162 



Prof. Karl Pearson. 



Table of Values of x- 



Sire 1 -0806 with all his offspring 0-3891 



„ 1-0782 „ his ^ „ 0-4242 



„ 1-1522 „ „ $ „ 0-3611 



Dam 0-1575 „ all her offspring 0-3954 



0-1315 „ her ^ „ 0-3521 



„ 0-1422 „ „ ? „ 0-3186 



Sire's sire 1-3372 „ all his offspring 0-4808 



„ dam 0-4023 „ „ her „ 0-4790 



Dam's sire 1-1536 „ „ his „ 0-4909 



Dam's dam 0-1134 „ „ her „ 0-4790 



Great grandparents .. 0-5824 „ all their offspring... 0-6592 



Wliole siblings, same litters 0-3108 



„ different litters 0-2980 



Half siblings, sire's side 0*3143 



„ 5, dam's side 0-3190 



Now, if there were no secular change due to artificial or other selec- 

 tion, h would remain the same in each generation, and therefore 

 o- = h/x would give a proper measure of the variability due to sex 

 or to relative position in ancestry. The table at once suggests a 

 number of interesting points, which I proceed to note. 



(a) Turning first to the offspring, as given in the second column, we 

 observe that the dogs with the longest pedigree have the largest x« 

 'We have, in fact, the values of 1/x for pedigrees stretching to great 

 grandparents, grandparents, parents, and merely to brethren, respec- 

 tively, as 



1-517 : 2-064 : 2-550 : 3*221, 



or, roughly, we have a geometrical series with the ratio of about 1-3. 



Now this result may be reached in more than one way, either (i) 

 decreasing h, or (ii) increasing a-. Increase of h would signify that, for 

 the longer pedigree, the mean of the quantity on which the coat-colour 

 depends is being thrust further into the tricolour section ; decrease of cr 

 would signify greater concentration in the tricolour section within 

 which the mean lies. Whether the longer pedigree signifies the more 

 modern hounds, or the more careful preservation of ancestors' names in 

 the more fashionable hounds, we reach practically the same conclusion : 

 the process of breeding is emphasising melanism. Further, by com- 

 paring the J and $ offspring in the case of both sire and dam, we 

 conclude that this process is sensibly more significant for the male than 

 the female offspring. As very often only one or two puppies out of a 

 litter are recorded in the ' Stud Book,' this apparently artificial selec- 



