146 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
the error of random sampling appears in the result. From 
(6) we conclude that organisms of the “ Bacillus coli’ category 
are present in 1 c.c. of water and absent in 1/100thc.c. Whether 
they are present in 1/10th c.c. is a matter of probability. If 
we had made 10 separate experiments, and considered each” 
separately, we should have found the organisms in 1/10th c.c. 
in 2 cases, and should have failed to find them in 4 cases. 
In 4 cases the reaction is ambiguous. So also with the other 
water examples: there is always a rather wide interval between 
the test which gives unequivocal evidence of the ‘presence of 
organisms and that which is unequivocal as to absence. 
When we employ a “ factor ” to convert the experimental 
results into numerical estimates of the pollution this margin 
of error becomes greater. In Hxample (7), organisms 
fermenting glucose and growing in bile-salt media are present 
in 1/5,000th part of a mussel, and are absent in 1/5,000,000th 
part. They may be present or absent in 1/50,000th and in 
1/500,000th part, and whether they are present or absent is a — 
probability easily read from the results as they are stated. 
This conclusion applies to the cultures examined after 4 days of 
incubation. If the 1-day cultures had been all that were made, 
the conclusion would have been that polluting organisms were 
present in 1/50th mussel, present or absent in 1/500th and 
1/5,000th mussel, and absent in 1/50,000th mussel. The 
chance that they were present in 1/500th was 4 in 5, and that 
they were present in 1/5,000th was 2 in 5. 
The Error of Expectation. 
In the last example there were 5 samples of 1 c.c., each 
taken from a flask containing 250 c.c. Of these 5 samples 
2 were positive and 3 negative. Itis a rather naive assumption 
to expect that 50 x 2 c.cs. in the flask would be positive and 
50 x 3 would be negative. 
