1905 - 6 .] Studies in Immunity : Theory of an Epidemic. 517 
3. The sudden increase of infectivity in the organism points to 
the occurrence of some stage in its life-history at present little 
understood. 
4. This increase may happen definitely seasonally, as in scarlet 
fever and enteric fever, or without apparent reason, as in the 
case of smallpox, which may continue smouldering in a town 
for a considerable period, and then suddenly give rise to an 
epidemic. 
5. The whole explanation of the organic course of an epidemic 
is not to be found in this alone. Other factors, which are not 
clear, seem to come into play, so as to bring about differences 
from the form of curve to be expected mathematically on this 
basis. 
6. That the epidemic ends because of the lack of susceptible 
persons has no evidence in its favour, either from the form of the 
curve or from the facts : e.g ., in the last epidemic of smallpox in 
London, it can hardly be believed that there were only about 8000 
susceptible persons out of a population of more than 5,000,000, and 
that these were all confined to a small region of London. 
7. And lastly, since epidemics of the same disease run pretty 
much the same course whether they occur in spring, summer, 
autumn, or winter, it would seem that the condition of the germ 
has much more to do with the causation of an epidemic than the 
constitutional peculiarity of the persons affected at the moment. 
Note on the Mathematical Method employed in this Paper. 
When any series of measurements are made of any natural 
object or phenomenon, it is in general seen that these different 
sizes of this object group themselves in a definite manner. These 
arrangements have been found by Professor Pearson capable of 
being represented by a series of curves distinguished as Types I., 
II., III., IV., V., and VI., which are the solution of the differ- 
ential equation, 
1 dy _ x 
y dx 
a + bx + cx 2 
