492 Correlation hetiveen Vaccination and Smallpox 
TABLE XXII. 
Patients 40 years of age and over, 1901 — 2. 
Recoveries 
Deaths 
Totals 
Unvaccinated 
Vaccinated or doubtful 
17 
1172 
34 
359 
51 
1531 
Totals 
1189 
393 
1582 
--4771. 
TABLE XXIII. 
Patients 40 years of age and over, 1901 — 2. 
Recoveries 
Deaths 
Totals 
Unvaccinated or doubtful ... 
Vaccinated 
98 
1091 
108 
285 
206 
1376 
Totals 
1189 
393 
1582 
}•= --4440. 
Of the two methods of dealing with the doubtful cases 1 have given my 
reasons above for preferring their inclusion with the vaccinated rather than the 
unvaccinated. As between Tables XIV. and XV., however, I think it possible 
that a majority of the "doubtful cases" under 10 were unvaccinated, in which case 
the value given by Table XV. would be the more accurate. 
On comparing the values of either series, however, we find that the value of r 
does not vary very much in the three periods under 30 years of age, whereas after 
the age of 30 there is a moderate fall in value. The maximum occurs in the 
period from 10 to 20. This result is in striking contrast to the opinion of the 
members of the medical profession as to the duration of immunity against attack ; 
which is that the protection afforded by vaccination is highest for the first few 
years after the operation and then tails off rapidly, so that at 10 or 12 years of age 
revaccination becomes desirable. So long as no statistics are available of the 
number of persons exposed to risk of infection by smallpox, it is impossible to 
calculate by mathematical methods the protection afforded by vaccination against 
attack. But the above opinion as to the duration of vaccination -immunity is 
really arrived at by methods identical in principle to the above fourfold tables, 
that is by recording the numbers attacked of vaccinated and unvaccinated persons 
at different ages, and contrasting these with the very roughly known proportion 
existing between vaccinated and unvaccinated persons in the community at large. 
Inside a smallpox hospital there is found a very high correlation between age and 
vaccination, say "9 or -8 (see Tables XXIV., XXVI. and XXVIIL). If there 
existed an equally high correlation among the whole community between age and 
vaccination, we might assume that vaccination either failed to protect, or protected 
with equal force throughout life. But if there is only slight correlation between 
