September 25, 1885.] 



SCIENCE. 



271 



try. Speaking generally, the farther his genealogy 

 goes back, the more numerous and varied will his an- 

 cestry become, until they cease to differ from any 

 equally numerous sample taken at haphazard from 

 the race at large. Their mean stature will then be 

 the same as that of the race; in other words, it will 

 be mediocre. Or, to put the same fact into another 

 form, the most probable value of the mid-ancestral 

 deviates in any remote generation is zero. 



For the moment let us confine our attention to the 

 remote ancestry, and to the mid-parentages, and 

 ignore the intermediate generations. The combina- 

 tion of the zero of the ancestry with the deviate of 

 the mid-parentage, is that of nothing with something; 

 and the result resembles that of pouring a uniform 

 proportion of pure water into a vessel of wine. It 

 dilutes the wine to a constant fraction of its original 

 alcoholic strength, whatever that strength may have 

 been. 



The intermediate generations will, each in its de- 

 gree, do the same. The mid-deviate of any one of 

 them will have a value intermediate between that 

 of the mid-parentage and the zero value of the an- 

 cestry. Its combination with the mid-parental devi- 

 ate will be as if not pure water, but a mixture of 

 wine and water in some definite proportion, had been 

 poured into the wine. The process throughout is 

 one of proportionate dilutions, and therefore the 

 joint effect of all of them is to weaken the original 

 wine in a constant ratio. 



We have no word to express the form of that ideal 

 and composite progenitor, whom the offspring of 

 similar mid-parentages most nearly resemble, and 

 from whose stature their own respective heights di- 

 verge evenly, above and below. He, she, or it, may 

 be styled the ' generant ' of the group. I shall shortly 

 explain what my notion of a generant is, but for the 

 moment it is sufficient to show that the parents are 

 not identical with the generant of their own offspring. 



The average regression of the offspring to a con- 

 stant fraction of their respective mid-parental devia- 

 tions, which was first observed in the diameters of 

 seeds, and then confirmed by observations on human 

 stature, is now shown to be a perfectly reasonable 

 law which might have been deductively foreseen. It 

 is of so simple a character, that I have made an ar- 

 rangement with one movable pulley, and two fixed 

 ones, by which the probable average height of the 

 children of known parents can be mechanically reck- 

 oned. This law tells heavily against the full hered- 

 itary transmission of any rare and valuable gift, as 

 only a few of many children would resemble their 

 mid-parentage. The more exceptional the gift, the 

 m.ore exceptional will be the good fortune of a par- 

 ent who has a son who equals him, and still more if 

 he has a son who overpasses him. The law is even- 

 handed : it levies the same heavy succession-tax on 

 the transmission of badness as well as of goodness. 

 If it discourages the extravagant expectations of 

 gifted parents that their children will inherit all their 

 powers, it no less discountenances extravagant fears 

 that they will inherit all their weaknesses and dis- 

 eases. 



The converse of this law is very far from being its 

 numerical opposite. Because the most probable de- 

 viate of the son is only two-thirds that of his mid- 

 parentage, it does not in the least follow that the 

 most probable deviate of the mid-parentage is f , or l-J 

 that of the son. The number of individuals in a pop- 

 ulation who differ little from mediocrity is so pre- 

 ponderant, that it is more frequently the case that 

 an exceptional man is the somewhat excexjtional son 

 of rather mediocre parents, than the average son of 

 very exceptional parents. It appears from the very 

 same table of observations by which the value of the 

 filial regression was determined, when it is read in a 

 different way, namely, in vertical columns instead of 

 in horizontal lines, that the most probable mid-par- 

 entage of a man is one that deviates only one-third as 

 much as the man does. There is a great difference 

 between this value of ^, and the numerical converse 

 mentioned above of |; it is four and a half times 

 smaller, since 4^, or |, being multiplied into ^, is 

 equal to f. 



Let it not be supposed for a moment, that these 

 figures invalidate the general doctrine that the chil- 

 dren of a gifted pair are much more likely to be gifted 

 than the children of a mediocre pair. What it as- 

 serts is, that the ablest child of one gifted pair is not 

 likely to be as gifted as the ablest of all the children 

 of very many mediocre pairs. However, as, notwith- 

 standing this explanation, some suspicion may remain 

 of a paradox lurking in these strongly contrasted re- 

 sults, I will explain the form in which the table of 

 data was drawn up, and give an anecdote connected 

 with it. Its outline w^as constructed by ruling a 

 sheet into squares, and writing a series of heights in 

 inches, such as 60 and under 61, 61 and under 62, 

 etc., along its top, and another similar series down 

 its side. The former referred to the height of off- 

 spring, the latter to that of mid-parentages. Each 

 square in the table was formed by the intersection 

 of a vertical column with a horizontal one; and in 

 each square was inserted the number of children out 

 of the 930 who were of the height indicated by the 

 heading of the vertical column, and who, at the same 

 time, were born of mid-parentages of the height indi- 

 cated at the side of the horizontal column. I take 

 an entry out of the table as an example. In the 

 square where the vertical column headed ^ 69- is inter- 

 sected by the horizontal column by whose side 67- is 

 marked, the entry 38 is found; this means, that, out 

 of the 930 children, 38 were born of mid-parentages of 

 69 and under 70 inches, who also were 67 and under 

 68 inches in height. I found it hard at first to catch 

 the full significance of the entries in the table, which 

 had curious relations that were very interesting to 

 investigate. Lines drawn through entries of the 

 same value formed a series of concentric and similar 

 ellipses. Their common centre lay at the intersec- 

 tion of the vertical and horizontal lines that cor- 

 responded to 68i inches. Their axes were similarly 

 inclined. The points where each ellipse in succession 



1 A matter of detail is liere ignored which has nothing to do 

 with the main principle, and would only serve to perplex if I 

 described it. 



