508 NATURE 
is due to the number of variable elements of which the stature is 
the sum. The best illustrations I have seen of this regularity 
were the curves of male and female statures that I obtained from 
the careful measurements made at my Anthropometric Laboratory 
in the International Health Exhibition last year. They were 
almost perfect. 
The multiplicity of elements, some derived from one progeni- 
tor, some from another, must be the cause of a fact that has 
proved very convenient in the course of my inquiry. It is that 
the stature of the children depends closely on the average stature 
of the two parents, and may be considered in practice as having 
nothing to do with their individual heights. The fact was proved 
as follows :—After transmuting the female measurements in the 
way already explained, I sorted the children of parents who 
severally differed 1, 2, 3, 4, and 5, or more inches into separate 
groups. Each group was then divided into similar classes, 
showing the number of cases in which the children differed 1, 2, 
3, &c., inches from the common average of the children in their 
respective families. I confined my inquiry to large families of 
six children and upwards, that the common average of each 
might be a trustworthy point of reference. The entries in each 
of the different groups were then seen to run in the same way, 
except that in the last of them the children showed a faint 
tendency to fall into two sets, one taking after the tall parent, 
the other after the short one. Therefore, when dealing with the 
transmission of stature from parents to children, the average 
height of the two parents, or, as I prefer to call it, the ‘* mid- 
parental ” height, is all we need care to know about them. 
It must be noted that I use the word parent without specifying 
the sex. The methods of statistics permit us to employ this 
abstract term, because the cases of a tall father being married to 
a short mother are balanced by those of a short father being 
married to a tall mother. I use the word ‘‘ parent” to save a com- 
plication due to a fact brought out by these inquiries, that the 
height of the children of both sexes, but especially that of the 
daughters, takes after the height of the father more than it does 
after that of the mother. My present data are insufficient to 
determine the ratio satisfactorily. 
Another great merit of stature as a subject for inquiries into 
heredity is that marriage selection takes little or no account of 
shortness or tallness. There are undoubtedly sexual preferences 
for moderate contrast in height, but the marriage choice appears 
to be guided by so many and more important considerations that 
questions of stature exert no perceptible influence upon it. This 
is by no means my only inquiry into this subject, but, as regards 
the present data, my test lay in dividing the 205 male parents 
and the 205 female parents each into three groups—tall, medium. 
and short (medium being taken as 67 inches and upwards to 70 
inches)—and in counting the number of marriages in each poss- 
ible combination between them. The result was that men and 
women of contrasted heights, short and tall or tall and short, 
married just about as frequently as men and women of similar 
heights, both tall or both short ; there were 32 cases of the one 
to 27 of the other. In applying the law of probabilities to 
investigations into heredity of stature, we may regard the 
married folk as couples picked out of the general population at 
haphazard. 
The advantages of stature as a subject in which the simple 
laws of heredity may be studied will now be understood. It is 
a nearly constant value that is frequently measured and recorded, 
and its discussion is little entangled with considerations of nur- 
ture, of the survival of the fittest, or of marriage selection. We 
have only to consider the mid-parentage and not to trouble our- 
selves about the parents separately. ‘The statistical variations of 
stature are extremely regular, so much so that their general con- 
formity with the results of calculations based on the abstract law 
of frequency of error is an accepted fact by anthropologists. I 
have made much use of the properties of that law in cross-testing 
my various conclusions, and always with success. 
The only drawback to the use of stature is its small variability. 
One-half of the population with whom I dealt varied less than 
1°7 inch from the average of all of them, and one-half of the 
offspring of similar mid-parentages varied less than 1°5 inch 
from the average of their own heights. On the other hand, the 
precision of my data is so small, partly due to the uncertainty 
in many cases whether the height was measured with the shoes 
on or off, that I find by means of an independent inquiry that 
each observation, taking one with another, is liable to an error 
that as often as not exceeds 4 of an inch. 
It must be clearly understood that my inquiry is primarily into 
[ Sept. 24, 1885 
the inheritance of different degrees of tallness and shortness. 
That is to say, of measurements made from the crown of the 
head to the level of mediocrity, upwards or downwards as the 
case may be, and not from the crown of the head to the ground. 
In the population with which I deal, the level of mediocrity is 
684 inches (without shoes). The same law, applying with 
sufficient closeness both to tallness and shortness, we may include 
both under the single head of deviations, and I shall call any 
particular deviation a ‘‘ deviate.” By the use of this word and 
that of ‘‘mid-parentage,” we can define the law of regression 
very briefly. It is that the height-deviate of the offspring 
is, on the average, two-thirds of the height-deviate of its mid- 
parentage. 
If this remarkable law had been based only on experiments on 
the diameters of the seeds, it might well be distrusted until con- 
firmed by other inquiries. If it were corroborated merely by 
the observations on human stature, of which I am about to 
speak, some hesitation might be expected before its truth could 
be recognised in opposition to the current belief that the child 
tends to resemble its parents. But more can be urged than this. 
It is easily to be shown that we ought to expect filial regression, 
and that it should amount to some constant fractional part of the 
value of the mid-parental deviation. It is because this explana- 
tion confirms the previous observations made both on seeds and 
on men, that I feel justified on the present occasion in drawing 
attention to this elementary law. 
The explanation of it 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 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 combination cf the zero of the ancestry with 
the deviate of the mid-parentage, is that of nothing with some- 
thing, and the result resembles that of pouring a uniform pro- 
portion 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 their degree 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 ancestry. Its combination with the mid-parental 
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 com- 
posite progenitor, whom the offspring of similar mid-parentages 
most nearly resemble, and from whose stature their own respect- 
ive heights diverge 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 constant fraction 
of their respective mid-parental deviations, which was first ob- 
served in the diameters of seeds, and then confirmed by observa- 
tions on human stature, is now shown to be a perfectly reason- 
able law which might have been deductively foreseen. It is of so 
simple a character that I have made an arrangement with one 
movable pulley and two fixed ones by which the probable aver- 
age height of the children of known parents can be mechanically 
reckoned. This law tells heavily against the full hereditary 
transmission of any rare and valuable gift, as only a few of many 
children would resemble their mid-parentage. The more ex- 
ceptional the gift, the more exceptional will be the good fortune 
of a parent who has a son who equals, 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 diseases. 
The converse of this law is very far from being its numerical 
a 
