SEA-FISHERIES LABORATORY. 147 
Let there be an experience of n cases, and let p/n of 
these be positive and q/n negative, p/n + q/n =1. Now let 
there be a second experience of m cases: what percentage of 
these may we expect to be positive? If n is very great 
compared with m we expect to find— 
100? + 67-45 a/ Bin x gin 
n m | 
but if, as in this case, m is greater than n we expect— 
Mi! 67-45 4/P ,. 4 oe) 
n n nm ‘Mm n 
When we sample the sea-water in the neighbourhood of a 
mussel bed we usually examine a few c.cs., say 10 (though it is 
not often that the sampling is so thorough as this). Ten 
plates, let us say, are made, and these give n, n,, 7, etc., 
colonies. The mean ism + PE, when we consider the probable 
error. Now there are certainly very many cubic metres of 
water in the neighbourhood of the spot where our 10 ¢.c. samples 
were collected. Are we to assume every c.c. of this volume 
contains » + PE organisms? The treatment of the error 
of expectation will follow the lines already indicated. 
The statistical precautions suggested here are in no way 
fantastic: one really does all this sort of thing, in a quite 
irregular way of course, every day in the ordinary affairs of life 
when we “take chances.” It is all done in a systematised 
and skilled way by actuaries and insurance companies, and 
in a practical, unscientific way by bookmakers. 
The Indicators of Faecal Pollution. 
What is looked for in such analyses as we have discussed 
are not the germs that cause enteric fever, but indications that 
such germs may, in certain circumstances, be present simul- 
