102 REPORT OF THE CONFERENCE ON GENETICS. 
what Pearson calls the ‘“ excess,’ i.e. indicating whether, and in what 
manner, the curve surpasses the limits of a binomial curve, skewness not 
regarded. Of course the total number of observations, m, must also be 
given. With these five indications the fluctuating variability of a stock 
as to the traits in question should mostly be sufficiently characterised. 
The computation of the mean (average, A) and the standard deviations 
(c) are well known. The skewness will be determined by the average 
value of the third powers of deviations from the mean (y,= (xf): ; see 
Davenport, “ Statistical Methods,” 2nd edit. p. 116. By complete symmetry 
p3=O0). As the simplest coefficient of skewness the relation p3: 07 may 
be regarded ; this expression being absolutely independent of any theory 
of variation. As empirical skewness, therefore, can be indicated S=pz : o°. 
As to the “excess,” it must be remembered that the average value of the 
fourth powers of deviations from the mean (u,=(a#4/) : 2) shall in case of 
the normal binomial frequency curve be py=8o'. Hence py: o4=3 in- 
dicates that there is no excess. Therefore the formula H=(p, : o4)—38 
gives the value and the sign of excess. This value E is, like §, an 
abstract number and also absolutely independent of any theoretical view 
of variability. 
As to the method of computation, I must refer to the highly practical 
computation scheme of Charlier, with its excellent controlling system. 
For the suggestion to limit the computation to the estimation of E and 
S without following any hypothesis of different types of variation-cunyes 
I am indebted to Thiele. 
When the biologist in this way is content to use these simple mathe- 
matical methods, the legitimacy of which is granted by all authorities, he 
is able to characterise his series of variation in a manner which gives a 
very good description of the variability. It is still a desideratum to deter- 
mine how good the accordance—as to S and E—may be between different 
series of the same organisms, e.g. the sections of the same pure line in 
culture in the same garden, &c. The variations in the environments 
may here give greater disturbances than in respect to the standard devia- 
tion. Special researches on this question have been commenced. 
As to biological questions concerning heredity and fluctuating varia- 
bility, it must again and again be emphasised that to procure the facts is the 
most important but most difficult point in the whole matter. To gather 
materials from forests, fields and gardens, or—as to man—to send in- 
quiry papers to families, schools and other institutions, may be good for 
many purposes of social statistics, but it is a quite fallacious method for 
biological research into heredity questions. And it is a fundamental 
error to believe that the inspection of variation-curves and correlation- 
tables can give any certainty to conclusions as to heredity in the true 
biological or physiological sense of this word. Pearson has, not only in 
working out his ideas of homotyposis, but perhaps still more by his 
recent researches (10) in the mental character of school-children, totally 
omitted to analyse the causes which may be the condition of greater 
resemblance between brothers and sisters than between children in 
general. In my own materials of beans I have observed a much greater 
resemblance between sister-beans than between other beans of the same 
pure line, and yet all these different individuals (or homotypical organs) 
