F. M. Turner 
493 
these two conditions among the population outside, which is most probably the 
case, the protection gained by the vaccinated in infancy must diminish as age 
advances. 
We seem therefore driven to the conclusion that protection against attack and 
protection against death, though both produced by the same operation, disappear 
at widely different rates. In a later part of this paper, however, I put forward a 
suggestion which I think accounts for the discrepancy in the figures, and allows 
us to suppose that the protections against attack and against death produced by 
vaccination are the same, not only in cause, but also quantitatively as measured 
by correlation coefficients. 
The effect of the age of the patients upon the value of r in Table I. is perhaps 
best shewn by comparing it with the values derived from Tables XIV.- — XXIII. 
The mean value of r from the five tables, in which the doubtful cases have been 
included with the vaccinated, is — '5234, against — "4246 of Table I. And the 
mean value from the other five tables is — '5795 against — 4922 of Table III. 
The effect has therefore been to diminish r. It is interesting, however, to use the 
formulae for multiple correlation to test the result. 
Taking the division of age at 10 years, we have the following table : 
TABLE XXIV. 
All Cases, 1901—2*. 
Under 10 
Over 10 
Totals 
Unvaccinated . . . 
1274 
1004 
2278 
Vaccinated 
1.34 
6811 
6945 
Totals 
1408 
7815 
9223 
r= + -9U. 
TABLE XXV. 
All Gases, 1901—2. 
Recoveries 
Deaths 
Totals 
Under iO 
991 
450 
1441 
Over 10 
7039 
1179 
8218 
Totals 
8030 
1629 
9659 
r = --3150. 
* I have inadvertently omitted the doubtful cases in calculating this table. As these high corre- 
lations are laborious to work oxit 1 have not thought it necessary to recalculate the value with the 
doubtful cases included. In all the tables of age and vaccination I have carried the series in r to twelve 
terms, and the terms beyond would certainly influence the third figure, probably the second also. The 
Tables XIV. and XV. also give series in r which converge slowly. In these two cases also I have 
stopped at twelve terms. 
