502 Correlation hetvjeen Vaccination and Smallpox 
TABLE E. 
All Exposed to Infection. 
Affected with Smallpox 
Not Diseased 
Totals 
Recovered 
Died 
Unvaccinated ... 
a 
1525 
753 
Vaccinated 
d 
G505 
876 
Totals 
9659 
8030 
1629 
19318 
If a. = 450 we get the two following fourfold tables : 
Not Diseased 
Diseased 
Totals 
Unvaccinated 
450 
2278 
2728 
Vaccinated 
9209 
7381 
16590 
Totals 
9659 
9659 
19318 
j-i= --5373. 
Alive 
Dead 
Totals 
Unvaccinated ... 
1975 
753 
2728 
Vaccinated 
15714 
876 
16590 
Totals 
17689 
1629 
19318 
r.i= - -5429. 
If a = 400 we find 
r^ = _-5611, r., = --5496. 
Whence by interpolation we get the correct solution : 
a - 434, d = 9225, 
r = — •5451. 
If, however, the number exposed to risk is not much larger than the number 
who contract the disease the values of r and r' more nearly coincide. Thus if the 
number exposed who do not contract the disease is equal to only one-tenth of 
those who do, we have g = 966, and I have calculated a = 39, r = — '4492. On 
the other hand if the number of persons exposed to infection was several times 
larger than that of those who developed the disease, the true value of r considerably 
exceeded — "54. 
