No. 632] SHORTER ARTICLES AND DISCUSSION 279 



/4N + %n = gametes from F x males, 

 3 / 8 NN + %Nn + %™ F 2 zygotes, 

 normal cataractous 



That is, % of the F 2 calves should be normal and % should be 

 cataractous. The observed results agree with the calculated 

 rather better than one would usually expect, for the observed 

 = 55 normal + 8 cataractous and the calculated = 55.125 nor- 

 mal +7.875 cataractous. The 8 F 2 cataractous calves were of 

 both sexes (2 heifers and 6 bulls). 



All these facts clearly indicate that the original sire, E. T. H., 

 was heterozygous, Nn. If mated to his own daughters he should 

 give results similar to those of his son, V. H. He was thus tested 

 and produced 7 offspring of which 3 (1 bull and 2 heifers) were 

 cataractous. Collecting all matings of the sire, E. T. H., and 

 his son, V. H. (both were Nn)'to P, daughters (NN + Nn) we 



59 11 70 



61.25 [ 8.75 I 70 



We may therefore conclude that congenital cataract in cattle is a 

 simple recessive Mendelian character. 



To prevent the reappearance of cataractous individuals in this 

 stock and to reduce the proportion carrying cataract as a re- 

 cessive is a matter of some economic importance. After all cat- 

 aractous individuals have been eliminated, there still remain one 

 half of the daughters and four sevenths of the granddaughters 

 of E .T. H. which carry a recessive factor for cataract. We can 

 not distinguish between the NN and Nn individuals, since N is 

 evidently dominant to n. Whatever the proportion of these two 

 types may be to each other, mating the cows to normal unrelated 

 bulls (which are almost unquestionably NN) will eventually re- 

 duce the cataractous-bearing individuals to a negligible mini- 

 mum. If we begin with r + s individuals of the genetic consti- 

 tutions NN and Nn respectively, and we back cross to normal 

 stock, NN, any number of times, p, then the genetic composition 

 of the last generation produced after p such back crosses will be 



[2*r+(2*— l)*]NN + *Nn. 



