38 
PROFESSOR Iv. PEARSON ON MATHEMATICAL CONTRIBUTIONS 
244 in the second, to be born of exceptional parents, while 858 in the first and 756 in 
the second are born of undistinguished fathers. In the former case the odds are about 
6 to 1, in the latter 3 to 1 against a distinguished son having a distinguished father. 
This result confirms what I have elsewhere stated, that we trust to the great mass of 
our population for the bulk of our distinguished men. On the other hand it does not 
invalidate what I have written on the importance of creating good stock, for a good 
stock means a bias largely above that due to an exceptional father alone. 
In addition to this the -fj of the population forming the exceptional fathers pro¬ 
duce 142 or 244 exceptional sons to compare with the 858 or 756 exceptional sons 
produced by the of the population who are non-exceptional. That is to say that 
the relative production is as 142 to 45"2, or 244 to 39"8, i.e., in the one case as more 
than 3 to 1 , in the other case as more than 6 to 1 . In other ivords, exceptional 
fathers produce exceptional sons at a rate 3 to 6 times as great as non-exceptional 
fathers. It is only because exceptional fathers are themselves so rare that we must 
trust for the bulk of our distinguished men to the non-exceptional class. 
Illustration III. Hereditij in Coat-colour of Hounds. —To find the correlation 
in coat-colour between Basset hounds which are half-brethren, say, offspring of the 
same dam. 
Here the classification is simply into lemon and white ( Iw ) and lemon, black and 
white or tricolour (t), 
The following is the table for 4172 cases : — 
Colour. 
t. 
Iw. 
Totals. 
t. 
1766 
842 
2608 
Iw. 
842 
722 
1564 
Totals 
2608 
1564 
4172 
Proceeding precisely in the same way as in the first illustration we find : 
a 1 = a 2 = '25024 
h = Jc = '318,957 
log KH = 1T57,6378 
e= -226,234. 
It will be sufficient now to go to r 4 . We have 
•226,234 = r+ '050,£67 r a + -134,480 r 3 + '035,587 r\ 
