Open main menu

Page:Carroll - Notes by an Oxford Chiel.djvu/24

This page has been validated.
14
THE EVALUATION OF π.

but, on application, J was found to exhibit a negative sign, which of course made the evaluation impossible.

We now proceed to describe the modern method, which has been crowned with brilliant and unexpected success, and which may be defined as


V. Evaluation Under Pressure.


Mathematicians had already investigated the locus of HPL, and had introduced this function into the calculation, but without effecting the desired evaluation, even when HPL was transferred to the opposite side of the equation, with a change of sign. The process we are about to describe consists chiefly in the substitution of G for P, and the application of pressure.

Let the function ϕ (HGL) be developed into a series, and let the sum of this be assumed as a perfectly rigid body, moving in a fixed line: let 'µ' be the coefficient of moral obligation, and 'e' the expediency. Also let 'F' be a Force acting equally in all directions, and vary-