486 Proceedings of Royal Society of Edinburgh. [sess. 
The result of these calculations has been to show that the curve 
of the solitary epidemic is singularly constant. It almost uniformly 
corresponds to that probability distribution which Professor Pearson 
has termed type IV., * so that this curve may be chosen for inter- 
polation, as one which gives a very clear representation of the facts. 
Even when the epidemic becomes symmetrical, it is to the form of 
type IV., where v is equal to zero, that the course approximates, 
and not to the normal probability curve. The precise limitation 
of an epidemic in point of time does not alter the form referred to, 
for in this case also the constants generally indicate a curve of 
type IV., though the latter is unlimited on either side. As the 
first example of curve fitting to the course of an epidemic wave, 
miliary fever (Table A, No. 1) f has been chosen. This instance 
does not afford an example of a curve which gives a good fit, but it 
is a disease of which the cause and the means of propagation are 
absolutely unknown, and therefore one which spreads as near as 
possible in natural conditions. It affects country districts, so that 
as new townships are invaded at all stages of the epidemic, and as 
these tend to become more numerous as the disease extends, a 
supply of susceptible persons is constantly furnished and a criterion 
given for the approximate estimation of the infectivity of the 
organism. It is, in addition, an explosive disease, and thus no 
difficulty arises about the start and close of the outburst. All the 
factors which make for the investigation of an epidemic type are 
thus present in this case. The course of an epidemic of this disease 
is illustrated in diagram I., along with the theoretical interpolation 
curve as well. As the number of persons exposed increased from 
the beginning to the end of the epidemic, it is seen that the decline 
in the number of cases must be due to the loss of infectivity in 
the germ itself, and not to the lack of individuals who may be 
supposed open to the contagion. Equally characteristic examples 
are afforded by the great plagues of London (Table A, Nos. 2 and 
3). That of 1665 is specially interesting, as we have many 
contemporary accounts of the conditions which obtained. Great 
migrations from the city began as soon as the plague established 
itself, but the disease had barely begun to abate when the return 
* See Note at end of paper. 
f Rayer, Histoire de Vepidemie de Suette Miliare, en 1821, Paris, 1822. 
