260 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
may pass to a general conception of regression. Let A and B be two correlated organs 
(variables or measurable characteristics) in the same or different individuals, and let 
the sub-group of organs B, corresponding to a sab-group of A with a definite value a, 
be extracted. Let the first of these sub-groups be termed an array, and the second a 
type. Then we define the coefficient of regression of the array on the type to be 
the ratio of the mean-deviation of the array from the mean B-organ to the deviation 
of the type a from the mean A-organ. The following are illustrations of types and 
arrays 
Type. 
Array. 
Organ of given magnitude in— 
Distribution of the correlated organs in— 
Parent . 
Fraternity. 
Offspring. 
Parentage. 
Wife. 
Male matage. 
Husband. 
Female matage. 
Given value of—- 
Distribution of correlated—- 
Height. 
Spans. 
Cephalic index. 
Alveolar indices. 
Barometric height .... 
Heights at second station. 
Local wages. 
Local pauper percentages. 
Etc. 
Etc. 
It will be seen in the sequel that for the same pair of correlated organs or charac¬ 
teristics. the coefficient of regression is, if the law of frequency be the normal law, 
the same for the arrays corresponding to all types. But the coefficient is not the 
same when the type and array organs are interchanged, e.g., the regression of 
husbands (male matage) on wives is not the same as the regression of wives (female 
matage) on husbands. 
(/<.) Panmixia .—Suppose that starting from a population of given mean and varia¬ 
tion for any particular organ, secular natural selection of definite amount takes place 
for p generations and produces a population of another definite mean and variation 
for this same organ. Now suppose natural selection, whether periodic or secular, to be 
suspended for q generations, and sexual selection to be non-extant or negligible, then 
those members of the general population which were formerly weeded out, will now 
mix with all the other members of the population, and the results of interbreeding 
are spoken of as panmixia. The mathematical measure of the result on the given 
organ of panmixia acting for q generations is the change in mean and variation of 
the population with regard to that organ during these q generations. Should the 
mean and variation of the population tend with increase of q to approach the mean 
and variation of the population p -f- q generations previously, panmixia may be said to 
reverse natural selection. 
