264 PROFESSOR K. PEARSON AND MR. L. N. G. FILON 



second will tend to produce a correlation between the third and fourth, i.e., if 

 r, 2 = r, 4 = ?%, = r.,4 = 0, we still have from (xl.) 



(e.) We may further illustrate these principles by one or two hypothetical examples 

 drawn from actual organs. 



Let the actual organs be (1) physique of father, (V) artistic sense of mother, 

 (3) physique of offspring, (4) artistic sense of offspring. Suppose in the general 

 population there is no correlation between physique of father and artistic sense of 

 mother, or between physique or artistic sense of parent, and artistic sense and 

 physique respectively of offspring. Then r n = 0, r H = 0, r.,% = 0, and, presumably, 

 r 34 = 0. Hence 



B v = V 



is the product of the two coefficients for inheritance of physique from father to 

 child, and for inheritance of artistic sense from mother to child. 



Now let a random selection be made out of the general population in which assor- 

 tative mating between physique in the male and artistic sense in the female presents 

 itself, i.e., let Ar,._> be sensible ; then we have, most probably, 



Ar :u Pi, [3 , 3i -i Ar ]2 = r n r, 4 Ar,,, 

 *""u 



or, a correlation between physique and artistic sense in the offspring will tend to be 

 developed. Generally, when r ;!4 and r n do not start from zero, we have, 



A ,- 'Vil + 2?W,t01.1 + 9'il) . 



(1 - rtf 



or, any increase of sexual selection in a group tends to emphasise the correlation of 

 the selected qualities in the offspring. 



Let the three characteristics be artistic sense (1) in a man, (2) in his mother, (3) 



in his wife. Then 



i s _ ,3 



*D 1 ~ ' I 4 * ' 13 



if we suppose n 3 to be zero. 



Hence any selected group with a higher coefficient of maternal inheritance of 

 heredity will have a less coefficient of sexual selection than the general population, 

 and vice versd. The tendency is, of course, independent of the magnitude of r, and 

 really of the particular character. Supposing likeness of faculty or character to be 

 a rough measure of " sympathy," we might conclude for any population with inheri- 

 tance and sexual selection, that on the average a selected sub-group of men having 

 greater sympathy with mothers than the general population will have less sympathy 

 with wives, and vice versd. 



