1212 REPORT—1885. 
A simple equation connects the three data of race variability, of the ratio of 
regression, and of co-family variability, whence, if any two are given, the third 
may be found. My observations give separate measures of all three, and their 
values fit well into the equation, which is of the simple form— 
22 
oS +fP=p*, 
where v=%, p=1°7, f=1'5. 
It will therefore be understood that a complete table of mid-parental and filial 
heights may be calculated from two simple numbers. 
It will be gathered from what has been said, that a mid-parental deviate of 
one unit implies a mid-grandparental deviate of 4, a mid-ancestral unit in the next 
generation of 4, and so on. I reckon from these and other data, by methods that I 
cannot stop to explain, that the heritage derived on an average from the mid- 
parental deviate, independently of what it may imply or of what may be known 
concerning the previous ancestry, is only $3. Consequently, that similarly derived 
from a single parent is only }, and that from a single grandparent is only ;.. 
The most elementary data upon which a complete table of mid-parental and 
filial heights admits of being constructed, are (1) the ratio between the mid- 
parental and the rest of the ancestral influences, and (2) the measure of the co- 
family variability. 
I cannot now pursue the numerous branches that spring from the data I have 
given,asfromaroot, I will not speak of the continued domination of one type over 
others, nor of the persistency of unimportant characteristics, nor of the inheritance 
of disease, which is complicated in many cases by the requisite concurrence of two 
separate heritages, the one of a susceptible constitution, the other of the germs of 
the disease. Still less can I enter upon the subject of fraternal characteristics, 
which I have also worked out. It will suffice for the present to haye shown 
some of the more important conditions associated with the idea of race, and how 
the vague word type may be defined by peculiarities in hereditary transmission, at 
all events when that word is applied to any single quality, such as stature. To 
include those numerous qualities that are not strictly measurable, we must omit 
reference to number and proportion, and frame the definition thus :—‘The type 
is an ideal form towards which the children of those who deviate from it tend 
to recress,’ 
The stability of a type would, I presume, be measured by the strength of its 
tendency to regress; thus a mean regression from 1 in the mid-parents to 3 in the 
offspring would indicate only half as much stability as if it had been to 3. 
The mean regression in stature of a population is easily ascertained, but I do not 
see much use in knowing it. It has already been stated that half the population 
vary less than 1-7 inch from mediocrity, this being what is technically known as the 
‘probable’ deviation. The mean deviation is, by a well-known theory, 1:18 times 
that of the probable deviation, therefore in this case it is 1‘9 inch. The mean loss 
through regression is 4 of that amount, or a little more than 0°6 inch. That is to 
say, taking one child with another, the mean amount by which they fall short of 
their mid-parental peculiarity of stature is rather more than six-tenths of an 
inch. 
With respect to these and the other numerical estimates, I wish emphatically 
to say that I offer them only as being serviceably approximate, though they are 
mutually consistent, and with the desire that they may be reinvestigated by the 
help of more abundant and much more accurate measurements than those I have 
had at command. There are many simple and interesting relations to which I 
am still unable to assign numerical vaiues for lack of adequate material, such 
as that to which I referred some time back, of the superior influence of the father 
over the mother on the stature of their sons and daughters. 
The limits of deviation beyond which there is no regression, but a new con- 
dition of equilibrium is entered into, and a new type comes into existence, have 
still to be explored. Let us consider how much we can infer from undisputed facts 
of heredity regarding the conditions amid which any form of stable equilibrium 
such as is implied by the word type must be established, or might be disestablished 
i iat 
