446 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 



oyster; repeating the same dilution from the last 

 mixture, we get another one in which 1 cc contains 

 1/ 10,000th oyster, and so on. Somewhere we Obtain a 

 dilution where there are no bacilli, at least we find none. 

 We then say that (for instance) 1/ 1000th oyster contains 

 B. coli, but 1/ 10,000th contains none. If we only make 

 one such trial this conclusion seems quite valid. 



But the flask containing the dilution, value 1/ 1,000th 

 oyster in 1 cc, contained very few bacilli : theoretically 

 it must contain not more than 10. Suppose it contained 

 5 organisms, and suppose the volume of liquid in the 

 flask is 100 cc If we take 1 cc,' the probability that it 

 contains one bacillus is 1 in 20, the probability that it 

 contains none is 20 to 1. We do not find a positive result 

 then, let us say, and we assume that B. coli is absent in 

 1/ 10,000th oyster; but the chances may really be 

 20 to 1 that it is present. 



Suppose now that the flask containing the dilution 

 (1/ 1,000th oyster = lcc) gives a positive result. But 

 it may be that this flask really contained very few 

 bacilli and that we just happened to get one, in spite of 

 the chances against it. But another trial may prove to 

 be negative. We must then state our conclusions in this 

 manner: B. coli was present in 1/ 1,000th oyster, but it 

 may have been absent; or it was absent in 1/ 1,000th 

 oyster, but it may have been present. All that we must 

 say is that B. coli was present in 1/ 100th oyster and 

 absent in 1/ 10,000th oyster, for the statistical error 

 clearly involves three dilutions. If we wish to be more 

 precise we must make a number of cultures from each 

 flask and then calculate the probabilities.* 



* All this is obvious enough and similar, or analogous, precautions 

 against error would be taken in chemical or biological research. But I 

 can find nothing in bacteriological literature to show that these consider- 

 ations affect public health bacteriological practice. 



