674 



THE AMERICAN NATURALIST [Vol. LI 



twin rams and twin ewes are significantly better breeders 

 than singles. Just why this result is obtained here in the 

 face of other contradictory data is difficult to understand. 



In order to combine the results of the two types of pedi- 

 grees it was deemed advisable to utilize the ratio of 

 1:4.118 twins to singles discovered by examination of 

 volumes 9 to 12, respectively, in order to have the normal 

 relationship between twins and singles. This involved 

 dividing the numbers of individuals in the twin group or 

 multiplying those in the single group. In the first case 

 errors would be increased, due to the elimination of cer- 

 tain groups, while in the second case errors would be in- 

 creased due to the exaggeration of differences between the 

 random sample in the pedigrees begun from single births 

 and the normal distribution of such a population. It was 

 deemed best to use the second method, since it permitted 

 the retention of the small groups, hence the ratio 1:4.118 

 was multiplied by the ratio 3,715 : 5,311, the numbers of 

 individuals in the pedigrees from twin and single births, 

 respectively, which gave the multiplying factor 5.887 for 

 the pedigrees started from single births. Of course, this 

 result is only suggestive; but it was impractical to record 

 the additional 4,300 odd pedigrees necessary to get a true 

 random distribution. Treated this way, multiplying Table 

 V by 5.887 and adding to Table IX, Table XV is produced. 



Trcatirm the Mie> a-^ in T.iblc> \'J and \, Table X\ 1 

 produced. 



