166 Mathematical Contributions to the Theory of Evolution. 



their mothers, while there is a small drop only in their average fertility. 

 In other words, an " heiress " is not to be looked upon as coming in 

 general from a sterile stock, but as having a mother, whose fertility 

 has a fictitious value, i.e., the apparent fertility of the record is not 

 the potential fertility, the inherited character, in the mother. In 

 other words " heiresses " are not as a rule due to sterile mothers, but in 

 the bulk are due to such causes as late marriages, restraint, incompati- 

 bility of husband and wife, absence of sons or death of other children, 

 &c., &c. 



7. Part III of the memoir contains the results of a somewhat 

 laborious investigation into the fecundity of brood-mares, which has 

 been a number of years in progress. Had better material been avail- 

 able for the inheritance of fecundity, we would gladly have adopted it 

 in preference to dealing with such an intricate subject as the breeding 

 of race-horses. Unfortunately the absence of place and means hindered 

 any experimental investigation on our part into the inheritance of 

 fecundity in some simpler type of life. Such investigation ought 

 certainly to be made by a trained biologist with the knowledge and 

 the laboratory at his disposal. 



After discussing at length the steps taken by us to measure and 

 tabulate the fecundity of brood-mares, we deduce the following con- 

 clusions : 



(i.) Fecundity in the brood-mare is inherited from dam to mare, 

 (ii.) It is also inherited from grand-dam to mare through the dam. 



In both these cases the intensity is much less than would be in- 

 dicated by the law of ancestral heredity, but the divergence is not such 

 that it could not be accounted for by a percentage of fictitious values 

 such as the peculiar conditions of horse-breeding warrant us in con- 

 sidering probable. 



(iii.) The latent quality, fecundity in the brood-mare, is inherited 

 through the sire ; this is shown not only by the correlation 

 between half-sisters, but by actual determination of the corre- 

 lation between the latent character in the sire and the patent 

 character in the daughter. 



(iv.) The latent quality, fecundity in the brood-mare, is inherited by 

 the stallion from his sire. This is shown not only by the 

 fecundity correlation between a sire's daughters and his half 

 sisters, but also by a direct determination of the correlation 

 between the latent quality in the stallion and in his sire. 



In both these cases of latent qualities the law of inheritance ap- 

 proaches much more closely to that required by the Galtonian rule 

 This is probably due to the fact that the determination of the correla- 

 tion is thrown back on the calculation of the means and variabilities of 



