96 
PROFESSOR K. PEARSON AND DR. A. LEE ON 
sires than grandsires. This is a rule I have now found true in a very great number 
of cases of inheritance. Parents are a fairly closely selected body of the general 
population, and so less variable than that population at large. This might appear 
pretty obvious in the case of thoroughbred horses when we are dealing with sires and 
grandsires. I have already pointed out that it was impossible to take 1000 to 1300 
colts or fillies with as many independent sires, the fashion in sires is too marked; and 
of course the number of independent grandsires was still fewer.* But even in the 
case of dams, where we have taken as many independent dams as fillies, we see this 
reduction in variability in the older generation. As it also occurs with stature, &c., 
in man as well as with coat-colour in horses—in which latter case we expect artificial 
selection—it deserves special consideration. Without weighting with fertility, there 
exists a selection of the individuals destined to be parents in each generation. We 
have to ask whether the change in mean and variability from parent to offspring in 
each generation is secular or periodic, or to what extent it is partly one and partly 
the other. The importance of settling this point is very great; it concerns the 
stability of races. So far as my fairly numerous series of measurements yet go, 
I cannot say that a “ stable population ” has definitely shown itself; the characters of 
each race when measured for two generations seem to vary both in mean and 
standard deviation. Palaeontologists tell us of species that have remained stable for 
thousands of years, but this is a judgment hitherto based on a qualitative apprecia¬ 
tion. A quantitative comparison of the means, variabilities, and correlations of some 
living species in its present and its fossil rej^resentatives would be of the greatest 
interest and value. For myself, I must confess that my numerical investigations so 
far tend to impress me with the unstable character of most populations. 
(b.) There is fairly good evidence that the horse is more variable than the marc in 
coat-colour. It would be idle to argue from the first four results of Table III. that 
the mare is more variable than the horse, in that these results show the dam to be 
more variable than the sire. For, as we have shown, the process of breeding and our 
method of extracting the data tend to produce a much more intense selection of sires 
than of dams. But if we compare the mean hay range in terms of the standard 
deviation of colts for our seven series of colts with that for the seven series of fillies 
in Table III., we find for the first 1'27458 cr c and for the second 1'33854 oy. Hence 
we are justified in concluding that ay is greater than ay. In fact in only one case out 
of the seven does the series of fillies give a less variability than the corresponding 
series of colts, i.e. , colts corresponding to dams are somewhat less variable than fillies 
corresponding to dams. It must, however, be remembered that this conclusion is 
based upon the coat-colour of the animals recorded as yearling foals, t Thus, the coat- 
* For some account of the extent of in and in breeding in the thoroughbred horse, see my memoir on 
“ Reproductive Selection,” ‘ Phil. Trans.,’ A, vol. 192, p. 257 ct seq. 
t The reader must always bear in mind that when we speak of the variability of colour in sire or 
dam, Ac., it means the variability of this class when they were yearlings. 
