20 Life and Letters of Francis Galton
array," the word array suggesting that we are dealing with a wider group than a single family.,
The next idea raised by Galton is very important for later researches. He goes to the root of his law of regression when he states that the somatic character of the parents does not fully define the somatic character of the offspring. The somatic character of the parents is not the full representative measure of the germ plasm of the stirp. This is represented by a long series of ancestors, who become so numerous as we go backward, that their mean value for a generation cannot differ from mediocrity. Regression in Galton's view is the result of the influence of parental heredity pulling the offspring so to speak tovJLrds the parental value and the mediocrity of the more distant ancestry pulling towards its own value of the character.
Now we may or we may not know something of the ancestry behind the first midparent. If we know nothing absolutely then the fact that the first midparent has a certain character value enables us to predict a certain probable value for the next midparent and so on. If we did know completely the ancestry, we might replace the whole ancestry by a single midancestor. To this midancestor, we may give the name "generant." Again we had better cite Galton's own words, because although the idea is suggestive he does not define it in a manner which enables us to determine mathematically its nature. From what we said above it is clear that we may have a true generant and a probable generant based on only a partial knowledge of the ancestry*.
Galton's Conception of the Generant.
" The explanation of it [Regression] is as follows : The child inherits partly from his parents, partly from his ancestry. Speaking generally the further his genealogy goes back, the more numerous and varied will his ancestry 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 midancestral deviates in any remote generation is zero.
" For the moment let us confine our attention to the remote ancestry and the midparentages, and ignore the intermediate generations. The combination of the zero of the ancestry with the deviate of the midparentage is the combination 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 the strength may have been.
"The intermediate generations will each in their degree do the same. The midderiate in any one of them will have a value intermediate between that of the midparentage and the zero value of the ancestry t. Its combination with the midparental deviate 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 midparentages most nearly resemble, and from whose stature their own, respective heights diverge evenly above and below. If he, she or it, is styled the "generant" of the group, then the law of regression makes it clear that parents are not identical with the generants of their own offspring."
* Journ. Anthrop. Instit. Vol. xv, pp. 252-3.
f This sentence is not, I think, correct as it stands. A man might easily have four grandparents all taller than his parents. Galton probably meant to insert the words "on the average."