144 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
The Error of Random Sampling in Houston’s Method of 
Decimal Dilutions with Bile-Salt Broth. 
Let the liquid of the measuring flask be diluted 10, 
100, 1,000, etc., times: we thus get a series of liquids, 
one c.c. of which contains respectively 1/50th, 1/500th, 
1/5,000th, 1/50,000th, etc., part of an average mussel. One 
c.c. of each dilution is put into a tube of bile-salt broth, and the 
cultures are incubated. The tubes containing 1/50 and 1/500th 
mussel give (say) positive reactions, and the tubes containing 
1/5,000th and 1/50,000th show no change, that is, 
1/50th +, 1/500th +, 1/5,000th —, 1/50,000th —. 
There must, therefore, have been at least one micro-organism 
in the c.c. of liquids inoculating the first two tubes, and there 
could not have been any in the c.c. used to inoculate the third 
and fourth tubes. The inference is that there are at least 
500 organisms present in an average mussel, but there are less 
than 5,000. If only one tube os inoculated from each dilution 
this method gives apparently definite results. The limits of 
dilution used above are wide ones, but obviously they can be 
narrowed so that we could apparently get closer approximations 
to the degree of pollution. : 
Now each c.c. of the 1/500th dilution was assumed to 
contain at least one micro-organism, and in making the 
1/5,000th dilution at least one organism must have been 
introduced. One c.c. of the 10 was taken, so that it is not 
absolutely certain that the higher dilution is sterile. Therefore 
this method only gives a probability of infection. 
This becomes quite evident when a number of tubes are 
inoculated from each dilution. 
The following examples illustrate this :— 
(1) Dilution 0... Ea oe ay wee #t+tt+4+4+4+44+4+ 
¥ 1/10th ... =e a ee A ee 
1/100th ... Ae ore . taaaanaaaad 
,  1/1000th a) Wo a oh err 
