Trinity College, Cambridge

July 12. 1836

My dear Talbot

I should have been most happy to have accepted your kind invitation to Lacock Abbey if I had not had already two invitations on my books – one to the Master of Magdalene’s at Botleigh

& the other to Bowood; I assure you that I very much regret my inability to come to you

I hope you are getting on with the printing of your paper ^{<1>} & it is a most valuable accession to our knowledge of a part of analysis which is not very extensively cultivated: Have you seen Poisson’s memoir in Crelle’s Journal? ^{<2>} I saw it yesterday for the first time I have been reading Jerrard’s ^{<3>} memoirs on the resolution of Equations of the 5^{th} & higher degrees: ^{<4>} I believe his position to be quite untenable: the assumption of more than n (the degree of the equation [illegible]) in the series

[illegible deletion] P + Qx +Nx^{2} + Sx^{3} [&c &c] = Y= 0

which is necessary for his method appears to me to be fatal to the whole [illegible]: for x^{n}, x^{2n}, x^{[3n?]} … x ^{[illegible]n} may be always expressed by means of the primitive equation, by terms of the [illegible deletion] powers of x which are less than n [&?] the coefficients of the equation. Hamilton started this objection & has shown that his [illegible deletion] reducing equation ([illegible] form) will seem illusory by its terms being all zero. I shall give the whole question a thorough examination before I come to Bristol

Believe me My dear Talbot most truly yours

Geo Peacock

H. F. Talbot Esq

31 Sackville St

London

#### Notes:

**1**. WHFT, ‘Researches in the Integral Calculus, Part Two’ *Philosophical Transactions of the Royal Society of London*.

**2**. Simon Denis Poisson (1781–1840), mathematician; August Leopold Crelle (1780–1855), German mathematician, editor of *Journal für die Reine und angewandte Mathematik*.

**3**. George Jerrard (1804–1863), mathematician.

**4**. This is the famous problem of the insolubility of the algebraic equation of the 5^{th} degree resolved by Abel and by Galois at about this time.