Multiple Influences 165 



had been influenced by neither factor; and the medium- 

 sized individuals in which the two factors had neutralized 

 each other. If the two latter had the same appearance, the 

 distribution of forms would be therefore 25 per cent short, 

 50 per cent medium, and 25 per cent tall. 



If we imagine four factors to be at work, two favorable 

 and two unfavorable, the general course of distribution 

 would be similar, but the number of classes would be five. 

 In such a population, 37.5 per cent would be of medium 

 size; and there would be an equal proportion of extremely 

 tall and extremely short amounting to 6.25 per cent each; 

 and 25 per cent would be considered medium-tall, and 25 

 per cent would be considered medium-short. For every one 

 in which both favorable factors had operated there would be 

 another one in which the two unfavorable factors had ex- 

 erted their influence. And for each one of these there would 

 be four in which the two favorable factors met one un- 

 favorable factor, and an equal number in which two unfavor- 

 able factors were in part neutralized by one favorable factor; 

 and there would be six individuals in which the favorable 

 factors either neutralized the unfavorable ones or in which 

 neither of these supposed influences operated. 



When the number of factors is increased to ten, for each 

 individual that had all of the influences in his favor there 

 would be ten with one favorable factor replaced by an un- 

 favorable one, and 120 in which there had been seven favor- 

 able and three unfavorable factors at work, while in 250 cases 

 the favorable and unfavorable factors counteracted each 

 other. 



The mathematician can thus find from the distribution 

 of types of variation mentioned that a very large number of 

 factors must be at work, some making for greater growth, 

 or for more pigment, or for more milk production, and so 

 on, and some factors working in opposite directions. 



The ordinary fluctuations that we find in any group of 

 plants or animals would seem from these considerations to 

 result from slight variations in the conditions that influenced 



