1905-6.] Studies in Immunity : Theory of an Epidemic. 503 
diagrams are examined. Without exception, these show near the 
height of the epidemic a difference, but it is at this point alone 
that much divergence of the actual statistics from the interpolation 
formula occurs. 
Although it might appear that the application of the preceding 
to endemic diseases was simple, yet such is not the case. Even 
when, from the course of an epidemic wave, it might seem easy to 
form equations of two succeeding epidemics, and combine them 
so that the sum would accurately represent the course of this 
epidemic, this is found to be difficult. Thus, on the introduction 
of a disease like plague, although the rise of the epidemic might 
be characteristic and the commencement of the decline also lead 
to the expectation that the outburst would soon approach its 
close, yet a recrudescence might occur before the first outbreak 
had finally subsided. In the case of the chief endemic diseases 
in this country, namely, scarlet and enteric fevers, there is 
a yet more difficult problem, because at no period of the 
year are they absent, while in the autumn epidemic out- 
bursts occur with great regularity. Solitary epidemics are not 
frequent. A number, however, of the latter have been investi- 
gated, with the result that they are seen, with one exception, 
to conform to the same type as has been found in other diseases. 
For scarlet fever, for instance, the epidemic in Halifax* in 1880-1 
gives the usual form (diagram XVIII., Table A, No. 27), while that 
of Thorshavn,f in the Faroe Islands, invaded in 1873-4 by 
scarlet fever for the first time for thirty years, is also seen to be of 
the same type (diagram XIX., Table A, No. 28). The asymmetry 
is, however, much greater, and the decline of the epidemic so 
much more gradual as to require a modification of the hypothesis 
that the infectivity declines according to the terms of a geometrical 
progression. 
It would seem that with scarlet fever a considerable variability 
may exist in the rate at which infectivity is lost. Two epidemics 
of enteric fever are also given, one of which, an outbreak due to 
contamination of the water supply in Coventry J (diagram XX., 
* Report of Medical Officer of Local Government Board, England, 1881, p. 60. 
t Nothnagel’s Encyclopaedia of Medicine, art. “ Scarlet Fever.” 
X Report of Medical Officer of Local Government Board, 1901-2. 
