80 MR. F. BALFOUR BROWNE ON AQUATIC COLEOPTERA 
associate of “ A,” although both species have appeared in the 
“ A ” collections their maximum number of times. “ B’s ” 
25 therefore should equal “ C’s ” 20. Both values must 
therefore be brought to a common series which is of course 
done by dividing each by itself and thus bringing them to 
unity. For simplicity it is perhaps better to work in 
hundreds, reckoning the maximum possibility in each case 
as 100. 
Thus if “ B ” occurs in 90 % of the “ A ” collections its 
value is 90 — 75, i.e., 15 % in favour of “ A.” This, if multi- 
plied by 100 and divided by the maximum 25 already 
determined will give us 60 % as the true value of “ B ” in the 
“ A ” collections. Similarly if “ C ” occurs in 35 % of the 
“ A ” collections its value is 35 — 20=15 % in favour of “ A,” 
and by multiplying this by 100 and dividing by the 
maximum 20 already determined we shall get 75 % as the 
true value of “ C ” in the “A” collections. 
Now if “ D ” occurs in only 8 % of the “ A ” collections 
its case is somewhat different from that of either “ B ” or 
“ C.” Had it occurred in 15 % of “ A ” collections its value 
in favour of “A” would have been o because it would have 
been equally common in the “A” and in the general 
collections. Since it occurs in less than 15 % of the “ A ” 
collections its value to “ A ” is less than o, or a minus quantity. 
If it had not occurred in any of the “ A ” collections its value 
to “ A ” would have been — 15, the lowest possible. Just as 
we converted the maximums into 100 so we can convert the 
minimum, and — 15 becomes — 100 %. Thus multiplying 
the 8 % by 100 and dividing by the minimum 15 will give 
us 53 % as the value of “ D " in the general collections, that 
is, — 47 % as the value to “ A.” 
By this process we can trace the relative value of every 
species as an associate of every other species. 
I have not yet carried the investigation far in this direction, 
and my object now is to bring the method before you rather 
than to attempt to divide up the various and complex 
associations of Water Beetles. However, in order to show you 
the application of the principle I have worked out the values 
