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 Mr Jerrard <4> has proposed a solution of algebraic equations of the 5th 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
Notes:
1. The British Association for the Advancement of Science.
2. Sir David Brewster (1781-1868), Scottish scientist & journalist
3. 'Researches in the Integral Calculus, Part One'. Read before the Royal Society 10 March 1836 and published Philosophical Transactions of the Royal Society of London, v. 126, part 1 (1836), p. 177 - 215.
4. George Jerrard (1804-1863) mathematician
5. Niels Henrik Abel (1802-1829), mathematician and Paolo Ruffini (1765-1822) had presented cases for the impossibility of solving equations above the fourth degree.
6. beyond reproach
7. Joseph Diez Gergonne (1771-1859), French mathematician edited Annales de math¨¦matiques pures et appliqu¨¦es.
8. The meeting at Bristol began on 22 August 1836.
9. Trinity College