I. Rationalisation.

The peculiarity of this process consists in its affecting all quantities alike with a negative sign.

To apply it, let H = High Church, and L= Low Church, then the geometric mean= √HL: call this 'B' (Broad Church).

- ∴ HL = B².

Also let *x* and *y* represent unknown quantities.

The process now requires the breaking up of U into its partial factions, and the introduction of certain combinations. Of the two principal factions thus formed, that corresponding with P presented no further difficulty, but it appeared hopeless to rationalise the other.

A '*reductio ad absurdum*' was therefore attempted, and it was asked 'why should π *not* be evaluated?' The great difficulty now was, to discover *y*.

Several ingenious substitutions and transformations were then resorted to, with a view to simplifying the equation, and it was at one time asserted, though never actually proved,