662 



NA TURE 



[October 31, 1901 



above," to the nearest ten-thousandth. They may be read 

 either as applying to fathers and their sons when adult, or to 

 mothers and their daughters when adult, or, again, to parent- 

 ages and filial couplets. I will not now attempt to explain 

 the details of the calculation to those to whom these methods 

 are new. Those who are familiar with them will easily 

 understand the exact process from what follows. There 

 are three points of reference in a scheme of descent which 

 may be respectively named "mid-parental," "genetic" and 

 "filial" centres. In the present case of both parents being 

 alike, the position of the mid-parenlal centre is identical with 

 that of either parent separately. The position of the filial 



STANDARD SCHEME OF DESCENT 



centre is that from which the children disperse. The genetic 

 centre occupies the same position in ihe parental series that the 

 filial centre does in the filial series. " Natural Inheritance " 

 contains abundant proof, both observational and theoretical, 

 that the genetic centre is not and cannot be identical 

 with the parental centre, but is always more mediocre, 

 owing to the combination of ancestral influences— which 

 are generally mediocre— with the purely parental ones, 

 'he regression from the parental 



It also shows 



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 approxi- 

 mately, but not exactly, half-way between the divisions that 

 bound it, and is as easily calculated for ihe 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 centres 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 

 centres. From ihescithe 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 centre 

 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 corre- 

 spondence 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 sufficient basis 

 for what I am about to say. Though it 

 does not profess to be more than approxi- 

 mately true in detail, it is certainly trust- 

 worthy in its general form, including as 

 it does the effects of regression, filial dis- 

 persion, 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 mean- 

 time 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 concen- 

 trating 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, 6 come from V parentages, 10 

 from U, 10 from T, 5 from S, 3 from R, 

 and none from any class below R. But 

 the numbers of the contributing parent- 

 ages have also to be taken into account. 

 When this is done, we see that the lower 

 classes make their scores owing to their 

 quantity and not to their quality; for 

 while 35 V-cIass parents suflice to pro- 

 duce 6 sons of the V class, it takes 2500 

 R-class fathers to produce 3 of them. 

 Consequently the richness in produce of V-class parentages is 

 to that of the R-class in an inverse ratio, or as 143 to i. Simi- 

 larly, the richness in produce of \-cla.ss children from parentages 

 of the classes U, T, S, respectively, is as 3, iii and 55, to i. 

 Moreover, nearly one-half of the produce of V-class parentages 

 are y or U taken together, and nearly three-quarters of them 

 are either V, U or T. If then we desire to increase the output 

 of V-class offspring, by far the most profitable parents to work 



NO. 1670, VOL. 64] 



