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



485 



It is to be noted from Table 1 11(B) that the percentage of twins 

 varies from 33.42 to 48.21, there being a gradual increase in percentage 

 of twins when twins and triplets occur as dams and granddams. The 

 greatest influence we should ascribe to the twin dam, as the occurrence of 

 the twin granddam does not increase the percentage nearly as much as 

 does that of the twin dam. 



We hesitate to calculate a correlation coefficient from Table III (A), 

 for the reason that we have no single number to mark each selected 

 array and would not feel justified in giving an interpretation to a correla- 

 tion coefficient obtained by taking the sum or mean value of the two 

 numbers associated with each array. We might weight the dam and 

 granddam, but such a system of weights would in the present state of 

 knowledge be little better than a set of guesses. 



We may note from the means of arrays and their probable errors that 

 there can be no reasonable doubt about the significance of the difference 

 in means when in one case the dams are singles and in the other they 

 are twins. Further, it is to be observ^ed that there appears to be a 

 slight influence of twin maternal granddams in increasing mean values. 

 Such influence is not, however, nearly so surely established as is the 

 influence of the dams. In fact, the difference in the case of single and 

 twin granddams with single dams is not quite three times the probable 

 error. 



Table IV shows the frequencies with which maternal granddams born 

 in states i, 2, or 3 beget recorded offspring born in states, i, 2, or 3. 

 There is a significant correlation given by 



r = o. 0433 ± o. 0067. 



Table IV. — Correlation between offspring and maternal granddams 



Means of arrays of offspring : 



(i) When the maternal granddams are singles i. 3784±o. 0045. 



(2) When the maternal granddams are twins i. 4i2o±o. 0052. 



(3) When the maternal granddams are triplets i. 556 ±0. 033. 



Table V(A) represents the distribution of offspring, dams, and ma- 

 ternal grandsires with respect to states 1,2, and 3 in a manner analogous 

 to that of Table I II (A). Here again, when dams are twins, we note 



