No. 590] SHOBTEB ARTICLES AND DISCUSSION 



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families, 61 are affected with cataract. This suggests that the 

 character is more likely to be inherited as a recessive than as a 

 dominant. Surely it is not possible to explain so many cases as 

 origin de novo or as due to faulty classification of the parents. 



In the second category given above (B), where one of the 

 parents is affected and the other normal, the number of defec- 

 tive children would be expected to be approximately the same 

 whether the character was inherited as a dominant or a recessive. 



If the abnormality is considered as a recessive character, the 

 ratio of 61 affected to 92 unaffected, already spoken of as having 

 been obtained in the first category of families, shows an excess 

 of recessives over the simple Mendelian expectancy for a mono- 

 hybrid. This is to be expected since the criterion for including 

 any family in the tabulation is the production of at least one 

 abnormal child. In families with a small number of children 

 it is probable that in some cases only normal children are pro- 

 duced in matings of heterozygote by heterozygote which should 

 give, on the average, one fourth recessive. The observed re- 

 sults must then be compared to a modified Mendelian ratio which 

 will allow for the omission of all-normal progenies. Such ratios 

 have been calculated by Apert (4) and by Wright (5). The 

 expected proportions given here are calculated according to the 

 method given by the latter. 



The proportion of recessives varies according to the number 

 of children in the family and ranges, for a three-to-one ratio, 

 from 100 per cent, in families with one child to very nearly 25 

 per cent, in families with fifteen children. The proportion is 

 calculated from the formula 



Z = 4[i-(!)-Y 



where N is the number of children. Since the criterion for in- 

 cluding any family is the production of one abnormal child, 

 all families with one child must have 100 per cent, abnormal chil- 

 dren. The proportion decreases, according to the law of chance, 

 as the number of children in the family increases, finally reach- 

 ing 25 per cent, as the number of children becomes large. 



Table I compares the results obtained with the theoretical ex- 

 pectancy, worked out according to this method. 



The method used for testing the agreement of the observed 

 result with the theoretical is the one given by Pearson (6) and 

 Elderton (7) . It was originally used to test various series of bio- 



