28 Pedigree Moth-breeding. 



is full of variations, and although the " median " of each characteristic 

 in each brood is on the average ahvays more mediocre than the 

 corresponding characteristic in the mean of the two parents. The 

 first of these events, "fraternal variability," increases the variability 

 of the population as a whole, and the latter event, which I call 

 " Regression," decreases it ; the two can be shown to counter- 

 balance each other, and give rise to a position of stable equilibrium. 

 The five constants are (1), the Median of the race ; (2), the Quartile 

 of the race; (3), the Quartile of the broods of the same parents, 

 i.e., brothers or sisters; (4), the Quartile of broods of a large 

 number of like parents, mixed together in a single group ; (5), the 

 coefficient of Regression. The laws in which these constants play 

 a part give calculated results that prove to be closely true to 

 observation in the ordinary cases of simple heredity, where there 

 has been no long-continued selection, but it does not at all follow 

 that they will hold true for the descendants of a long succession of 

 widely divergent parents. It is this that I want to test. The 

 point towards which Regression tends cannot, as the history of 

 Evolution shows, be really fixed. Then the vexed question arises 

 whether it varies slowly or by abrupt changes, coincident with 

 changes of organic equilibrium which may be transmitted here- 

 ditarily ; in other words, with small or large changes of type. 

 Moreover, the values of the Quartile in (3) and (4) cannot be 

 strictly constant, and are probably connected in part with the 

 value of the median, and require a modified treatment by using 

 the geometrical law of error instead of the arithmetical one (Proc. 

 Royal Soc, 1879). Again, the diminution both of fertility and of 

 vitality that accompany wide divergence from racial mediocrity 

 have yet to be measured, by comparing the A and Z broods with 

 the M broods. It was assumed not to vary in the approximative 

 theory of which I spoke. 



