INHERITANCE, WITH SPECIAL REFERENCE TO MENDEL'S LAWS. 



77 



and is quite independent of the number of couplets. It is, however, a function of ^, 

 the size of the family used in forming the table. We have the following values : 



The value of fraternal correlation thus varies with the size of the family dealt with 

 from '3 to '4. Probably the more correct way of looking at any fraternal correlation 

 table would be to suppose it a random sample of all the pairs of brothers which would 

 be obtained by giving a large, or even indefinitely large, fertility to each pair, for 

 what we actually do is to take families of varying size and take as many pairs of 

 brethren as they provide. In this case we ought to reach a fraternal correlation of '4. 

 precisely the value reached by the ancestral law when we take FRANCIS GALTON'S 

 original series of ancestral correlations.* 



Thus we conclude that on the general theory of the pure gamete here dealt with, 

 the fraternal correlation is slightly larger than the parental. This is in accordance 

 with the general result of biometric investigations on populations. But the value, as 

 in the case of the parental correlation, is very sensibly lower than the value-- --about 

 '5 found from recent investigations on man. It is further very inelastic even if we 

 allow r for some variation in the size of families dealt with. There can be little doubt 

 that fraternal correlation varies from character to character and species to species in 

 a manner sensibly beyond what can be accounted for by differences in the size of the 

 family dealt with.f 



Corollary. We can exhibit the regression in the form : 



Mean of array mean of general population 



_ v\ - p.) Deviation O f brother from mean of general population}, 

 1 + v 



by observing that 1 /x = |-(l + "/*)> whence 



* ' Roy. Soc. Proc.,' vol. 62, p. 410. 



t There is sensible variation even for different characters, when we take the same series of pairs of 

 brothers, and only one pair from each family. 



