Volume I 
AUGUST, 1902 
No. 4 
THE MOST SUITABLE PEOPOETION BETWEEN 
THE VALUES OF FIKST AND SECOND PEIZES. 
By FRANCIS GALTON, F.R.S. 
A CERTAIN sum, say £100, is available for two prizes to be awarded at a 
forthcoming competition ; the larger one for the first of the competitors, the 
smaller one for the second. How should the £100 be most suitably divided 
between the two ? What ratio should a first prize bear to that of a second one ? 
Does it depend on the number of the competitors, and if so, in what way ? Similar 
questions may be asked, but will not be answered here, when the number of prizes 
exceeds two. What should be the division of the £100 when three prizes are to 
be given, or four, or any larger number ? 
The interest of this memoir does not depend solely upon the answer to the 
above questions, but more especially on its bringing to evidence a new property of 
the law of frequency of error, upon which I stumbled while engaged upon a side 
branch of the inquiry. The problem then before me (of which the results are 
still unpublished) was the probability that the winner of a first or of a second 
prize in a given year, would succeed in winning first or second prizes in subsequent 
years. The data assumed the following form : — 100 winners of a first place 
supplied in(l) winners of a fiist place, and n{l) winners of a second place in 
subsequent years, while 100 winners of a second place supply m (2) winners of 
a first place and n (2) winners of a second place. What are the future prize- 
winning capacities of winners of first and second places respectively ? Let the 
most appropriate values of fii'st and second prizes be called a and /3, then 
a _a.m(l) + /3 .n{l) 
a.m{2) + ^ .n{2y 
whence ^ can be determined. 
Having found its value for the cases with which I was dealing, I sought to 
compare it with another obtained through the ordinary law of frequency of error, 
on the following bases : 
Biometrika i 41 
