January 5, 1899] 



NA TURE 



139 



same. The number of students last year was 1 171. If any one 

 figure can be taken as a measure of the efficiency of a well- 

 conducted school, it is the ratio of the total number of students 

 to the number of instructors in actual service. In the case of 

 the Institute of Technology, without counting lecturers, there 

 is one instructor to every eight or nine students— one of the very 

 highest ratios in the United States. 



SOCIETIES AND ACADEMIES. 



London. 



Royal Society, December S, 1S98. — " Mathematical Contri- 

 butions to the Theory of;Evolution. VI. Reproductive or Genetic 

 Selection. Part I. Theoretical." By Karl Pearson. " Part 

 II. On the Inheritance of Fertility in Man." By Karl Pearson 

 and Alice Lee. " Part III. On the Inheritance of Fecundity 

 in Thoroughbred Race-horses." By Karl Pearson, with the 

 .assistance of Leslie Bramley-Moore. 



The object of this memoir is twofold : first, to develop the 

 theory of reproductive or genetic selection ' on the assumption 

 that lertility and fecundity may be heritable characters ; and, 

 secondly, to demonstrate from two concrete examples that 

 fertility and fecundity actually are inherited. 



The problem of whether fertility is or is not inherited, is one 

 of very far reaching consequences. It stands on an entirely 

 different footing to the Question of inheritance of other char- 

 acters. That any other organ or character is inherited, pro- 

 vided that inheritance is not stronger for one value of the organ 

 or character than another, is perfectly consistent with the 

 organic stability of a community of individuals. That fertility 

 should be inherited is not consistent with the stability of such a 

 community, unless there be a diflerential death-rate, more intense 

 for the offspring of the more fertile, i.e. unless natural selection 

 or other factor of evolution holds reproductive selection in 

 check. The inheritance of fertility and the correlation of fertility 

 wiih other characters are principles momentous in their results 

 for our conceptions of evolution ; they mark a continual tendency 

 in a race to progress in a definite direction, unless equilibrium 

 be maintained by any other equipollent factors, exhibited in the 

 form of a differential death-rate on the most fertile. Such a 

 diflerential death-rate probably exists in wild life, at any rate 

 until the environment changes and the equilibrium between 

 natural and reproductive selection is upset. How far it exists 

 in civilised communities of mankind is another and more diffi- 

 cult problem, which I have partially dealt with elsewhere. At 

 any rate it becomes necessary for the biologist either to affirm 

 or deny the two principles stated above. If he affirms them, 

 then he must look upon all races as tending to progress in 

 definite directions — not necessarily one, but possibly .several 

 different directions, according to the characters with whicli fer- 

 tility 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 

 lecundity contained in Parts II. and III. of the present 

 memoir. 



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

 fertility be a function of any physical characters which are 

 ihemselves inherited according to the law of ancestral heredity, 

 ihen 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. 



Further points dealt with are the influence of "record- 

 making " on apparent fertility and fecundity. The fertility of 

 mothers is always found to be more and their variability 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. 



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 be- 

 tween a latent character in one sex and a patent character in 



1 I have retained the term "reproductive" selection here, although 

 objection h;i^ been raised to it, because it has been used in the earlier 

 memoirs of this series. Mr. Gallon has kindly provided me with "genetic" 

 and " proliferal" selection. The term is used to describe selection of pre- 

 dominant types owing to the different grades of reproductivity being in- 

 herited, and without the influence of a differential death-rate. 



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. 



The effect of a mixture of correlated and uncorrelated ma- 

 terial on correlation and variation is next investigated, and it is 

 shown that the former is more seriously aft'ected than the latter. 

 Incidently the problem of the mixture of heterogeneous 

 materials uncorrelated in themselves is investigated, and it is 

 shown that a correlation will result in the mixture. This spurious 

 correlation 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 correlation is zero. 



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 inoves up towards 

 he value required by the law of ancestral heredity. 



The inheritance of fertility from father to son is then considered ; 

 this is really rather an inheritance of sterility or tendency to 

 sterility, for the full fecundity of a man is not usually exhibited 

 in monogamic union. It is rather a problem of whether his 

 fecundity lasts as long as his wife's. We find definite inheritance 

 from father to son of this sterile tendency, although for the 

 reason just given it falls below that indicated by the law of 

 ancestral heredity. 



Lastly, the inheritance of fertility in the woman through the 

 male line is dealt with, and it is shown that a woman's fertility 

 is as highly correlated with that of her paternal as with that of 

 her maternal grandmother. In other words the latent character, 

 fertility in the woman, is transmitted through the male line, 

 and with an intensity which approximates to that required by 

 the law of ancestral heredity. 



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

 laborious investigation into the fecundity of brood-mar;s, which 

 has been a number of years in progress. 



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

 mare. 



{2) It is also inherited from grand-dam to mare through the 

 dam. 



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

 indicated by the law of ancestral heiedity, but the divergence i^ 

 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 considering probable. 



(3) The latent quality, fecundity in the brood-mare, is in- 

 hetiled through the sire ; this is shown not only by the cor- 

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

 correlation between the latent character in the sire and the patent 

 character in the daughter. 



(4) The latent quality, fecundity in the brood-mare, is in- 

 herited 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 inheritaiice 

 approaches much more closely to that required by the Galtonian 

 rule. 



Parts II. and III. accordingly force us to the conclusion that 

 fertility is inherited in man and fecundity in the horse, and 

 therefore probably that both these characters are inherited in all 

 types of life. It would indeed be difiicult to explain by evolu- 

 tion the great variety of values these characters take in allied 

 species, if this were not true. That they are inherited according 

 to the Galtonian rule seems to us very probable, but not demon- 

 strated to certainty. It is a reasonable hypothesis until more 

 data are forthcoming. 



Paris. 



Academy of Sciences, December 26, 189S.— XL Wolf in 

 the chair. —Some peculiarities of the elasticity of muscle explained 

 by comparison of the case of muscular substance in action w ith 

 that of inert materials, by M. A. Chauveau. An experimental 



NO. 1523, VOL. 59J 



