emerson, who had assisted in the re- 

 vision of it, recommended an entire and separate publication. 

 It is valuable, not merely from its scarceness, but also from its 

 forming a comment, in some measure from authority, upon the 

 original text, as will be seen from the following passages which 

 occur in the preface. 



" Being unwilling to commit any mistakes that might be in- 

 jurious to my readers, I had recourse to Mr Stirling himself, 

 and he was so obliging as to give me all the assistance I need- 

 ed on this occasion, and particularly his correction and amend- 

 ment of example 2, f p. 132, concerning which I had some 

 suspicion." 



" In a postscript of a letter that I had the honour to re- 

 ceive from Mr Stirling, dated the 18th of May 1747 1 had, 



he says, almost forgot to give an answer to that part of your 

 obliging letter, where you say that some eminent mathemati- 

 cians had observed to you, that I had nowhere shown from a 

 given series, how to find the equation of the successive terms : 

 to which I answer, that the thing is self-evident, or easy in 

 such series as I proposed to sum or interpole; but in many 

 kinds of series, the equation to the terms cannot be found, at 

 least if their relation be considered in the manner I have done. 

 For this reason, 1 gave no rule for finding the equations to 

 the terms of the series which I considered, and I did not pro- 

 pose to solve the problem generally, because 1 knew that it 

 was not to be done." 



In November 1729, Stirling was elected fellow of the lioyal 



* Upon this plan a translation was begun of Brooke Taylor's Method us 

 Incrementorum, given with "a due medium between a paraphrase and a 

 verbal translation." It had not, however, proceeded beyond the first ten 

 propositions when it was stopped by the termination of the publication. 



t Kxp. y. to Prop. xxvi. 



