Sept. 24, 1885 | 
NATURE 
509 
opposite. Because the most probable deviate of the son is only 
two-thirds that of his mid-parentage, it does not in the least 
follow that the most probable deviate of the mid-parentage is 
8, or 13 that of the son. The number of individuals in a popu- 
lation who differ little from mediocrity is so preponderant, that 
it is mcre frequently the case that an exceptional man is’ the 
somewhat exceptional son of rather mediocre parents, than the 
average son of very exceptional parents. It appears from the 
very same table of observations by which the value of the filial 
regression was determined, when it is read in a different way, 
namely, in vertical columns instead of in horizontal lines, that 
the most prohable mid-parentage of a man is one that de- 
viates only one-third as much as the man does. There 
is a great difference between this value of } and the numer- 
ical converse mentioned above of #; it is four and a half 
times smaller, since 43, or $, being multiplied into 3, is equal 
to . 
Let it not be supposed for a moment that these figures invali- 
date the general doctrine that the children of a gifted pair are 
much more likely to be gifted than the children of a mediocre 
pair. What it asserts is that the ablest child of one gifted pair 
is not likely to be as gifted as the ablest of all the children of 
very many mediocre pairs. However, as, notwithstanding this 
explanation, some suspicion may remain of a paradox lurking in 
these strongly contrasted results, I will explain the form in which 
che table of data was drawn up, and give an anecdote connected 
with it. Its outline was constructed by ruling a sheet into 
squares, and writing a series of heights in inches, such as 60 and 
under 61, 61 and under 62, &c., along its top, and another 
similar series down its side. The former referred to the height 
of offspring, the latter to that of mid-parentages. Each square 
in the table was formed by the intersection of a vertical column 
with a horizontal one, and in each square was inserted the number 
of children out of the 930 who were of the height indicated by 
the heading of the vertical column, and who at the same time 
were born of mid-parentages of the height indicated at the side 
of the horizontal column. I take an entry out of the table as 
an example. Inthe square where the vertical column headed? 
69- is intersected by the horizontal column by whose side 67- is 
marked, the entry 38 is found ; this means that out of the 930 
children 38 were born of mid-parentages of 69 and under 70 
inches, who also were 67 and under 68 inches in height. I found 
it hard at first to catch the full significance of the entries in the 
table, which had curious relations that were very interesting to 
investigate. Lines drawn through entries of the same value 
formed a series of concentric and similar ellipses. Their common 
centre lay at the intersection of the vertical and horizontal lines, 
shat corresponded to 68} inches. Their axes were similarly in- 
clined. The points where each ellipse in succession was touched 
by a horizontal tangent, lay ina straight line inclined to the 
vertical in the ratio of $; those where they were touched bya 
vertical tangent, lay in a straight line inclined to the horizontal 
in the ratio of 3. These ratios confirm the values of average 
regression already obtained by a different method, of 3 from 
mid-parent to offspring, and of 4 from offspring to mid-parent. 
These and other relations were evidently a subject for mathe- 
matical analysis and verification. They were all clearly depend- 
ent on three elementary data, supposing the law of frequency 
of error to be applicable throughout ; these data being (1) the 
measure of racial variability, (2) that of co-family variability 
(counting the offspring of like mid-parentages as members of the 
same co-family), and (3) the average ratio of regression. I noted 
these values, and phrased the problem in abstract terms such asa 
competent mathematician could deal with, disentangled from all 
reference to heredity, and in that shape submitted it to Mr. J. 
Hamilton Dickson, of St. Peter's College, Cambridge. I asked 
him kindly to investigate for me the surface of frequency of error 
that would result from these three data, and the various particu- 
lars of its sections, one of which would form the ellipses to which 
I have alluded. 
I may be permitted to say that I never felt such a glow of 
loyalty and respect towards the sovereignty and magnificent 
sway of mathematical analysis as when his answer reached me, 
confirming, by purely mathematical reasoning, my various and 
laborious statistical conclusions with far more minuteness than I 
had dared to hope, for the original data ran somewhat roughly, 
and I had to smooth them with tender caution. His calculation 
corrected my observed value of mid-parental regression from 
1 A matter of detail is here ignored which has nothing to do with the main 
principle, and would only serve to perplex if I described it. 
i 
Be 1756) 
ellipses was changed 3 per cent., their inclination was changed 
less than 2°. It is obvious, then, that the law of error holds 
throughout the investigation with sufficient precision to be of real 
service, and that the various results of my statistics are not 
casual determinations, but strictly interdependent. 
In the lecture at the Royal Institution to which I have referred, 
I pointed out the remarkable way in which one generation was 
succeeded by another that proved to be its statistical counterpart. 
I there had to discuss the various agencies of the survival of the 
fittest, of relative fertility and so forth; but the selection of 
human stature as the subject of investigation now enables me to 
get rid of all these complications, and to discuss this very curious 
question under its simplest form. How is it, I ask, that in each 
succéssive generation there proves to be the same number of men 
per thousand who range between any limits of stature we please 
to specify, although the tall men are rarely descended from 
equally tall parents, or the short men from equally short? How 
is the balance from other sources so nicely made up? The 
answer is that the process comprises tw opposite sets of actions, 
one concentrative and the other dispersive, and of such a char- 
acter that they necessarily neutralise one another, and fall into a 
state of stable equilibrium. By the first set, a system of scattered 
elements is replaced by another system which is less scattered ; 
by the second set, each of these new elements becomes a centre 
whence a third system of elements are dispersed. The details 
are as follows :—In the first of these two stages, the units of the 
population group themselves, as it were by chance, into married 
couples, whence the mid-parentages are derived, and then by a 
regression of the values of the mid-parentages the true generants 
are derived. In the second stage each generant is a centre 
whence the offspring diverge. The stability of the balance 
between the opposed tendencies is due to the regression 
being proportionate to the deviation ; it acts like a spring against 
a weight. teen 
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— 
the relation between the major and minor axis of the 
pk 2 2 
w rr +f = 
where v = 3, p = 1°7,f = 15. ; 
It will therefore be understood that a complete table of mid- 
parental and filial heights may be calculated fom 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 3, a 
mid-ancestral unit in the next generation of 3, 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, 1s only 3. 
Consequently, that similarly derived from a single parent is only 
i, and that from a single grandparent is only 7’5- 
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, as from a root. I will not speak of the 
continued domination of one type over others, nor of the per- 
sistency 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 have 
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 regress.” 
The stability of a type would, I presume, be measured by the 
