ON THE INFLUENCE OF PKEVIOUS VACCINATION 
IN CASES OF SMALLPOX. 
By W. R. MACDONELL, LL.D. 
In Biometrika, Vol. l. Part ll. p. 177 et seq., Professor Karl Pearson's method of 
finding the correlation coefficients and other constants of characters not quantita- 
tively measurable* was extensively applied to the case of characters quantitatively 
measurable, in order to avoid the very considerable labour involved in forming 
correlation tables of the usual detailed kind. I have since used the method in an 
investigation in which quantitative scales are unobtainable, and to which therefore 
it is peculiarly applicable, viz., the degree of effectiveness of vaccination in small- 
pox, and the object of this note is to give my results. 1 propose to show the 
correlation, first, between degree of effective vaccination and (1) strength to resist 
smallpox and (2) type of disease ; and secondly, between type of disease and 
(1) degree of foveation, (2) scar area and (3) number of scars. The data have been 
extracted from the First Report of the Vaccination Commission, 1896, from a 
Report by Dr R. S. Thomson and Dr E. L. Marsh on the cases admitted to the City 
of Glasgow Smallpox Hospital, Belvidere, during the epidemic outbreak in 1892-5, 
and from the Times newspaper of November 30 and January 13 last. 
1. The Commissioners' Report, pp. 55 — 58, gives statistics of the following 
epidemics: Sheffield 1887-8, London 1892-8, Dewsbury 1891-2, Warrington 
1892-3, Leicester 1892-3 and Gloucester 1895-6 ; the facts were obtained from 
the local reports upon the epidemics in the six towns, and with regard to these 
reports the Commissioners write as follows (§ 212) : " It is quite possible that the 
" classification " (vaccinated and unvaccinated) " may not be strictly accurate, 
" though great pains appear to have been taken to make it so. Doubtful cases 
" were in general included amongst the vaccinated class, and care was taken to see 
" that none should be included in the unvaccinated class except those who properly 
" came within it. Where the doubtful cases were separately stated in the reports 
' we have added them to the vaccinated class for the purpose of our calculations." 
^ Phil. Trans. Vol. 195, pp. 1—47. 
