with special reference to Right- and Left- Handedness. 509 



Clearly the mode of clasping the hands is inherited in some 

 way : it remains to find a reason why neither the right- nor the 

 left-handed character breeds true. 



It seems probable to us that the explanation is to be found 

 in the "accidental" conversion of genetically right-handed in- 

 dividuals into the left-handed condition, and vice versa. If this 

 were the case, among a number of apparent rights there would be 

 a certain proportion of genetic lefts ; so that their failure to breed 

 true to the right-handed character would in part be due to the 

 admixture of genetically left-handed persons with the apparently 

 right-handed. Further, the same possibility of accidental reversal 

 would apply to the offspring, so that, even if genetically pure right- 

 handed individuals interbred, a certain proportion of the children 

 would appear to be left-handed. All this would of course apply 

 equally to the mating of the left-handed, real and apparent. 



Making certain assumptions as to the way in which accidental 

 causes affect the appearance of a character it is easy to see how 

 the inheritance of the character will be modified. The simplest 

 assumptions seem to be that a constant proportion of individuals 

 are affected, and that the change takes place indifferently in either 

 direction. Let the population consist of true homozygous domi- 

 nants {BD), heterozygotes {DR), and homozygous.recessives {RR) 

 in the proportion 



DD.DR: RR = p : 2q : r. 



Then for stability through successive generations the equation 



pr = q^ (1) 



must be satisfied*. 



Now let 6 be the fraction of accidental changes taking place 

 either way, so that the apparent distribution of dominants to 

 recessives will be given by 



{p + 2q) (1 — ^) + rO _ number of dominants (D) 

 r(l — d) + (p-\-2q)6 number of recessives (J?) " 



The value of this ratio is of course known from a count of the 

 population. 



We assume that the mating is random, and examine first the 

 offspring resulting from the mating of apparent dominants. Since 

 the proportion of true dominants to factitious ones in the apparent 

 dominants is 



(p + 2q)(l-d):rd, 

 the true matings will be in the proportion 



dominant x dominant : dominant x recessive : recessive x recessive 



= {{p + 2q) (1 - d)Y ■.2r(p + 2q) {1-6)6: r'6\ 



* G. H. Hardy, Science, N.S., xxviii. 1908, p. 49. 



