TALBOT5058

Lacock Abbey
8 Sept^r 1844

Dear Sir

I shall have great pleasure in forwarding to M^rs Somerville ¹ and also to yourself copies of the mathematical memoirs ² – I think they will travel very well by post.

I had advanced the subject a good deal further than appears in those memoirs, but I never could find time to put the materials into proper order for publication.

The subject however is a great favourite of mine & I should be very glad to continue it, and equally glad if anybody else would continue it – at every [illegible deletion] step you take, you start coveys of beautiful theorems (excuse a September metaphor) which hardly by any other means can be got hold of, else Legendre ³ and others would certainly have found them. Will you give me leave to ask a mathem^l question or two which occur to me relative to this subject?

What is the definition of an Abelian integral? ⁴ for it appears to me that most integrals possess the Abelian property.

What is the definition of a Cone of the second order? I must be under a delusion of course, for I cannot see how it differs from a common oblique cone.

Is it not the same thing, presented differently to the contemplation?

Yours very truly
H. F. Talbot

Sir J Herschel
&c &c