J. F. TOCHKR 
303 
in the main produced by a heterogeneity depending solely on the presence of a 
macrocephalic or of a microcephalic group alone. In the case of stature, the values 
of are considerably larger. The skewness of the distribution is more marked 
and is largely due in the case of females, and to some extent in the case of males, 
to the existence of a dwarf element in the "entire insane" population. This 
element in the females is in the main identical with the group termed "ex- 
ceptionals," removed from the " entire insane " population in the manner already 
explained. 
Some peculiarities of the " exceptionals " deserve to be noted. Among the 
males the head height of the group is much greater than that of the " general 
insane" population — in other words the male "exceptionals" are a hypsicranial 
group. The female "exceptionals" are small sized generally; in all characters 
the means are significantly less than the "general insane" population. The 
variability of the ' exceptionals " for all head characters and for stature is very 
great indeed and is found to be due to excess frequencies on both sides of the 
range and a corresponding defect in the frequencies about the mean. The ex- 
ceptionals are thus mainly a mixture of two groups, one, larger sized in all 
characters — a megameric group, and another smaller sized in all characters — 
a micromeric group. An inspection of the following table (Table II.) will serve to 
emphasize these points. 
TABLE II. 
"Entire Insane" Population 
" General Insane" Population 
Exceptionals 
Character 
Mean 
S. D. 
Mean 
S. D. 
Mean 
S. D. 
L$ ... 
195-5 
6-78 
195-5 
6-55 
196-7 
16-37 
B£ ... 
151-5 
5-53 
151-5 
5-39 
151-7 
13-42 
H$ ... 
136-7 
5-85 
136-7 
5-58 
147-2 
20-75 
S $ ... 
65-7 
2-90 
65-9 
2-84 
65-4 
4-22 
L ? ... 
186-4 
6-23 
186-5 
6-04 
176-5 
10-97 
B ? ... 
145-2 
5-03 
145-3 
4-91 
142-9 
13-17 
H ? ... 
131-0 
5-54 
131-0 
5-43 
125-3 
14-62 
s 9 ... 
60-9 
2-72 
61-2 
2-58 
58-4 
5-77 
The mean is less than the mode for all characters except auricular lieight, 
and $, in which cases it is sensibly greater. Since the "general insane" 
population forms a pretty long series, one can hardly compare the asymmetry 
values with those of the very much shorter series of Fawcett and others, since the 
probable errors in these latter cases are relatively very large. Four long series 
from general sane populations are however available for stature : {a) Baxter's 
American recruits*, Powys's New South Wales observations f, (7) Weldon's 
Verona statistics! (Italian conscripts and recruits), and (8) Macdonell's 3000 English 
* Pearson : Phil. Trans. Vol. 18G A, p. 385. 
t Powys : Biometrika, Vol. i. pp. 43 — 46. 
X Pearson : Biometrika, Vol. iv, p. 506. 
39—2 
