142 MAINE AGRICULTURAL EXPERIMENT STATION. 1909. 



quality than in the case of fertility. This is again to be 

 explained as the result of the closer selection with reference to 

 the one character than to the other. The mothers' mean fertility 

 of eggs is not significantly above the general population mean. 

 Hence the daughters' mean shows no sensible lowering as com- 

 pared with the mothers. On the other hand the mothers' mean 

 percentage of fertile eggs hatched is well above the general 

 population mean (52.96 as compared with 37.24) and conse- 

 quently it is to be expected that there will be a relatively more 

 pronounced reduction of the daughters' mean. 



Let us now examine more particularly the result stated in 

 paragraph i, viz., that there is no apparent parental inheritance 

 of these characters, fertility and hatching quality of eggs. It 

 is conceivable that the observed correlation coefficients have 

 their values reduced by the action of various circumstances 

 affecting the statistical material, not yet taken account of. In 

 other words there may be a real inheritance of these characters, 

 fertility and hatching quality of eggs, and yet it may be so 

 masked by other factors as to show no trace of itself in the 

 statistical table. It is necessary to determine, if possible, 

 whether this is the case. 



First, let us see whether the selection of mothers may have 

 been the factor which has reduced the parental correlation. It 

 has been shown by Pearson * that when the selection of a parent 

 is stringent with reference to any character, the correlation 

 between parent and offspring will be much reduced. The 

 formula covering the case which we have to deal with here is, 



i?„= 



'•4 



i^-iY' 



wherein the significance of the letters is as follows, stated in 

 terms of the present problem : 



R12 ^= correlation between mother and daughter after selec- 

 tion of mothers has occurred. This is the observed coefficient 

 of correlation of Table XXII. 



,s', = standard deviation of mothers after selection. 



<r, standard deviation of general population from which 

 mothers were drawn. 



* Phil. Trans. Roy. Soc. Vol. 200 A, p. 39. 



