TALBOT5515

Lacock Abbey, Chippenham
Oct 7. 1835

My Dear Sir

Can you inform me to whom I ought to apply to know whether I am a member of the British Association-¹ I believe that Brewster ² proposed my name some years ago, but he seems to know nothing about it, or to have forgotten it. I was not aware till lately that there was any pecuniary payment to be made, esle of course I should have forwarded my subscription that might be due.

I am engaged in preparing a mathematical paper ³ for the Royal Society, that I have had in hand, at intervals, a long time- It is on the Integral Calculus, and offers, in my opinion at least, a very satisfactory solution of the problem of finding an algebraic sum of a series of integrals like ƒφ(X) αγ where φ is any function whatever of the rational polynomial X. I have reason to suppose that this very much extends the frontier of the science in that direction.

I see in the scientific journals that M^r Jerrard ⁴ has proposed a solution of algebraic equations of the 5^th degree. Is this true? I almost suspect a fallacy, and should recommend it to be put to the test of several arithmetical examples;- Ruffini, Abel, ⁵ and others have shown the problem to be impossible, but their reasoning does not appear to be ¨¤ l¡¯abri de toute reproche. ⁶ There is also a singular solution in Gergonne's Annals ⁷ of the equation xⁿ + ax + b = 0 which has no demonstration appended, and for want of it appears to have been unattended to. The author is a Swedish Officer- I tried it upon an arithmetical example, which came out right, but that may have been accident. However since the subject has been revived, I would point out the memoir in question to the attention of mathematicians- The next meeting of the British Association being to be held at Bristol, ⁸ in my neighbourhood makes me anxious to know whether I have the honour to belong to that illustrious Confraternity.

Believe me to remain Yours very Truly
H.F. Talbot

1835 London October eight WF Strangways
Rev. W. Whewell
Trin. Coll. ⁹
Cambridge