PROF. K. PEARSON ON TOE MATHEMATICAL THEORY OF EVOLUTION. 257 
individuals, are said to be correlated, when a series of the first organ of a definite size 
being selected, the mean of the sizes of the corresponding second organs is found to be 
a function of the size of the selected first organ. If the mean is independent of this 
size, the organs are said to be non-correlated. Correlation is defined mathematically 
by any constant, or series of constants, which determine the above function. 
The word “ organ ” in the above definitions of variation and correlation must be 
understood to cover any measurable characteristic of an organism, and the word 
“ size,” its quantitative value. 
(c.) Natural Selection. —This is of two kinds: Secular Natural Selection is 
measured by the changes due solely to mortality, in the mean and standard deviation 
of the variation-curve as we pass from one adult generation to the next. In 
statistical observations on man it is by no means easy—as we shall indicate later—to 
differentiate it from the effects of sexual selection, and of altered sanitary conditions. 
Periodic Natural Selection may leave no trace of itself in the adult variation-curves 
of successive generations ; it is measured by the changes due solely to mortality in 
the mean and standard deviation of the variation curves at successive stages of the 
same generation— due allowance being made for the changes of the variation-constants 
due to growth. In other words, if we watched a generation from birth to the adult 
stage, carefully preserving it from any form of selective mortality, such as arises from 
the struggle for existence, we should still find changes in the variation-constants due 
to the law of growth. Tf now the same generation be subjected to the struggle for 
existence, i.e., placed in its natural surroundings, the variation-constants will differ 
from their values at the corresponding stages of the unselected growth. This 
difference is due to the selective mortality, i.e., to natural selection. But this 
selective mortality may go on and still leave the variation-constants of the adult 
stage of each generation the same. In this case we speak of it as periodic natural 
selection. It repeats itself in each generation, but produces no secular change. It 
maintains an adult standard, but is not a factor of progressive evolution. 
No estimate of periodic natural selection can be formed until the law of growth 
has been accurately ascertained by a series of observations on individuals. The 
influence of secular natural selection will be allowed for in our investigations by 
supposing the means and standard deviations of successive adult variation-curves to 
be not necessarily the same.* 
(d.) Sexual Selection. —Sexual Selectiont is of two kinds, due respectively to what 
* Variation-curves for non-adult populations appear to be frequently skew. I propose in another 
‘paper to discuss the general law of selection on the basis of skew curves and with any arbitrary law of 
growth. 
t I think Darwin’s view would be of the following kind. Let A be the most attractive female, a the 
most efficient male, Z the least attractive female and z the least efficient male. Then supposing only 
these four, a. and z would both desire A with the result that (1) a would drive away z or (2) kill him. 
In the first case z would be free to mate with Z, but if he did so they would tend to produce a miserable 
MDCCCXCVI.—A. 2 L 
