Page:Complete Works of Lewis Carroll.djvu/1144

1124 down to our own time, been considered as purely arithmetical. It was reserved for this generation to make the discovery that it is in reality a dynamical problem: and the true value of π which appeared an ignis fatuus to our forefathers, has been at last obtained under pressure.

The following are the main data of the problem:

Let U = the University, G = Greek, and P = Professor. Then GP = Greek Professor; let this be reduced to its lowest terms, and call the result J.

Also let W = the work done, T = the Times, p = the given payment, π = the payment according to T, and S = the sum required; so that π = S.

The problem is, to obtain a value for π which shall be commensurable with W.

In the early treatises on this subject, the mean value assigned to π will be found to be 40.000000. Later writers suspected that the decimal point had been accidentally shifted, and that the proper value was 400.00000: but, as the details of the process for obtaining it had been lost, no further progress was made in the subject till our own time, though several most ingenious methods were tried for solving the problem.

Of these methods we proceed to give some brief account. Those chiefly worthy of note appear to be Rationalization, the Method of Indifferences, Penrhyn's Method, and the Method of Elimination.

We shall conclude with an account of the great discovery of our own day, the Method of Evaluation under Pressure.

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