506 
Miscellanea 
curve as anything with which we are acquainted *. The fact is that there are so many other 
factors on which selection depends that we get no "curtailing" of the distribution at all. I 
should imagine that it would be precisely the same with those who are selected to incur small- 
pox. The selection depends on so very much else than a certain absolutely fixed grade of 
immunity. This point is of such importance that I think it worth illustrating by an example. 
It is one which Professor Weldon has most kindly provided me with out of the extensive 
reductions he has made of Italian conscripts and recruits. In the Province of Verona in the 
five years between 1875 and 1879 there were 16,203 conscriptst and from these were selected 
3810 recruits i. The following table contains the two distributions : 
J3 
Ci 
—H 
s^ 
C5 
»-< 
en 
0> 
50 
So 
So 
SO 
so 
>c 
>-'^ 
CO 
Stature in 
—H 
— ^ 
—1 
1 
■—I 
>-( 
Centimetres 
1 
1 
CO 
1 
oo 
1 
1 
1 
CO 
1 
00 
1 
1 
i 
1 
CO 
1 
00 
1 
1 
1 
1 
CO 
1 
00 
1 
©J 
eo 
so 
so 
~=^ 
ICS 
lO 
CO 
>--H 
'-I 
—H 
—1 
—1 
'-I 
'-I 
>-( 
■—I 
Conscripts 
4 
2 
1 
1 
1 
2 
7 
7 
22 
33 
55 
117 
225 
626 
725 
1027 
1503 
Selected Recruits 
16 
148 
239 
354 
Stature in 
Centimetres 
so 
CO 
CO 
CO 
1 
CO 
—1 
16G—167 
168—169 
1 
o 
>^ 
l-l 
172—173 
>^ 
•-^ 
1 
"—I 
176—177 
?^ 
i 
Co 
>^ 
180—181 
so 
00 
— i 
1 
CO 
—1 
00 
1 
00 
'-1 
186—187 
188—189 
190—191 
192—193 
Totals 
Conscripts 
Selected Recruits 
1869 
471 
2065 
542 
2125 
538 
1703 
425 
1525 
414 
1058 
256 
699 
170 
384 
133 
205 
55 
131 
35 
45 
9 
24 
3 
7 
4 
2 
1 
16203 
3810 
In the diagram the two distributions with their corresponding curves are given, and we see 
that in the selected recruits there is not the slightest approach to a curtailed normal curve. In 
fact, if we examine the fundamental constants of the distribution § we find: 
For the Co)}!>rripts For the Eecruits 
\% = -1658 ± -0130 _ \% = -3409 ± -0268 
[3., = 3-75] 6 ± -0260 (3., = 2-7989 ± "0536. 
The probable errors are those which would arise if the distribution were truly normallT. The 
deviations from symmetry are for the two cases 12-6 and 12-7 times their probable errors respec- 
tively. It is impossiV)le therefore to say more than that the two curves are Ijoth markedly skew 
and deviate equallj' from normality in this respect. In the next place the deviations from meso- 
kurtosis arc in the two cases 28'9 and 3'8 times their probable errors ; in other words the curve 
fcir the conscripts diverges indefinitely more fi'om the normal curve than that for the selected 
recruits. This is only one instance out of many which emiihasise the same points, i.e. that 
there is no approach in the selected curve to curtailment and it differs on the whole less from 
normality than is the case with the unselected material. 
See, for example, Baxter's statistics for U.S. recruits discussed, Phil. Trans. Vol, 186, A, p. 385. 
t R. Livi, "Classificazione delle stature dei coscritti delle leva di terra negli anni 1875-79." 
Annali di Statiatica, Vol. viii. 1883, pp. 144—9. 
i E. Livi, Antropometria Militare, Parte i., p. 260, Roma, 1898. 
§ Phil. Trans. Vol. 186, A, p. 368. Biometrika, Vol. iv., pp. 174—7. 
1 Phil. Trans. Vol. 198, A, p. 278. 
