Mathematical Contributions to the Theory of Evolution, 159 



possibly overworked sires lose some of their hereditary influence, 

 while not losing their power of fertilising the dam.* 



(c) The great reduction in the degeee of fraternal correlation when 

 we turn from whole to half siblings is very remarkable, and is, at any 

 rate for half siblings on the dam's side, not very explicable. 



Had we assumed the parental correlation to be 0*3507, and found 

 7 from (xxvii), i.e. = 1*4722, we should have deduced from (xxviii) 

 for the fraternal correlation the value 0*5236, which is in fair accord- 

 ance with the observed result for whole siblings. But, as we have seen, 

 (xxvii) and (xxviii) belong to a theory which gives very poor values 

 for the grandparental and great-grandparental correlations, i.e., 0*1753 

 and 0*0877, instead of 0*1326 and 0*0402. Further, we should on 

 that theory have expected the average correlation for half siblings 

 to be half the value above, since one-half of the common ancestry is 

 cut off, i.e., 0*2618, and not 0*1646, as it actually is. Thus the fra- 

 ternal correlation does not appear to be in accord with the theory of 

 blended inheritance. Its determination in the general case of exclu- 

 sive inheritance with reversion seems a problem of considerable diffi- 

 culty, which in this case is rendered much greater by the immense 

 prepotency of the dam, so that it would seem very desirable to diff'er- 

 entiate the sexes when dealing with the resemblance of siblings revert- 

 ing to ancestral types. 



(9) Ajpjplication of the Theory of Reversion to Basset Hounds. — We have 

 for mean values = 0*3507, = 0*1326, p.^ = 0*0404. Now these 

 correlations certainly do not obey the relation pi = 2/)2, p-i = ^p^ 

 required, when we take (xxiii) to govern the law of ancestral heredity 

 {'f. § 6 (iii) ). A glance at the table on p. 149 will show that such a 

 series of /o's as the above cannot fit into it. Still less do they appear 

 consonant (except to the first roughest approximation) with Mr. Galton's 

 form of that law, i.e., y = 1. Nor do they satisfy for the same reasons 

 the law of reversion when we start the reversion series from the 

 parents, i.e., put /5 = y as in § 7 (ii). 



Accordingly, I have tried to find what would be the value of ps, if pi 

 and p-2 had the values given above, and our generalised law of reversion 

 were correct. Turning to § 3, and substituting in (xviii) and (xix) for 

 Pi and p > we have : 



S = 0*286336, c = 0*698761, 



* Tliere is also to be considered the possibilitj of error of tlie record in the 

 sire's case. Griveu a large stud of hounds and servants of ayerage carelessness, and 

 a bitch may easily go astray even after she is lined by the dog required. Sir 

 Everett Millais, in a lecture on Telegony, delivered at St. Thomas' Hospital, in 1895, 

 stated that he knew of "quite two dozen such examples resulting in supposed 

 telegony." " The master is the last person to whom such little lapses of duty are 

 confided." But if two dozea mesalliances can be palmed off as telegony, how 

 many alliances within the blood may be conveniently overlooked ? 



