702 



THE AMERICAN NATURALIST [Vol.L 



Both Pearl 13 and Jennings 14 have followed him in this point. If 

 the thousand litters studied by Parker and Bullard come from a 

 population homozygous and heterozygous with respect of a pair 

 of rudimentary nipples in the 1:2:1 proportion and mating at 

 random, 15 then three out of four males as compared with one out 

 of four females should, if Wentworth's hypothesis be correct, 

 show the pair of rudimentaries. Thus the average number of 

 mammae in the males should be 1 higher than in the females. As 

 a matter of fact it is .529 ± .024 higher. 



Further discussion on the basis of the present data would of 

 course be idle. 



In his largest paper Wentworth 16 has presented data which 

 indicate sensible parental and grandparental correlations for 

 number of mammae. In view of the irregularity of the frequency 

 distributions due to the modes on the even numbers and the 

 smallness of the series, as well as the fact that the number of 

 boars was very limited, little weight is to be given to the exact 

 numerical values of his coefficients. 



A more detailed analysis of the extensive series of data col- 

 lected by Parker and Bullard may throw considerable light upon 

 the problem of inheritance. The results must be expressed in 

 terms of fraternal or sororal correlation. Those who are so ob- 

 sessed with Mendelian theory that they are unwilling to learn 

 anything about a series of data for which their method fails, 

 should discontinue the reading of this review at this point. 



Correlation between the number of nipples in siblings may be 

 very readily found by means of intra-class correlation formulae 17 

 involving first and second moments for the individual classes 

 (litters). 



Let x m be the number of nipples in a male, Xf the number of 

 nipples in a female pig, n m the number of males and n f the num- 

 ber of females in a litter of n m + n f = n individuals. Let 2 

 denote summation within the litter and 8 a summation for litters. 

 For any litter the moments are therefore S(s m ), 2(z m 2 ), 2(%), 



"Pearl, E., Amer. Nat., 47: 606-609, 1913. 



1* Jennings, H. S., Genetics, 1 : 64, 1916. 



"Random mating of course applies only to the particular character in 

 question, which is one which would hardly be consciously selected by any 



"Wentworth, E. N„ "Inheritance of Mammae in Duroc Jersey Swine," 

 Amer. Nat., 47: 257-278, 1913. 



"Harris, J. Arthur, Biomeirika, 9: 446-472, 1913. 



