Open main menu

Page:Carroll - Notes by an Oxford Chiel.djvu/20

This page has been validated.
10
THE EVALUATION OF π.

that the y's were all on one side. However, as repeated trials produced the same irrational result, the process was finally abandoned.


II. The Method of Indifferences.


This was a modification of 'the method of finite Differences,' and may be thus briefly described:—

Let E = Essays, and R = Reviews: then the locus of (E + R), referred to multilinear coordinates, will be found to be a superficies (i.e. a locus possessing length and breadth, but no depth). Let v = novelty, and assume (E + R) as a function of v.

Taking this superficies as the plane of reference, we get—

E = R = B
∴ EB = B² = HL (by the last article.)

Multiplying by P, EBP = HPL.

It was now necessary to investigate the locus of EBP: this was found to be a species of Catenary, called the Patristic Catenary, which is usually defined as 'passing through origen,