

INHERITANCE, WITH SPECIAL REFERENCE TO MENDEL'S LAWS. 65 



Secondly. That this correlation appears to vary slightly from character to 



character. 

 Thirdly. That it does not appear to be absolutely the same for all species. 



It is most unfortunate for this general theory of the pure gamete, that it throws 

 the Mendelian back into the position of the biometrician of 1885.* One might have 

 hoped that the generality involved in n couplets would have led to the requisite 

 elasticity, or, failing this, to a numerical value of parental correlation nearer the 

 cluster point of existing measurements than ^. We can only say, at present, that a 

 generalised theory of the pure gamete leads to precisely the same general features of 

 regression as have been observed by the biometricians, but it appears numerically too 

 narrow to describe the observed facts. 



(7.) PROPOSITION V. To find the Standard Deviation of the Array of Offspring 

 due to Fathers with s-allogenic Collets. 



We have to find the standard deviation cr s of the combination of binomials dealt 

 with in the previous proposition. Each component standard deviation must, of 

 course, be weighted with the total frequency of the component, and there must be 

 the proper reduction to the mean of the array as a whole. 



The (i + l) th binomial (%u -f ?')"- ; has V\n i)% X t for its standard deviation, 

 and the distance of its mean from the mean of the array 



= [n +"l - (i + 1 + 1 (n - i))} - [$n - J- (n - *)} 



~ ~ ~~ s ) ~~ 2^' 



~S 



Further, the frequency of this component is 



We thus see that it contributes 



i , 



-+ 



n s 2 



3 2 



to the total second moment about the mean of the array. This gives us 

 f * T'-' v , r 2 - 



/! x 6 x <r s = 



* " GALTON'S law makes the amount of inheritance an absolute constant for each pair of relatives. It 

 would thus appear not to be a character of race or species, or one capable of modification by natural 

 selection." More ample statistical experience of populations since 1885 shows that absolute constancy of 

 the heredity coefficients is not consonant with actual measurements. ' Roy. Soc. Proc.,' vol. 62, p. 411, 



t 'Phil. Trans.,' A, vol. 185, p. 373. 



VOL. CCIII. A, K 



