5IO Journal of Agricultural Research voi. iv, no. 6 



results derived from Tables 11(A), VII(A), XXIV(A), XXXIII(A), and 

 XXXIV (A). 



(4) There appears to be a small but significant correlation between 

 sizes of litters in which sires are born and sizes of litters in which their 

 offspring are born. It seems probable that this correlation should be 

 attributed almost entirely, if not wholly, to correlation between sires 

 and male offspring. The correlations seem to differ with the sexes. 

 The correlation coefficients for sires and female offspring are so small that 

 their significance is much in doubt even with the large numbers we have 

 used. See results derived from Tables VIII (A), IX(A), XXV (A), 

 XXVI (A), XXXI (A), and XXXI I (A). 



(5) There appears to be a significant correlation between maternal 

 granddams and offspring, but we are unable to assert any significant 

 correlation for the other grandparents and offspring. It would surely 

 require immense numbers to establish the significance of such correlation, 

 if it exists. 



(6) The means of arrays show the small but general tendency of either 

 or both twin parents and twin maternal granddams to produce a larger 

 proportion of twins than are produced when the corresponding individuals 

 in the ancestry are singles. 



(7) As it requires large numbers to establish the significance of the 

 differences which we have found, it should not be surprising if within 

 a flock of fair size, say, a flock of 100, one may in some cases get even a 

 larger percentage of twins from single parents than from twin parents. 

 Such fluctuations should be expected to occur occasionally in taking a 

 random sample of no more than 100 individuals, even if in the long run 

 twins tend to produce a somewhat higher percentage of twins than do 

 singles. 



