Sept. IS. 191S Resemblance of Parents and Offspring of Sheep 



491 



offspring recorded, say, with two individual offspring recorded, the index 

 number may fall only into one of the three classes, i, 2, or 1.5, when we 

 neglect the rare case of triplets. For index numbers approaching i but 

 not equaling i, a larger number of offspring is required; for example, it 

 would require at least 7 offspring, 6 bom in singles and i in twins, to 

 enter the class i.i, and it would require at least 6 twins and i single to 

 enter class 1.9. 



These facts seem to account for the smaller numbers contiguous to 

 the ends of the range than are found at other intermediate points. 



ANALYSIS OF DATA ON SIRES AND PATERNAL GRANDPARENTS 



Tables X (A) and X (B) represent the distribution of paternal grand- 

 dams and sires of offspring treated in Tables II and IX. The means of 

 arrays show that the tendency to produce twins is increased by the use 

 of twin sires instead of singles sires, but that this tendency is not changed 

 significantly by the use of twin paternal granddams instead of single 

 paternal granddams. 



This result is further supported by obtaining from Table XI (A) for 

 the correlation coefficient 



r= —0.0 100 ±0.0084. 

 We are thus unable to assert the existence of a significant correlation. 



Table X(A). — Correlation between offspring and paternal granddams 



Means of arrays of offspring: 



(i) When sire and paternal granddam are singles 



(2) When sire is a single and paternal granddam is a twin 



(3) When sire is a twin and paternal granddam is a single 



(4) When sire is a twin and paternal granddam is a twin 



(5) When either sire or paternal granddam is a triplet. . 



I. 3828±o. 0067. 

 i-3754±o. 0072. 

 1. 4376±o. 0093. 

 I. 4003 ±0. 0082. 

 I. 520 ±0. 025. 



