MENDELISM AND BIOMETRY 229 



horses, which would have been classed unhesitatingly 

 as instances of heredity by all biometricians in 1902. 

 Bateson's instinct did not fail him when he divided 

 these problems into those of continuity and those of 

 discontinuity respectively, although at the present time 

 the realm of continuous variation and inheritance is 

 being steadily encroached upon owing to the analysis 

 of complex characters into definite constituents. 



In 1904 Karl Pearson struck a blow at the prospect 

 of conformity between biometrical and Mendelian 

 results in his memoir, ' On a Generalized Theory of 

 Alternative Inheritance, with special reference to 

 Mendel's Laws.' Pearson's treatment of the subject 

 involved advanced mathematical reasoning, and we 

 can, therefore, only give a brief summary of his main 

 results. Pearson proposes special terms for the A and 

 the a elements respectively of a couplet or pair of 

 allelomorphs. He proposes to call the A element a 

 protogene, and the a element an allogene, and he thus 

 distinguishes between the two sorts of homozygotes 

 by calling A A a protozygote and aa an allozygote. 



Pearson considered the case of a population breeding 

 together at random, in which a single measurable 

 character, such as stature, is determined by the combined 

 action of an indefinite number of pairs of allelomorphs, 

 and he proceeded to work out the value of parental 

 correlation which was to be expected under these 

 circumstances. This value he found to be exactly 

 one-third, a value which happens to be identical with 

 Galton's original determination of parental correlation 

 from his statistics of human stature. A considerable 



