several Ancestor to the total Heritage of the Offspring. 405 



relative efficacy in this respect is as 58 to 51, say 114 to 100 ; accord- 

 ing to the B data, it is as 47 to 32, say 147 to 100. Taking all the 

 data together, it is as 54 to 45, say 120 to 100, or as 6 to 5. 



It does not seem to me that this ratio of efficacy of 6 to 5 is suffi- 

 cient to overbear the statistical advantages of grouping the sexes as 

 if they were equally efficient, the error in one case being more or less 

 balanced by an opposite error in the other. It is true that the 

 reciprocal forms of mating are by no means equally numerous, the 

 prevailing iendency to use tricolours as sires being conspicuous. 

 Still, as will be found later, on the application of a general test, the 

 error feared is too insignificant to be observed. Should, however, a 

 much larger collection of these data be obtained hereafter, minutiae 

 ought to be taken into account which may now be disregarded, and 

 the neglect of female prepotency would cease to be justified. 



The law to be verified supposes all the ancestors to be knoivn, or to 

 be known for so many generations back that the effects of the 

 unknown residue are too small for consideration. The amount of 

 the residual effect, beyond any given generation, is easily determined 

 by the fact that in the series \ + \ &c, each term is equal to the 

 sum of all its successors. Now in the two sets of cases to be dealt 

 with the larger refers to only two generations, therefore as the effect 

 of the second generation is \, that of the unknown residue is J also. 

 The smaller set refers to three generations, leaving an unknown 

 residual effect of J. These large residues cannot be ignored, amount- 

 ing, as they do, to 25 and 12'5 per cent, respectively. We have, 

 therefore, to determine fixed and reasonable rules by which they 

 should be apportioned. 



The requisite data for doing this are given in Table III, which 

 show^s that 79 per cent, of the parents of tricolour hounds are tri- 

 colour also, and that 56 per cent, of the parents of non-tricolour 

 hounds are tricolour. It is not to be supposed that the trust- 

 worthiness of these results reaches to 1 per cent., but they are the 

 best available data, so I adopt them. 



It will be convenient to use the following nomenclature in calcula- 

 tion: — 



a stands for a single member of the offspring. 



a,i for a single parent ; a 2 for a single grandparent, and so on, the 

 suffix denoting the number of the generation. A parallel nomen- 

 clature, using capital letters, is : — 



A stands for all the offspring of the same ancestry. 



A x for the two parents ; A 2 for all the four grandparents, and so on. 

 Consequently A n contains 2 n individuals, each of the form a n , and A„ 

 contributes (0"5) H to the heritage of each a ; while each a n contributes 

 (0-5) 2 » to it. 



In the upper part of Table IY the ratios are entered of the average 



VOL. LXI. 2 V 



