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THE AMEBIC AN NATURALIST [Vol. XLV 



found the genotypes of Hydra to differ in the average number of ten- 

 tacles merely by the fraction of a tentacle. That even smaller heredi- 

 tary differences are not described is certainly due only to the impossi- 

 bility of more accurate measurements; the observed differences go 

 straighl down to the limits set by the probable errors of our measures. 



Proposition 3. — These genotypes are rigid hereditary 

 units; by a process of mutation one may give rise to 

 another, but selection within the genotype is incapable 

 of effecting a change. 



This theory is everywhere so prominent in the writ- 

 ings of the genotypists that discussion or explanation is 

 superfluous. 



III. The Cardinal Proposition of the Genotype 

 Theory 



Of these three essential propositions of the genotype 

 theory of heredity, the first two might be accepted by 

 Darwinian or Lamarckian or by a member of almost any 

 school. If the proposition concerning the exceeding 

 smallness of the differences be true, the theory might 

 seem to present the greatest difficulty to the de Vriesian, 10 

 for with smaller and smaller genotypes there is a con- 

 stant approach to continuity, but we are assured that 

 continuity is never realized. 11 



The third proposition — that genotypic differences are 

 rigid and unchangeable except by mutation — is there- 

 fore the essential one. The most obvious way in which 

 this hypothesis can be tested against concrete facts is to 

 determine the effect of selection upon genotypes. 



The very heart of the pure line theory is the proposi- 



