No. 600] SHORTER ARTICLES AND DISCUSSION 



753 



mality in a haploid or a diploid state meeting with a heterozy- 

 gous normal, in random mating, which would be necessary to 

 produce affected children. According to Danforth's calcula- 

 tions the probability of heterozygotes in the general population 

 is one in thirty. He shows that Harman's tables give in some 

 eases as high as eight out of nine individuals mating with nor- 

 mals and producing affected children, thereby showing that the 

 normals are heterozygous on the recessive hypothesis. In the 

 previous publication we did not give consideration to this point 

 which is of noteworthy significance and we are indebted to the 

 writer for calling our attention to it. 



This apparently high proportion of heterozygotes in the gen- 

 eral population would be a serious objection to our simple re- 

 cessive hypothesis if it were not for the fact that there is a con- 

 siderable amount of consanguinity recorded in the pedigrees 

 given by Harman. With each of the pedigrees including from 

 one to many families there is a definite statement as to whether 

 a record was made and, if so, whether or not consanguinity was 

 present. Tabulating these statements shows that in sixty of the 

 pedigrees no record was made. In twenty-four no consanguinity 

 and in eleven consanguinity was definitely recorded. Then in 

 those cases in which a record was made nearly 50 per cent, of 

 the pedigrees show more or less intermarrying. Altogether 

 there are seventeen cousin marriages. 



With this amount of intermarrying among affected stocks the 

 proportion of heterozygous individuals carrying the abnormality 

 in a simplex condition would be greatly increased over the pro- 

 portion in the general population, and Danforth's most serious 

 objection to our hypothesis loses its force. Evidently no con- 

 sideration was given to this point when he says " a more strik- 

 ing refutation of the assumption could hardly be found" (p. 

 447). 



With regard to the second main condition which is raised 

 against the assumption of cataract as a single, recessive, unit 

 character Danforth seems to be partly in error, if we understand 

 his statement correctly. He states: "If congenital cataract 

 were recessive the normal children of a cataraetous parent should 

 themselves produce affected children in half as many cases as do 

 their cataraetous sibs, and the total number of affected children 

 produced should be one half as great in the first case as in the 

 second " (p. 446). Since on the recessive hypothesis only het- 

 erozygous normal and homozygous abnormal sibs are produced 



