TALBOT3194

31 Sackville S^{t 1}

Tuesday

Dear Sir

I think Sir W. Hamilton’s statement ² is very clear, & he seems decidedly of opinion now that Mr J’s method ³ is erroneous – But even if the first part of it were correct, I do not see that the Problem would be solved.

Let the given equation be x⁵ + x = a
Let y = P + Qx + Rx² + … + Zx⁹ [1]
Suppose it possible to determine the coëff^ts P, Q &c so that the resulting equation in y may be of Demoivre’s ⁴ solvible <sic> form, therefore the value of y becomes known.

But even granting this, it is not the thing required, which is to find the value of x.

Now x is only found from y, by solving the eqⁿ of the 9^th degree [1]

But I do not at all admit that the coëff^ts P, Q &c can be determined in the manner required without the solution of an equation of the same degree with the proposed.

Believe me
Yours very Truly

H. F. Talbot