284 



SCIENCE. 



[N. S. Vol. IX. No. 217. 



record, she is agaia weighted with her fer- 

 tility. 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 variabilitj' less than the 

 fertility and variability of daughters. Ac- 

 cordingly from the apparent fertility and 

 variability of the record the actual values 

 in each genei-ation must be deduced. The 

 difBculties and the theory of this investiga- 

 tion 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 re- 

 sults 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 relationship, e. g., half- 

 sisters, and we rapidly get numbers too 

 large for forming correlation tables in the 

 usual manner. Accordingly methods are 

 developed for finding correlation coefBcients 

 from the means of ' arrays.' These methods 

 are of considerable importance, for they 

 enable us to ascertain the correlation be- 

 tween 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 correla- 

 tion 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. 



5. The brood-mare is for many causes, 

 detailed at length in the paper, a highly ar- 

 tificial product, and accordingly the record 

 gives a considerable percentage of fictitious 

 fecundities. The efifect of a mixture of 

 correlated and uncorrelated material on 

 correlation and and variation is next inves- 



tigated, and it is shown that the former is 

 more seriously affected than the latter. 

 Hence results based on variation are more 

 likely to be trustworthy than those which 

 use correlation. Incidently the problem of 

 the mixture of heterogeneous materials un- 

 correlated in themselves is investigated, 

 and it is shown that a correlation will re- 

 sult in the mixture. This spurious correla- 

 tion is of some importance for the question 

 of mixtures of classes in fertility problems, 

 but it is also significant of the general 

 danger of heterogeneity in bio-statistical 

 investigations, and further indicative of the 

 possibility of creating correlation between 

 two characters by breeding between small 

 heterogeneous groups in which this correla- 

 tion is zero. This illustration suflSces to 

 indicate how correlation between characters 

 does not necessarily indicate a causal rela- 

 tionship. 



6. Part II of the memoir deals with the 

 inheritance of fertility in man. It is first 

 shown by large numbers that fertility is 

 undoubtedly inherited from mother to 

 daughter, but that if we include all types 

 of marriages the inheritance is largely 

 screened by other factors. An attempt is 

 made to remove one by one these factors) 

 and the more stringently this is done the 

 more nearly the regression of daughter on 

 mother moves up towards the value re- 

 quired by the law of ancestral heredity. 

 If we could take onlj^ marriages in which 

 both daughter and mother were married 

 during the whole of their fecund period 

 there is little doubt that we should find in- 

 heritance according to the law of ancestral 

 heredity. The sparseness of homogeneous 

 material hinders, however, such an investi- 

 gation. 



The inheritance of fertility from father 

 to son is then considered ; this is really 

 rather an inheritance of sterility or ten- 

 dency to sterility, for the full fecundity of 

 a man is not usually exhibited in mono- 



