1905-6.] Studies in Immunity : Theory of an Epidemic. 495 
of the curves representing the cases and those representing the 
deaths. The disease shows a marked rise at practically the 
same period, year after year. During the seasons at which it is 
nearly absent, the figures giving the weekly number of deaths 
are almost absolutely constant. Whether these deaths are due to 
the same form of diarrhoea as that which causes the summer out- 
burst is not clear, but these numbers indicate a distribution which 
is essentially different from that given by the terminal portions of 
the probability curves. So that if the epidemic be fitted to such 
a distribution, some allowance must be made. The most natural 
assumption is to subtract a number equal to the average number 
of cases in the inter-epidemic period from the weekly or monthly 
numbers during the epidemic period. 
Zymotic diarrhoea forms the sole example in which an average 
can be obtained for the course of an epidemic, as the annual out- 
burst lasts only about three months and has a well-defined be- 
ginning and end. As a first example the statistics of Glasgow * 
have been chosen, as they have been for many years less subject 
to these fashions of death certification which make the returns of 
the Registrar-General for England difficult of interpretation. The 
Medical Officer of Health for Glasgow has been in the habit of 
specially classifying these cases for himself. The result is that, 
while the figures may not absolutely accurately represent the true 
number of deaths from zymotic diarrhoea, the statistics are homo- 
geneous. The period chosen concerns the years 1890-1903. The 
result is represented in the figure (diagram XII., Table A, No. 19), 
and is seen to be an instance of a really good fitting curve. When 
tested by Professor Pearson’s method, the probability is found to 
be about ‘35, which, considering the kind of case, is a good fit. 
As curves of cases and deaths (diagrams XIII. and XIV., Table 
A, Nos. 21 and 22), the figures of the Children’s Hospital in 
Manchester f are given. Here, again, as a period of ten years is 
embraced in the statistics, an average is obtained. In these 
epidemics a curve very nearly normal in character is given by the 
cases of the disease, while the corresponding deaths have a dis- 
* From the Notebook of the Medical Officer of Health. 
f Supplement to the Report of Medical Officer of Local Government Board 
for 1887 on Diarrhoea and Diphtheria, p. 68. 
