Mathematical Contributions to the Theory of Evolution. 161 



not be denied that the difference is of extreme biological interest. In 

 the former case we have a comparatively small total reversion widely 

 spread ; in the latter a much larger total reversion concentrated 

 on the first stages of ancestry. Which system is more accordant 

 ■with facts ? It needs far wider observation and experiment than are 

 yet available to settle this. So far we can only say that the former 

 case covers Mr. Galton's as a special sub-case, and that the data for 

 Basset Hounds appear capable of treatment under the wider rule, but 

 can only be fitted with some straining to the special case. Are there 

 or are there not physiological reasons for supposing that resemblance 

 to a parent arises from a diff"erent source from reversion to an ancestor 1 

 Here reversion to an ancestor must not be measured by cases of 

 resemblance to an ancestor, for a portion of this resemblance is due to 

 common likeness to the parent ; we must approach the matter from 

 the standpoint of cases in which the offspring inherits a character like 

 that of the grandparent or higher ancestor, and unlike that of the 

 parent.* Current use of the term " reversion " at least justifies us for 

 the time being in not speaking of all inheritance, including likeness to 

 jjarents as reversion, and in our theory we may be permitted to dif- 

 ferentiate parental and reversional inheritance of exclusive characters, 

 if we find it needed by our numerical data. Here, as elsewhere, we 

 sadly need a widely extended range of observation and experiment. 



(10) On the VariaUlity of Basset Hounds having regard to Sex and 

 Pedigree, — We have already indicated that our justification in applying 

 the methods of normal correlation to coat-colour is considered in 

 another memoir. We merely suppose at present that there is some 

 variable, following approximately the law of normal variation, on which 

 the coat-colour can be thrown back. This being so, let h in terms of 

 this variable be the distance of its mean value from the division line 

 between tricolour and non-tricolour, and let a- be the standard devia- 

 tion of this variable for the same group. Then if x = ^V^) we easily 

 deduce by aid of tables of the probability integral from the correla- 

 tion tables in § 8 the following results : — 



* Of C and D brown-eyed parents, A and B, tlie offspringi have respectively 

 brown and blue eyes. Is the process by wliicli B gets the blue eyes of his grand- 

 father or great grandfather qualitatively different from that by which A gets the 

 brown eyes of his parents ? The problem can hardly be answered at present, 

 but I see no d priori reason for a negative. 



