600 Validity of the Doctrine of Mutation. 
are, in their opinion, merely the extreme deviations 
brought about by ordinary variability; 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 bulbosus semiplenus 
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 23 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 1 and statisticians. 2 It is, as KOR- 
SCHINSKY has lately shown, directly contradicted by horti- 
cultural experience; 3 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 
1 Among my numerous critics I mention here CH. SCHRODER, 
Die Variabilitdt der Adalia bipimctata L., Allgem. Zeitschrift fur 
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 butterflies. See Effects of Natural Selection 
and Race-Tendency Upon the Color-Patterns of Lepidoptera, Museum 
Brooklyn Inst. of Arts and Sc., 1902, Vol. I, No. 2, p. 31. 
2 See the journal Biometrika and especially the articles in it by 
WELDON. 
3 S. KORSCHINSKY, Mem. Acad. Imp. Petcrsbourg, 1899, IX. 
