IMPROVEMENT OF THE HUMAN BREED. 225 



theoretical, that the genetic center is not and cannot be identical with 

 the parental center, but is always more mediocre, owing to the combina- 

 tion of ancestral influences — which are generally mediocre — with the 

 purely parental ones. It also shows that the regression from the 

 parental to the genetic center, in the case of stature at least, would 

 amount to two thirds under the conditions we are now supposing. The 

 regression is indicated in the diagram by converging lines which are 

 directed towards the same point below, but are stopped at one third 

 of the distance on the way to it. The contents of each parental class 

 are supposed to be concentrated at the foot of the median axis of that 

 class, this being the vertical line that divides its contents into equal 

 parts. Its position is approximately, but not exactly, half-way be- 

 tween the divisions that bound it, and is as easily calculated for the ex- 

 treme classes, which have no outer terminals, as for any of the others. 

 These median points are respectively taken to be the positions of the 

 parental centers of the whole of each of the classes; therefore the posi- 

 tions attained by the converging lines that proceed from them at the 

 points where they are stopped, represent the genetic centers. From 

 these the filials disperse to the right and left with a 'spread' that can 

 be shown to be three quarters that of the parentages. Calculation easily 

 determines the number of the filials that fall into the class in which 

 the filial center is situated, and of those that spread into the classes on 

 each side. When the parental contributions from all the classes to each 

 filial class are added together they will express the distribution of the 

 quality among the whole of the offspring. Now it will be observed in 

 the table that the numbers in the classes of the offspring are identical 

 with those of the parents, when they are reckoned to the nearest whole 

 percentage, as should be the case according to the hypothesis. Had the 

 classes been narrower and more numerous, and if the calculations had 

 been carried on to two more places of decimals, the correspondence 

 would have been identical to the nearest ten thousandth. It was un- 

 necessary to take the trouble of doing this, as the table affords a suffi- 

 cient basis for what I am about to say. Though it does not profess to 

 be more than approximately true in detail, it is certainly trustworthy 

 in its general form, including as it does the effects of regression, filial 

 dispersion, and the equation that connects a parental generation with a 

 filial one when they are statistically alike. Minor corrections will be 

 hereafter required, and can be applied when we have a better knowledge 

 of the material. In the meantime it will serve as a standard table of 

 descent from each generation of a people to its successor. 



Economy of Effort. 



I shall now use the table to show the economy of concentrating our 

 attention upon the highest classes. We will therefore trace the origin 



VOL. LX. — 15. 



