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



507 



In order to eliminate the possible effects of the repetitions of grandsires, 

 we shall investigate further the cases of maternal grandsires and dams by 

 means of index numbers, such as are explained in the sections on "Anal- 

 ysis of data for sires and offspring" and "Tables for sires and offspring." 

 The results with such index numbers may be stated as follows : 



For maternal grandsires bom in singles, we have i. 4462 ±0. 0073. 



For maternal grandsires bom in twins, we have i. 4574 ±0. 0093. 



While the mean index number for twin maternal grandsires is thus a little 

 larger than for single maternal grandsires, the difference is not large 

 enough to enable us to assert its significance, when compared to fluctua- 

 tions in sampling. 



Tables XXXII to XXXIV are correlation tables for sizes of litters in 

 which sires and male offspring, dams and male offspring, and dams and 

 female offspring are bom. In each of these cases we find significant 

 correlations. The differences of these correlations are so small that we 

 are unable to assert that the differences are significant. The values of 

 these correlation coefficients are : 



For sires and male offspring r =0. 073 ±0. 012. 



For dams and male offspring r=o. o75±o. on. 



For dams and female offspring r=o. 0925±o. 0080. 



Table XXXII(A). — Correlation between male offspring and sires 



Means: 



For sires i. 43io±o. 0066. 



For male offspring i. 4i8o±o. 0067. 



Table XXXII(R). — Percentages of the male offspring in states I, 2, and j to correspond 

 to the states i, 2, and j of the sires 



