ey 
TRANSACTIONS OF SECTION H. LEE 
column by whose side 67— is marked, the entry 38 is found; this means that 
out of the 980 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, that corresponded to 68 
inches. Their axes were similarly inclined. The points where each ellipse in 
succession was touched by a horizontal tangent, lay in a straight line inclined to 
the vertical in the ratio of 2; those where they were touched by a vertical tangent, 
lay in a straight line inclined to the horizontal in the ratio of 3. These ratios con- 
firm 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 mathematical analysis and verification. 
They were all clearly dependent 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 (8) the average 
ratio of regression. I noted these values, and phrased the problem in abstract 
terms such as a 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 particulars 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 re- 
: 1 6 
gression from 3 to 7 
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 sufli- 
cient 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 
suryival 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 com- 
plications and to discuss this very curious question under its simplest form. How 
is it, I ask, that in each successive 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 two opposite sets of actions, one 
concentrative and the other dispersive, and of such a character 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 scat- 
tered ; 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. 
the relation between the major and minor axis of the 
