John Brownlee 
321 
are unvacciuated at the present day certain statistics exist. The chief of these 
are contained in the account of the epidemic in Sheffield in 1887 presented in 
Dr Barry's report to the Local Government Board. In this case a census was 
taken of nearly the whole population. The facts are tabulated so as to give the 
number of cases at each period who were ixnvaccinated, vaccinated, or revacci- 
nated, and also those who had previously had smallpox. The state as regards the 
vaccination of the inhabitants of those houses actually invaded by smallpox is 
also tabulated separately. On account of the size of the epidemic this census 
must be held as the most important group of statistics at our disposal. It seems 
better to consider fully in the first instance the conclusions which may he 
based on these figures, and afterwards to compare the results with the statistics 
affecting naturally much smaller numbers which have been published with regard 
to other towns. 
Considering, in the first place, the alterations in su.sceptibility to smallpox 
among the unvacciuated which takes place as the age increases, and expressing 
the relationship in terms of the correlation coefficients between those exposed 
to infection who escape, and those exposed who are attacked for each two 
succeeding age periods, it is found that these coefficients vary in the following 
TABLE VI. 
Correlation between those who were Attacked, and those who Escaped in Vaccinated 
and Unvaccinated respectively, at each age and. that immediateli/ succeeding. — 
Sheffield, 1887—8. 
kge Periods 
Vaccinated 
Unvaccinated Age Periods 
Vaccinated 
Age Periodi= 
Unvaccina 
0- 
-Ik 1—5 
-■10 
- -28 
0- 
- i & i- 
- 5 
- ^28 
1- 
- 5 & 5—10 
-•21 
- -17 
1- 
- 5 & 5- 
-10 
-•47 
5- 
-10 & 10—15 
-•34 
- -ys 
5- 
-10 & 10- 
-15 
- -84 
10- 
-15 & 15—20 
- -29 
•72 
10- 
-15 & 15- 
-20 
- ^20 
15- 
-20 & 20—25 
•04 
•04 
15^20 & 20— 
-25 
•04 
15- 
-20 & 20- 
-25 
- -18 
20- 
-25 & 25—30 
•01 
■38 
20—25 & 25— 
30 
•04 
20- 
-25 & 25- 
-30 
■24 
25- 
-30 & 30—35 
■09 
■14 
25—30 & 30— 
35 
•13 
25- 
-30 & 30- 
-35 
■34 
30- 
-35 & 35—40 
■26 
•24 
30—35 & 35— 
-40 
■31 
30- 
-35 & 35- 
-40 
■54 
35- 
-40 & 40—45 
•47 
•75 
35—40 & 40— 
-45 
•53 
35- 
-40 & 40- 
-45 
■73 
Ifi- 
-45 & 45—50 
•48 
- ^25 
40—45 & 45— 
50 
•67 
40- 
-45 & 45- 
-50 
■47 
J^- 
-50 & 50—55 
•01 
•80 
46—50 & 50— 
55 
•68 
45- 
-50 & 50- 
-55 
•95 
50- 
-55 & 55—60 
•15 
- -n 
50—55 & 55— 
-60 
77 
50- 
-55 & 55- 
-60 
■93 
55- 
-60 & 60— 
•02 
•04 
55—60 & 60— 
■79 
55- 
-60 & co- 
■92 
way. From 
birth till between 
ten and .fifteen 
years 
they 
are 
negative 
in 
dicating 
that the susceptibility steadily increases to this age, as was before found by 
Duvillard, and that thereafter each succeeding coefficient is positive of greater 
or less amount. If the susceptibility under one year is chosen for comparison 
with that of each succeeding age period it is seen that the strength of resistance 
which was less marked between ten and fifteen years has between twenty and 
thirty again increased so as to be equivalent to that in the first year of life, and 
thereafter steadily becomes greater. The period of maximum susceptibility 
between ten and fifteen years is one which is well marked in a large number 
of epidemics, although incapable of any very accurate measurement. The number 
Biometrika iv 41 
