22 NATURE AND NURTURE 



yellow balls. We will now make the remainder of our 

 card-drawings, another n-p, but if x-u hearts occur, 

 we shall not take x-u yellow balls, but draw another n-p 

 balls at random out of the bag of balls. Let us suppose 

 the result to be y-u yellow balls. The total number of 

 yellow balls will no longer be the same as the total 

 number of hearts, only u hearts and balls are certainly 

 the same, x~u hearts and y-u balls have been obtained by 

 perfectly independent processes, and these numbers are in 

 no way related to each other. The absolute value of y, the 

 number of yellow balls, is no longer fixed, but the average 

 v^alue of y for a given value of x, the average number 

 of yellow balls when a given number of hearts has been 

 drawn, can easily be determined, either theoretically or 

 experimentally. If we take the ratio of the deviation of 

 the mean value of y for a given value of x from the mean 

 value of all y^s to the deviation of the given value of x 

 from the mean of all values of x, this ratio is constant 

 and equal to /)/m, i.e. to the number of cases of absolute 

 association of hearts and balls to the total number of 

 draws. This quantity is clearly less than unity, and 

 becomes zero as we reduce the number of associated cases. 

 It is termed the coefficient of correlation, and clearty 

 measures the ratio of the number of absolutely associated 

 contributory causes to the total number of such causes. 



Now you must not go away with the idea that this 

 illustration is the theory of correlation. It is not so, 

 but it will give you a suggestion as to the actual nature 

 of correlation. The theory of correlation is a calculus 

 by which we measure the ratio of the common causal to 

 the non-common contributory factors in two variable 

 quantities. If we measure a character in father and son, 

 these resemble each other in part because they are due to 



