488 
Correlation between Vaccination and Smallpox 
between area and number of scars with severity of disease, we have, when (i) area 
is constant and (ii) number is constant respectively, 
r 
= - -0897, 
Pas = 
V(l-r^^«)(l-rV) .. 
'AS ' NS' AN 
\/(l-rV.)(l-r^^7) 
= -•1733. 
Dealing in the same manner with area and foveation of scar, we have the 
following table : 
TABLE XI. 
Vaccinated cases only, 1901 — 2. Area and Foveation of Scars. 
Area < 5 inch 
Area > i inch 
Totals 
Scars less than half foveated ... 
Scars more than half foveated . . . 
1530 
145 
4255 
893 
5785 
1038 
Totals 
1675 
5148 
6823 
And 
'/•=.• + -2386. 
r^5 = --2997, 7v^=--1664, r^^= + -2386, 
Pfs = 
V(l-r^^^)(l-rV) 
•1012, 
Pas- 
r.o - r. 
V(l-rV.)(l-rV) 
= -•2719. 
It seems therefore not improbable that among cases with equal area of vac- 
cination marks, there is no difference in the amount of protection afforded by 
different numbers of scars. The apparent protection afforded by foveation of the 
scars, though not very great in itself, can with less probability be attributed to 
secondary association of foveation with large scars. 
It would be a good thing if these two points could be definitely settled, for a 
great deal of time is spent in smallpox hospitals in observing and recording these 
data, some of which may possibly be unnecessary. 
The fact that p,vs above calculated is not equal to 0 may be due to the fact 
that some scars grow considerably between infancy and adult life. This of course 
would tend to lessen r^g (the area being measured many yeai^s after the operation), 
but would leave rj^g unaltered unless, as is probably not common, one or more 
scars disappeared entirely. The above formulae also apply only to linear correla- 
tion, while the correlation in these cases may be skew. 
