508 
Proceedings of Royal Society of Edinburgh. [sess. 
another, it would be expected that the average would he easily 
expressed by an epidemic curve, the base line of which represented 
the zero prevalence. In actual trial the former gives a much 
better representation of the facts than the latter, which seemed at 
first sight the more probable assumption. Two examples are given 
for comparison : one, the average number of deaths from scarlet 
fever in London * for the last thirty years ; and the other, the 
average number of cases of enteric fever f for the last thirteen 
years (diagrams XXIV. and XXY.). It is seen that the fit in 
both cases is a comparatively good one, and is much better than 
any I have succeeded in forming on the basis of the second 
hypothesis. 
Before making any special application of the foregoing notes on 
the regular course of epidemics and the nature of the laws which 
they obey, one other point requires to be investigated. Is the 
distribution of an epidemic in space subject to anything like the 
same kind of law which regulates the distribution of the cases in 
regard to time? Here an answer seems easy. Given a certain 
amount of infection in a limited space in the midst of a uniformly 
distributed population, it seems natural to assume that the chance 
of any individual coming into the zone of infection will 
approximate to that given by a normal probability surface of 
which the maximum corresponds to the area in infection. Further, 
this assumption being granted, if the persons infected from this 
source also infect in a corresponding manner, it follows that the 
derived distribution will also be a normal surface, with, however, 
a standard deviation of a great amount. 
When a disease spreads in a city, however, there are many 
factors which make the distribution just conjectured a form to 
which only an approximation can be expected. The population of 
a city is not equally disposed ; the conditions under which people 
live in different districts are not identical as regards the spread of 
infection : especially in regard to smallpox, the amount of vaccina- 
tion performed among the inhabitants of certain parts is much less 
than in others. Apart from these sources of error, it might be 
thought, as the process of spread of an epidemic is analogous to 
* Reports of the Registrar-General for England. 
f Reports of the Medical Officer of Health for County of London. 
