64 MODES OF RESEARCH IN GENETICS 



evidently a waste of time to calculate such cor- 

 relations. Further, if it cannot be clearly shown 

 that the method of determining such correlations 

 is such as to lead to a biologically valid result, 

 the application of the method in biology is 

 equally idle. As the point here under consid- 

 eration is one of fundamental importance, it 

 will be well to give it full discussion with a con- 

 crete illustration. 



It has been frequently maintained by Pearson l 

 that the "law of ancestral inheritance," which 

 states that the correlation between offspring and 

 their ancestors decreases in a geometrical progres- 

 sion as the number of included ancestral genera- 

 tions increases, involves no biological implication 

 whatever regarding inheritance. Further, it has 

 been stated on the same authority that the method 

 by which this law is deduced (namely, by determin- 

 ing the correlations which exist between offspring 

 and their ancestors) is valid whatever may be 

 the biological basis or mode of inheritance. Now, 

 as a matter of fact, practically all of the work 

 which has been done upon inheritance by Pearson 

 and his co-workers seems to the writer to involve 

 from its very beginning a fundamental biological 

 assumption. This assumption is that a correct 

 determination of the correlation in respect to 

 external, somatic characters between genetically 

 related individuals, is an adequate measure of the 



1 Cf. for example, Biometrika, Vol. II, p. 217, 1909. 



