n the _average_ in a less degree. It is reduced to a
definite fraction of its amount, quite independently of what its amount
might be. The fraction differs in different orders of kinship, becoming
smaller as they are more remote. When the kinship is so distant that its
effects are not worth taking into account, the peculiarity of the man,
however remarkable it may have been, is reduced to zero in his kinsmen.
This apparent paradox is fundamentally due to the greater frequency of
mediocre deviations than of extreme ones, occurring between limits
separated by equal widths."

As to the application of this law, let Galton himself speak: "The Law of
Regression tells heavily against the full hereditary transmission of any
gift. Only a few out of many children would be likely to differ from
mediocrity so widely as their Mid-Parent [i. e., the average of their
two parents], allowing for sexual differences, and still fewer would
differ as widely as the more exceptional of the two parents. The more
bountifully the parent is gifted by nature, the more rare will be his
good fortune if he begets a son who is as richly endowed as himself, and
still more so if he has a son who is endowed yet more largely. But the
law is evenhanded; it levies an equal succession-tax on the transmission
of badness as of goodness. If it discourages the extravagant hopes of a
gifted parent that his children on the average will inherit all his
powers, it not less discountenances extravagant fears that they will
inherit all his weakness and disease.

"It must be clearly understood that there is nothing in these statements
to invalidate the general doctrine that the children of a gifted pair
are much more likely to be gifted than the children of a mediocre pair."
To this it should be added that progeny of very great ability will arise
more frequently in proportion to the quality of their parents.

It must be reiterated that this is a statistical, not a biological, law;
and that even Galton probably goes a little too far in applying it to
individuals. It will hold good for a whole population, but not
necessarily for only one family. Further, we can afford to reemphasize
the fact that it in no way prevents the improvement of a race by
selection and assortative mating.

Stature is the character which Dr. Galton used to get an exact
measurement of the amount of regression. More recent studies have
changed the value he found, without invalidating his method. W