412 Mathematical Contributions to the Theory of Evolution. 



culty would be to some extent met by introducing the coefficient 7, 

 which I would propose to call the coefficient of heredity, and con- 

 sider as capable of being modified with regard to both character and 

 race. As such a law would cover Mr. Galton's case, there does not 

 seem any objection to using the more general formula, until it is 

 found that the strength of heredity is the same for all characters and 

 races. Of course it may well be argued that heredity is something 

 prior to evolution, itself determining evolution, and not determined 

 by it. If this be so, its absolute fixity for all organs and races ought 

 to be capable of observational proof. 



(ii) For the inheritance of fertility in man from parent to offspring, 

 Miss Alice Lee has recently worked out 6,000 male, and 4,000 female 

 cases. The result shows that fertility is probably a heritable cha- 

 racter, but the correlation between parent and offspring is scarcely 

 one-tenth of that given by Galton's law. The difficulties of any 

 fairly exact determination of the amount of fertility inherited in man 

 under the present artificial conditions are very great, but even allow- 

 ing for these, I think we must assert that fertility is inherited in 

 man, but in a degree very much less than Galton's law would 

 require. 



I hold, then, that, as far as our knowledge goes at present, we 

 must be cautious about treating <y as exactly equal to unity. That is 

 a, limiting value which certainly gives strikingly good results for a great 

 deal of what is yet known, but we must wait at present for further 

 determinations of hereditary influence, before the actual degree of 

 approximation between law and nature can be appreciated. Even 

 with regard to such determinations, there must be no haste to assert 

 that they actually do contradict Galton's law. That law states the 

 value of certain 'partial regression coefficients, the total regression 

 coefficients that we have deduced from them are only correct on certain 

 limiting hypotheses, the most important of which are the absence of 

 reproductive selection, i.e., the negligible correlation of fertility with 

 the inherited character, and the absence of sexual selection. I pro- 

 pose to deal with the results of Galton's law, when assortative 

 mating is taken into account, especially in the case of in-and-in 

 breeding, in another paper. At present I would merely state my 

 opinion that, with all due reservations, it seems to me that the law 

 of ancestral heredity is likely to prove one of the most brilliant of 

 Mr. Galton's discoveries ; it is highly probable that it is the simple 

 descriptive statement which brings into a single focus all the complex 

 lines of hereditary influence. If Darwinian evolution be natural 

 selection combined with heredity, then the single statement which 

 embraces the whole field of heredity must prove almost as epoch- 

 making to the biologist as the law of gravitation to the astronomer. 



