142 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
getting the vertical pots 10, 13-3, 15 and 16, read from 
above downwards. From these poimts horizontal lines, 
“lL range,” etc., are drawn to cut the curve, and from the latter 
points of intersection vertical lines are drawn to cut the 
horizontal axis. The points on the latter axis thus obtaimed, 
and read on the horizontal scale, give us various ranges of 
counts with their respective probabilities of occurrence. 
Thus :— 
hh 
1 of all the counts lie between 0 and 16, 
Be nob s u 0 and 21, 
$ 55 9 = 0 and 24, 
+ 5 “ 0 and 26, 
and also :— 
It is 1 to 1 that there were less than 16 colonies on a plate, 
It is 2 to 1 i rf 21 =. oa 
It is 3 to 1 s 4 NS 
It is 4 to 1 4 $9 26 
39 99 
We have now clear ideas as to the degree of pollution, 
for any one of the admissible estimates is qualified by its 
degree of probability. If we wish to minimise the pollution 
we might say that there were less than 16 colonies on a plate, 
that is, less than 16 x 50 = 800 organisms per average mussel, 
but we ought also to say that the chance that there are less 
than this number, and not more, is only 1 to 1—*“ the odds 
areeven.” If, on the other hand, we wish to make the pollution 
as grave as possible we might say that there were not less than 
26 colonies per plate, that is, not less than 26 x 50 = 1,300 
organisms per average mussel, but the probability that the 
pollution is less than this is 4 to 1. 
Suppose that we make 1,000 organisms per average mussel 
a “standard of permissible impurity.” This corresponds to a 
count of 20 colonies on a plate. Reading the graph inversely 
we see that 20 colonies per plate corresponds to a range of 2 of 
the total range of counts, and thus the probability that the 
number of organisms found was less than the standard was 
