116 PARASITES OF GIPSY AND BROWN-TAIL MOTHS. 
been present in the spring the insect could never, by any possibility, 
increase beyond the abundance then prevailing. If the increase each 
year was 6 egg masses for each 1 of the year before, it was merely 
necessary to destroy 5 out of every 6 in order to maintain the status 
quo. If the increase was tenfold, the destruction of 9 out of every 10 
ege masses would be required, etc. The same would obtain if 5 out 
of every 6 or 9 out of every 10 eggs in each and every mass were 
similarly destroyed. 
Reduced to percentages, this would be equivalent to the destruction 
of 83.33 per cent or of 90 per cent, respectively, a rate of parasitism 
which was physically an impossible accomplishment for the egg 
parasites alone. Additional parasitism of the caterpillars or pup 
would be a requisite to success, and such parasitism would of neces- 
sity be similarly limited in many instances through circumstances as 
completely beyond our control as the physical inability of Schedius or 
Anastatus to parasitize more than the uppermost layer of eggs in each 
mass attacked. Without attempting to go into any of the details 
of the processes by which conclusions were reached, it was finally 
determined, beyond any doubts arising through arguments which 
have been presented up to the present time, that an aggregate parasit- 
ism of 83.33 per cent would be absolutely necessary if a sixfold 
increase was to be met, but that it made no difference whether this 
was brought about by one species or two or a dozen, or whether they 
attacked the egg, the caterpillar, or the pups. It was also deter- 
mined that the aggregate percentage necessary could not be secured 
by simply adding together the figures representing the parasitism 
resulting through attack by each of two or more species. It was 
going to be necessary to combine these several aggregates in a dif- 
ferent manner. To illustrate: A 50 per cent parasitism of the eggs, 
if it could possibly be secured, followed by another 50 per cent parasit- 
ism of the caterpillars, could not by any possibility be considered as 
resulting in 100 per cent parasitism or complete extinction, but only in 
50 per cent parasitism added to 50 per cent of what remained, which 
amounted, in effect, to 25 per cent of the whole. In this manner an 
ageregate of 75 per cent only is secured. 
As is illustrated by the table on page III, it requires the combina- 
tion of an imposing array of figures representing relatively small per- 
centages of parasitism in each instance to acquire a sufficiently large 
ageregate. 
Tt was further determined that any specific amount of parasitism, 
as 20 per cent of the eggs, was neither more nor less, but exactly as 
effective as 20 per cent parasitism of the caterpillars or pupe, in so far 
as its value in constructing the final aggregate was concerned. 
It can not be denied that when the validity of these conclusions 
became established and when in addition the possibility that a much 
