Mutation Within Mutation Periods. 209 



necessary consequence of the continuation of the cause, 

 which gave rise to the first deviation, however shght it 

 may have been.^ 



A sharp distinction between the selection and the 

 mutation theory was not drawn at the time when Del- 

 BOEUF was writing, so that his attention was directed 

 indiscriminately to both of them. I shall consider the 

 application of Delboeuf^s thesis to the latter only. And 

 I shall further limit my analysis to the consideration of 

 those cases in which the new form is immediately con- 

 stant, and this, as we saw in § 25, is almost always the 

 case. 



Delboeuf starts with the supposition that a mutation 

 does not arise only once but is given off e^•ery genera- 

 tion in a definite although perhaps a small number of 

 individuals for just so long as the cause of the mutation 

 continues. He further supposes that the new form can 

 multiply in peace, and that its increase is neither aided 

 nor hindered by the struggle for existence. Under these 

 conditions the new form must always increase in numl)cr 

 of individuals in relation to the parent form with a speed 

 which will vary directly with the percentage of mutating 

 individuals produced in each generation. From a knowl- 

 edge of this percentage one could calculate the number 

 of generations it would take for the new form to equal 

 the old one in number, and also how man}- years must 

 elapse before the new form entirely replaces its pro- 

 genitor. 



In the numerical tables of Delboeuf's paper some 



of the more important cases are worked out in detail. 



The general principle, however, is quite clear: A ncn' 



^J. Delboeuf, Ein auf die Umzvandlungsthcoric anzvendharcs 

 mathcmatischcs Gesets, Kosmos, 1877-1878, Jahrg. i, Bd. II. pp. 

 105-127, especially p. 112. 



