108 BIOMETRY 
and both are the same as the mean height of the general 
population, the coefficient of regression is simply equal 
to the reciprocal of the correlation coefficient between 
fathers and sons. In actual practice this condition is 
seldom realized, and it is then necessary to use a more 
elaborate method in order to determine the value of 
the regression coefficient. 
Professor Pearson has extended the idea of correla- 
tion to the case of characters which are not capable of 
exact quantitative measurement. This extension is 
based upon the assumption that such characters follow 
a normal law of distribution in their variation, just in 
the same way as such a character as human stature was 
found to do. There is considerable doubt as to how 
far this assumption is justified, so that at the outset 
we may feel disposed to attach less importance to the 
actual values arrived at in this way than we should in 
the case of characters which can be shown to vary 
normally. The method of calculation actually em- 
ployed involves somewhat complicated mathematical 
processes, but on Professor Pearson’s authority we 
may assume both the validity of the method and the 
accuracy of the results obtained—so far as the actual 
process of computation is concerned. For the purpose 
of making the necessary calculations the data were 
arranged in such a form as in the table on p. 109. 
By the suitable treatment of these figures the 
value 0°45 was obtained as representing the coefficient 
of correlation between sire and filly. 
The amount of reliance which is to be placed in the 
