John Brownlee 
331 
In the accompanying table those cases of revaccinated persons attacked by 
smallpox during the London epidemic of 1902 are given ; the number is ninety- 
two in all, and among these two deaths occurred, in both of which the period 
of the latest vaccination had been at least twenty-four years previously. Few 
inferences can be drawn from this table ; it is, however, to be noted that more 
than a third of the cases occur in persons revaccinated before the age of fifteen 
years, who, as far as the statistics of this hospital go, constitute a very much 
smaller proportion of the total revaccinated persons, indicating again that the 
operation performed at this age affords less permanent protection than when 
done later. 
In conclusion, it is necessary to state that all the correlation coefficients in 
this paper were calculated by the short method given at the end of Prof Pearson's 
memoir on the correlation among attributes not quantitatively measurable * by 
means of the formula 
. TT ( I ] , , A^ahcdN'' 
r = .sm - J. - , y , where = ; — ^ — 7^-,-, . 
2 jVl 4- /c- J {(^d- hcY {a + d) {b + c) 
If the values of r corresponding to log from 1 to 4 be first calculated, as is 
easily done with the help of a table of Gaussian addition logarithms, then it is 
a matter of only a few minutes to obtain a correlation coefficient. Prof. Pearson 
has found this formula true in most instances within the probable error; I 
myself have checked it with about twenty examples and only once found it give 
a result outside that error, so for the accuracy required in this paper it may be 
considered sufficient. When the numbers are in nearly all cases small the probable 
error is large, and little stress can be placed on the accuracy of an individual 
coefficient. A far better test in a subject like this, when very large numbers of 
coefficients have to be calculated, is their general concordance. In many cases 
they form part of a series which is d 'priori continuous, and consequently each 
affords a mutual check on the other of much greater value considering the number 
of cases involved than the calculation of the probable error. Considering the 
series tabulated in this paper, many instances will be seen where the coefficients 
fall so out of line with their immediate neighbours that it is evident that some 
large error is present. 
REFERENCES TO ORIGINAL SOURCES OF THE FIGURES ON WHICH 
THIS PAPER IS BASED. 
DuviLLARD. Analyse et tableaux do rinfluence de la petite verole sur la mortalitu h, chaque age. 
Paris, 1806. 
Macdonell. Biometrika, Vol. i. p. 375, Vol. ii. p. 135. 
General Board of Health. History and Practice of Vaccination, 1851. 
Local Government Board. Epidemic of Smallpox at Sheffield, 1887-8. 
Royal Commission on Vaccination : Appendices on Eiiidemics in Warrington, Dewsbury, 
Gloucester and Leicester. 
Report of the Metropolitan Asylums Board Hospitals, 1870-1902. 
* Phil. Trans. Vol. 195, A, p. 16. 
42—2 
