282 MEMORIES OF MY LIFE

analogous problem that interested me a few years previously [159]. I have had more than once to assist in determining how a given sum allotted for prizes ought to be divided between the first and second men when only two prizes are given. The same problem has to be solved by the judges of cattle shows, and it is, if a little generalised, of very wide application. I attacked it both theoretically and practically, and got the same results both ways. When the number of candidates is known, and the distribution of merit follows the well-known Gaussian law, the calculation is easy enough, but when the number of candidates is not known it is a different matter ; moreover, the Gaussian law may not apply to the case, though it will probably do so pretty closely. So I calculated what the ratios would be in classes of different numbers and according to the Gaussian law. The ratio in question is that between' the excess of the first performance over the third, and the excess of the second performance over the third. The third being the highest that gets no prize at all, forms the starting-point of the calculation. When the numbers of candidates were either 3, 5, 10, 20, 50, Too, i,ooo, io,ooo, or 100,000, I found, to my surprise, that the ratio was much the same. The appropriate portion of the total of one hundred pounds which should be allotted to the first prize proved to be seventy-five pounds, leaving twenty-five or one-third of its amount for the second prize. Even when the number of candidates were at the minimum of 3, the first prize would be £67 ; if 5, it would be £7 r ; if 10, it would be £73; and if ioo,ooo, it would be 675 (to the nearest whole figures).