198 
NAT ORE 
[JUNE 29, 1899 
LETTERS TO THE EDITOR. 
[The Editor does not hold himself responsible for opinions ex- 
pressed by his correspondents. Neither can he undertake 
to return, or to correspond with the writers of, rejected 
manuscripts intended for this or any other part of NATURE. 
No notice ts taken of anonymous communications. | 
Physical Measurement of Public Schoolboys. 
I ENCLOSE photographs of two lecture diagrams which were 
used for a paper on the physical development of public school- 
boys read to the Medical Officers of Schools Association last 
Easter. The curves represent the various different schemes of 
growth followed by schoolboys from the age of 10} to 184, 
according as they are developing into large, small, or medium 
sized men. They are constructed from corresponding series of 
curves of distribution, which curves are constructed from a 
large number of observations recorded at various public schools. 
From 14,000 to 15,000 observations have been collated for the 
construction of each series, and I regard them as being fairly 
CT es 
Fn 
> 
SW QG ee 
XU ers ENAT UND XIILGNE XIV sS0UNXVII EEX VI SUNTNID VII NEXUIIE 
Fic. 1.—Grade curves for height of public schoolboys from 103 to 18} years 
ofage. The figures on the base line refer to age. The figures down 
the centre of the diagram are the numbers of the grades, which are 
bounded by the two curves between which the several numbers are 
placed. There is no lower limit to grade 20, nor upper limit to grade 1. 
trustworthy in form between the ages of 12 and 18. Beyond 
these limits the form of the curves may be slightly at fault, 
owing both to insufficient number of observations and to the 
process of natural selection which influences the physical status 
of the majority of boys who come early and stay late at a public 
school. The curves in Fig. 1 are constructed by marking off 
on the vertical line through each age the various heights at 
which the curve of distribution for that age crosses the 5 per 
cent., 10 per cent., 15 per cent., . . . 95 per cent. lines. Each 
series of corresponding points is then joined up-by a flowing 
curve, with the result shown. The central line, between-the 
numbers 10 and 11, shows where the various curves of distribu- 
NO. 1548, VOL. 60] 
tion cross the 50 per cent. line, and consequently indicates the: 
scheme of growth of the mean boy. 
It was contended in the paper that since each of these curves. 
represents the growth of a boy, who develops in such a manner 
as to preserve always the same relative position amongst his. 
fellows, they give an accurate idea of the growth which may be 
reasonably expected from a boy at any stage of his develop- 
ment, whatever his physical status may be. A glance at the: 
diagram will show that the rate of growth, which is measured 
by the pitch of the curves, varies considerably for boys of the 
same age but of different physique. The period of maximum 
growth is reached much sooner by a boy of a high grade tham 
by one of a low grade, and lasts much longer. Thus the steepest 
pitch of the topmost curve occurs between the ages of 134 and 
144, and is sensibly uniform during that period, the correspond- 
ing steepest pitch in the mean line lies between the ages of 15, 
and 154, in the lowest line it lies between 164 and 17. Con- 
sequently, during the period of fastest growth, all boys may be 
expected to grow at nearly the same rate ; but this rate of growth 
is reached by some boys three or four years later than by others.. 
AV. 
ASS 
\\ 
\ 
NX \ 
LI 
\ 
60 
XI XI Xm = Xlv XVaL 
Fic, 2.—Similar grade curves for weight. 
Fig. 2 represents the corresponding series of curves for 
weight, and teaches much the same lessons; it is evident, 
however, that the rate of growth in height declines much more 
rapidly after the period of maximum growth is passed than 
the rate of growth in weight, consequently boys of the same 
height but of different ages may be expected to differ consider- 
ably in weight. That this is generally the case was clearly 
shown by another set of curves exhibited at the lecture. 
The curves shown have been used for constructing tables of 
grades, by means of which the limits of twenty grades are fixed, 
in some one of which a boy can be immediately placed if his 
measurements are known. From the mode of construction it 
is evident that, @ fréovz, each of these grades is equally probable. 
The tables have in actual practice been found to be of great use 
in estimating the progress of individuals, and of gymnastic 
