TALBOT3012

My dear Sir,

The Letter ¹ you did me the favor to write I transmitted to M^r Peacock. ² I never doubted that your result was correct, & therefore I see no use in pushing your numerical example to more places of figures.

Pray refer to Legendre’s 2^nd Supplement ³ p 163 & to his 3^rd Supplement, also to a recent paper by Poisson ⁴ in Crelle’s Journal vol XII. p. 101. M^r Peacock & myself both think it indispensable that you should notice Abel’s Theorem, ⁵ which has created a revolution in this branch of mathematics.

It is very desirable moreover that the constant should be determined if possible.

In your first example & employing the notation of Legendre 2^nd Supplement p 163 I find

Now making successively

which are your equations.

Pray let me hear from you when you have compared the method of Abel with your own.

If you wish to have Legendre’s Supplements out of the Library of the Royal Society I will get them out for you & send them you by coach.

I am, dear Sir, Yours very truly,
J W Lubbock

29 Eaton Place ⁶

27 Nov^r 1834