CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
225 
I do not suggest for a moment that tliese curves give a final solution of the problem 
of determining the stature of any individual in the range of 90 to 250 centims. from 
the lengths of his long bones, but they seem to me to give the best results obtain¬ 
able with the data at present availal^le. 
Reduced to a formula a curve of this type would be of little service, for both x and 
y are linear functions of the probable stature and the observed length of the long 
bone. Hence we should have a quintic equation to find the probable stature from 
the long bone. But if these curves be plotted once for ail, we have a graphical 
means of at once determining, by simply running the eye along a line, the probable 
stature corresponding to any given length of long bone. With care we can find the 
probable stature to "5 centim., but a,s a rule to the nearest centimetre is sufficient. 
As the lines of regression for the normal population are given as part of our curves, 
it is clear that the diagrams attached to this memoir (Plates 3, 4) will also serve for the 
determination to a like degree of exactitude of the probable stature of individuals or 
races falling within the ordinary range of statures. In view of the fact that the 
diagrams serve all practical purposes, I have not considered it needful to deduce from 
the above quintics numerical approximations for the value of the stature in terms of 
the lengths of the various long bones. 
(22.) If the reader will examine the diagrams, he will see the twelve giants 
A, B, C, . . . K, L marked by small dots; from these the curves were determined, 
and he will notice that they strike fairly well through the groups. The triplet 
O, M, N contains three pseudo-giants, or sub-giants ; these as well as the dwarfs, 
S, U, V, T, were not used in the determination of the curves. One remarkable 
feature of the curves must be noted, namely, that in the region of what may be 
termed sub-giants and super-dwarfs, namely, from about 180 to 200 centims. and 
150 to 130 centims., a very small change in the long bone makes a remarkable change 
in stature. This is specially noteworthy in the case of the radius. Thus between 
normal individuals on the one hand and giants or dwarfs on the other, there appears 
to he what may be termed a region of instability, in which an insignificant change in 
long bone may throw tlie individual across a considerable range of stature. The 
points of inflexion of our curves—other than those at the origin—may accordingly 
have a biological as well as a purely mathematical interest. 
The following are all the data which I have been able to collect for giants and 
dwarfs having any degree of probable truth. 
o 
O' 
VOL. oxen.— A. 
