LAW OF ANCESTRAL LNHERITANCE 327 



inadequate nurture, are smoothed out. It is noteworthy that 

 in the case of Mendehan phenomena, which some regard as 

 fatal to Galton's Law, there is frequently a very precise pro- 

 portion in the numbers of offspring favouring the two original 

 parental types which were crossed at the beginning of the ob- 

 served lineage. 



But the general worth of Galton's Law is not invalidated, 

 though it be found with further inquiry that the series \ -\- \ + \ 

 -I- yV +• • • •» should be replaced by some other series. In point 

 of fact, Pearson's studies led him to conclude that the series 

 0*6244, 0"i988, o"o630, etc., was more accurate than the series 

 o"5, o'25, 0'i25, etc. 



Pearson's Statement of the Law of Ancestral Inheritance. — 

 Galton's Law states that in a given generation the average herit- 

 age is made up of ancestral contributions — \ parental, \ grand- 

 parental, I great-grandparental, and so on. 



This is a statistical conclusion, not a physiological inter- 

 pretation. It deals with average heritages and applies to masses 

 rather than to the component individuals considered separately. 

 Thus he says, " The neglect of individual prepotencies is justified 

 in a law that avowedly relates to average results " (1897, p. 402). 



But while Galton did not mean his Law to apply to individual 

 cases, it must be approximately true of a large number of indi- 

 vidual cases in any generation. If it is true as an average 

 formula, it must find approximate illustration in a large number 

 of individual cases, though the precise fractions \ -\- \ -\- \ 

 -1- . . . ., will not apply. 



Prof. Karl Pearson has given a statement of the law of ancestral 

 inheritance somewhat different from Galton's, but his methods 

 and general results are practically the same. The following 

 quotation (1903a, p. 215) is useful : 



" Taking our stand, then, on the observed fact that a know- 

 ledge neither of parents nor of the whole ancestry will enable 

 us to predict with certainty in a variety of important cases the 



