530 EMPROVEMENT OF THE HUMAN BREED. 



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

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

 nation 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 toward the same point below, but arc 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, halfway be- 

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

 extreme 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 positions 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 tin 1 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 tilial 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 

 parentage, 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 bave been identical to the nearest ten thousandth. It was unnec- 

 essary to take the trouble of doing this, as the table affords a sufficient 

 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, tilial 

 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 knowl- 

 edge 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. 



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

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

 of the V class, which is the highest in the table. Of its 34 or 35 sons 



