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Proceedings of the Royal Society of Edinburgh. [Sess. 
as was deduced as a possible one for the epidemic time wave. What has 
preceded is to a certain extent hypothetical in so far as the assumption of 
a form for the frequency of <x is connected ; otherwise it is directly deduced 
in the case of the epidemic from the consideration of a large number of 
typical epidemics, and in the second place by Professor Pearson by a rigid 
mathematical result from the assumptions already referred to. 
The next assumption is the rate at which infective organisms are evolved. 
This may be taken as represented by <p(x), so that at any point x the 
ordinate will be represented by the integral of the curve taken between 
x — c and x-\-c. We then, finally, obtain as the form of the epidemic 
fx+c r™ 
y = y o 4>( x ) I <r 2ne 0-2 * 2 
J x ~ c Jo 
It will be shown later that good agreement of theory with fact is 
