OF A CERTAIN PENNSYLVANIA FAMILY. 79 



the same strain who possessed a lower degree of the characteristic in 

 question. 



Again we may regard an occurrence of calculating ability as due to a 

 number of determiners, a single dose of determiners producing a lower 

 ability than a double or quadruple dose, their joint action not differing 

 in kind, but differing only in quantitative effect. Here, too, if the num- 

 ber of determiners is relatively large, there is the probability of an 

 individual who shows high ability carrying a larger number of these 

 determiners than the number carried by one who shows low ability; 

 but whether this ability be due to a single determiner varying in potency 

 or to several determiners, we may now profitably ask what measure of 

 agreement do we find between behavior of these hypothetical deter- 

 miners and the behavior of dominants and recessives in the typical 

 Mendelian proportion? 



If we let C stand for comparative presence of determiners for cal- 

 culating ability, and c stand for their comparative absence, we have 

 the following combinations possible in the union of germ-plasms: 

 CC, Cc, cc. CC would develop relatively high calculating abiUty, 

 which we may indicate by H. Cc would develop mediocre abiUty, 

 indicated by M. cc would develop very low or no calculating ability, 

 indicated by L. 



Distribution of these abilities from various types of mating may be 

 represented as follows: 



cc and cc = 100 per cent cc. All children show very low or no ability. 



Cc and cc = 50 per cent Cc and 50 per cent cc. Half the children show medium 



abihty, half very low or no abiUty. 

 Cc and Cc = 25 per cent CC and 50 per cent Cc and 25 per cent cc. One-fourth 



the children show high ability, half show medium, and one-fourth 



very low or no ability. 

 cc and CC = 100 per cent Cc. All children show medium abiUty. 

 Cc and CC = 50 per cent Cc and 50 per cent CC. Half show medium ability and 



half high ability. 

 CC and CC = 100 per cent CC. All children show high abiUty. 



In the studies of distribution as actually occurring in the networks 

 under consideration, the germinal constitution has been inferred in 

 accordance with the formulae just given, that is, low abiUty has been 

 taken to indicate the germinal constitution cc, or all germ-cells without 

 determiners necessary for calculating ability; in the same way, medium 

 ability indicates the germinal constitution Cc, or half the germ-cells 

 with sufficient determiners and half without; while high ability indi- 

 cates the germinal constitution CC, or all germ-cells with sufficient 

 determiners for the functioning of this faculty. 



We will examine first the distribution of various grades of this 

 ability from parent to offspring in the Rufer group. Although measure- 

 ments are far more difficult than with most physical traits, still we may 

 arbitrarily fix the following three classes, the various grades of the 



