TRANSACTIONS OF SECTION H. 1209 
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 popu- 
lation at haphazard. 
The advantages of stature as a subject in which the simple laws of heredity may 
be studied will now be understood. It isa nearly constant value that is frequently 
measured and recorded, and its discussion is little entangled with considerations 
of nurture, of the survival of the fittest, or of marriage selection. We have only 
to consider the mid-parentage and not to trouble ourselves about the parents 
separately. The statistical variations of stature are extremely regular, so much 
so that their general conformity 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 con- 
clusions, 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 indepen- 
dent inquiry that each observation, taking one with another, is liable to an error 
that as often as not exceeds % of an inch. 
It must be clearly understood that my inquiry is primarily into 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 confirmed 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 frac- 
tional part of the value cf 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-ancestrai 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 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 their degree do the same. The mid- 
deviate of any one of them will have a value intermediate between that of the mid- 
