262 



Prof. K. Pearson. On a Criterion which may [Mar. 4, 



" On a Criterion which may serve to Test various Theories of 

 Inheritance." By Karl Pearson, F.B.S., University College, 

 London. Eeceived March 4, — Read March 17, 1904. 



(1) One of the most difficult problems in the treatment of heredity 

 is that of obtaining a satisfactory criterion which will enable us to dis- 

 tinguish the truth or falsehood of various hypotheses. As a rule, all 

 the criteria used have been based upon a determination of the type of 

 offspring due to parents of selected types. Unfortunately such a 

 method of approaching the problem of heredity fails wholly to reach 

 some of the most important modern theories, for the reason that these 

 theories start from the assumption that the type of the offspring is 

 not any, or at least any precise and simple function of the parental 

 types. The type is said to be a factor which at present can only he 

 determined by direct observation or by experimental crossing. 



Mr. Galton in his ' Natural Inheritance,' it is true, used the term 

 " midparent " to denote an individual compounded, in a simple way, 

 from the two parental types, and giving offspring of a definite type. 

 In generalising, however, Mr. Galton's conceptions in my " Law of 

 Ancestral Heredity,"* I purposely placed before myself the aim 

 of reducing the theory to a purely statistical theory, and discarded 

 entirely the conception that the type of offspring was settled by the 

 parental types. The generalised midparent of any generation became 

 a compound of the deviations from type of the ancestry of that 

 generation, and no assumption was made as to any inheritance of 

 absolute type ; the theory became purely a statistical theory of the 

 distribution in various generations of the deviations from type. At 

 a somewhat later date the Mendelians gave up the conception that 

 the- type of the offspring was known from the parental types. The 

 actual effect of crossing two individuals was compared to the formation 

 of a chemical compound, the character of which could not a priori 

 be predicted from the known nature of the components. It was a 

 matter to be determined by observation or experiment only. With 

 this wider view the original Mendelian theory of " dominant " and 

 " recessive " characters has disappeared, and that theory has thus far 

 approximated itself to the " Ancestral Law." 



In a second paper communicated to the Eoyal Society! entitled the 

 " Law of .Reversion," I endeavoured to work out a general theory of 

 alternative inheritance, on the hypothesis that a certain number of the 

 offspring were for any character like one or other parent or like 

 some one or other ancestor, the proportions of offspring like ancestral 

 types diminishing in number with the distance of descent. This 



* ' Roy. Soc. Proc.,' vol. 62, pp. 387 and 388. 

 t ' Roy. Soc. Proc.,' vol. 66, p. 142 et seq. 



