No. 546] MENDELIAN PROPORTIONS 345 



should, after all the long period of its existence, find 

 only a few persons with the condition. 



On the " presence and absence" theory lefthandedness 

 is due to the loss or "dropping out" of the factor or de- 

 terminer for righthandedness. If such loss could occur 

 in the past, why not from time to time now? If so, why 

 would not the proportion of lefthanded people continu- 

 ally increase? 



In a population where the dominant, the heterozygote 

 and the recessive have a certain proportion, slight 

 changes in the relative numbers seem to have no perma- 

 nent effect. There is a tendency to stability and unless 

 a certain point is passed because of the appearance of an 

 unusual number of recessives, there will be a return to 

 the usual ratio. The mathematical features of the case 

 have been discussed by Dr. W. J. Spillman, 4 and by Mr. 

 Gr. H. Hardy. 5 The earliest clear statement of the case 

 which I have seen is by Dr. George H. Shull 6 in his dis- 

 cussion of elementary species in Bursa bursa-pastoris. 



The fact of the stability of certain ratios and instabil- 

 ity of others can be readily comprehended from the fol- 

 lowing tables (I, II, III). We may let RR represent a 

 pure righthanded individual, Rr, a heterozygous right- 

 handed individual, and rr, a lefthanded individual. As 

 a first example it may be supposed that a large popula- 

 tion exists in which the various types occur in the fol- 

 lowing proportions, viz. : 



1 pure righthanded : 2 heterozygous righthanded: 

 1 lefthanded, or, 

 RR:2Rr:rr. 



Random matings would occur in such fashion that mem- 

 bers of each group would mate with those of their own 

 group or with members of other groups. The various 

 possibilities are represented in Table I. The filial gen- 



