164 Prof. K. Pearson, Miss A. Lee, and Mr. Bramley-Moore. 



he affirms them, then he must look upon all races as tending to pro- 

 gress in definite directions not necessarily one, but possibly several 

 different directions, according to the characters with which fertility 

 may be correlated the moment natural selection is suspended ; the 

 organism carries in itself, in virtue of the laws of inheritance and the 

 correlation of its characters, a tendency to progressive change. If, on 

 the other hand, the biologist denies these principles, then he must be 

 prepared to meet the weight of evidence in favour of the inheritance of 

 fertility and fecundity contained in Parts II and III of the present 

 memoir. 



2. The theory discussed in Part I opens with the proof that if fer- 

 tility be a function of any physical characters which are themselves 

 inherited according to the law of ancestral heredity, then it must itself 

 be inherited according to that law. As fertility would certainly appear 

 to be associated with physique, we have thus an a priori argument in 

 favour of its inheritance. 



3. In the next place the influence of " record " making on apparent 

 fertility is considered. The mother with more offspring has a greater 

 chance than one with fewer of getting into the record which extends 

 over several generations, and, further, if every possible entry be taken 

 from the record, she is again weighted with her fertility. Thus a 

 record is not a true account of the fertility of successive generations. 

 The fertility of mothers is always found to be more and their varia- 

 bility less than the fertility and variability of daughters. Accordingly 

 from the apparent fertility and variability of the record the actual 

 values in each generation must be deduced. The difficulties and the 

 theory of this investigation are developed at some length, and methods 

 determined by which it can be ascertained whether a secular change in 

 fertility is actually taking place. The results obtained are extended 

 to fecundity. 



4. In the case of thoroughbred horses, their number is so few and 

 in-breeding so great owing to the fashion in sires and stocks, that we 

 have to deal with a large array of offspring of the same sire. It is 

 easy accordingly to obtain 50,000 to 150,000 pairs of a given relation- 

 ship, e.g., half-sisters, and we rapidly get numbers too large for form- 

 ing correlation tables in the usual manner. Accordingly methods 

 are developed for finding correlation coefficients from the means 

 of " arrays." These methods are of considerable importance, for they 

 enable us to ascertain the correlation between a latent character in one 

 sex and a patent character in another, or between characters latent 

 in two individuals. Thus, it is shown that the correlation between the 

 brood-mare's fecundity latent in two related stallions can be deduced 

 from the correlation between the mean fecundities of their two arrays 

 of daughters. In this way a numerical estimate can be formed of the 

 inheritance of latent characters. 



