600 Validity of the Doctrine of Mutation. 



are, in their opinion, merely the extreme deviations 

 brought about by ordinary variabihty ; for the further 

 these are from the mean, the rarer they are, and the 

 greater are the intervals by which they are separated. 

 The number of petals in Ranunculus hulbosus semiplcniis 

 oscillates around 9 or 10, frequently reaching 14, very 

 seldom 20-23. Only in one case did I observe a larger 

 number, which happened to be 31 (see p. 252). The 

 gap between 22> and 31 is, however, not a discontinuous 

 variation. It is perfectly normal, and quite a common 

 occurrence in this part of Quetelet's curves. In a 

 general way, gaps of this kind in the curves of variation 

 may be thus explained, and according to my opponents 

 the so-called springs and jumps have to be explained in 

 the same manner. They are assumed to be no more than 

 the extreme variants of series which when investigated 

 further, would prove to be continuous ones. 



This view is chiefly maintained against my opinion 

 by morpholgists^ and statisticians.^ It is, as KoR- 

 SCHINSKY has lately shown, directly contradicted by horti- 

 cultural experience ;'^ and the absence of transitions and 

 the stability of my new species of Oenothera prove that, 

 in this case at any rate, true mutations do occur. The 

 greatest obstacle in the way of agreement on this point, 

 however, lies in the phenomena of transgressive varia- 

 bility, which to the morphological observer so often give 



' Among- my numerous critics T mention here Ch. Schroder, 

 Die J'ariahilitat dcr Adalia hif^uuctata L., Allgeni. Zeitschrift fiir 

 Entomologie, Vols. VT-VIT, 1901-1902. The view taken by Schroder 

 has since been proved to be erroneous by the experiments of A. G. 

 Mayer on the colors of Initterflies. See Effects of Ahifural Scleciion 

 and Race-Tendency Upon the Color-Patterns of Lcpidoptera, Museum 

 Brooklyn Inst, of Arts nnd Sc, 1902, Vol. I, No. 2, p. 31. 



^ See the journal Biometrika and especially the articles in it by 

 Weldon. 



^ S. KoRSCHiNSKV, Mem. Acad. Imp. Petershourg, 1899, TX. 



