500 Proceedings of Royal Society of Edinburgh. [sess. 
tion of the manner in which single epidemics vary from the 
average. This reason probably accounts for the larger part of the 
differences seen between the actual and the theoretical distributions. 
The striking fact is that epidemics in general hold a course whose 
constants with very great regularity are those of a single member 
of the large class of frequency distributions. It can hardly be ex- 
plained on any other hypothesis than that the law which under- 
lies the propagation of infectious diseases is such as in general to 
produce such a distribution. The investigation of this is much 
more easily attempted a posteriori. The assumption that the 
infectivity of an organism is fconstant, leads to epidemic forms 
which have no accordance with the actual facts. If there be 
given a number of susceptible persons in a community, and if one, 
say, infect three, the whole body of the susceptible persons will 
become involved, and the last few remaining finally swept off. 
Even when allowance is made, on various hypotheses, for the chance 
of infection being small, because of dilution of the susceptibility 
