DOES HYBRIDISATION INCREASE FLUCTUATING VARIABILITY ? 101 
mentioned famous Galtonian- law should hereafter—if my view has a 
~ general bearing—only be the statistical expression for the circumstance 
that populations mostly are mixtures, containing different “ biotypes.” 
Galton’s law is then only a statistical law, but not at all a true biological 
law. My researches, which have been of no short duration, have given 
me a very considerable stock of facts in full accordance with this view, 
thus forming a supplement to the Mendelian and Syalof experiments as 
to the appreciation of the effects of selection. And as to my researches 
we stand upon that ground—dquantitative studies—on which the still 
prevalent conception is based: that selection is able to shift a type in the 
same direction as that in which the selection of its fluctuations is 
carried on. 
This conception, which I regard as absolutely erroneous, involves the 
idea that evolution proceeds through continuous variation. 
Biological study of the behaviour of the traits that are qualitatively 
characterised, as in the classical examples of Mendel, does not usually 
require special mathematical treatment beyond some little calculation of 
probabilities. But when we attempt researches respecting quantitatively 
characterised traits, or, it may be, the fluctuations of qualitative traits, 
we must use the armoury of collective-measuring statistics. Here we 
find that a-long series of prominent mathematicians have worked out 
methods of computation and other devices. From Gauss and Laplace 
through Fechner, Quetelet-and Galton to Thiele, Lipps, Pearson, Bruns, 
Kapteyn, Udny Yule, Charlier and Davenport in modern times, the theory 
of exact observation has been developed and enriched with instructions 
for the treatment of collective series of measures. As to the finer 
methods the mathematicians are not at all in accord, and the biologist 
eager to learn from them is too often a witness to very sharp discussions 
between mathematicians as to the finer fitting of the mathematical 
implements which are offered to us. I cannot say that the nature of 
these discussions gives special reasons to regret that most of the biologists 
are not able to follow those finer methods in question. And, indeed, 
even the five or six special equations and formulas for different types of 
frequency-curves elaborated by Pearson are not of much use for 
biological students. Here I suppose that Charlier’s (7) simplification of the 
computation, giving only room for two different types of curves, represents 
areal progress. But also these formulas and equations are too compli- 
cated for general biological use ; and perhaps future mathematical specu- 
lation will give us simpler proceedings. 
After having tried to understand the fundamental principles in the 
publications of Thiele (8) and Charlier, and after studying Davenport's 
“ Statistical Methods ”’ (based especially on Pearson’s important work) (9), I 
suppose that the biologist can satisfy the claim to exactitude without too 
much trouble in all those cases where the different characters are to be 
regarded independently. In the case of correlated variability some greater 
complication is needed. When only one character is to be regarded at a 
time it is sufficient—and may be said to be necessary—to compute the 
mean value (average) of the variants, the standard deviation, and, as 
expressions for the total shape of the frequency curve, two coefficients, 
the one giving the asymmetry or skewness of the curve, the other giving 
