86 
its highest point, the cycle is extended to nine and eight 
years, and after prolonged and severe epidemics of whooping 
cough in 1790 and 1805 the interval is longer than usual. 
4. When a small epidemic, or an attempt at an epidemic, 
occurs in the middle of a period, the interval is usually 
rather longer. This happens with measles in 1789 and in 
1796, and in one case the gap between the highest points of 
the curve is eight and in the other nine years, instead of 
six or seven, as in other instances. In 1793 and 1817 there 
are also small waves of whooping cough postponing the 
usual outbreak of this disease from four or five to seven 
and nine years respectively. 
It is interesting further to notice in this regard the 
inverse ratio that holds between the height of the epi- 
demic and the lowness of the disease in the periods pre- 
ceding and following it. 
This is especially noticeable in the chart of whooping cough, 
in which the amount of disease constantly present graduaUy 
diminishes, and the epidemic waves rise higher and higher 
until the }mar 1806, and after this date the reverse process 
1ms been pursued. The disease, in fact, imitates the ocean 
in its spring and neap tides — though from a different 
cause — its ebb and flow following the same rule of a high 
tide with a low subsequent ebb. 
U])on tlie hypothesis now before us all these facts would 
be readily explained by the varieties in the densities of the 
susceptible populations. 
The degi ee of proximity of susceptible persons would be 
much more readily obtained in England in her crowded 
towns, and with her large number of births in proportion 
to acreage. In many parts of the country, in fact, it would 
probably be difficult for an epidemic to clear the ground 
so completely that in another year it would not again be 
filled up with a number of persons in sufficiently close 
Mioximity to one another to allow the disease to spread. In 
