338 



MetJwd of estimatinrj Bacterial Density 



and even when grouped in the most unfavourable manner, by throwing 

 together consecutive positive and negative residuals, a method suggested 

 by Mr Udny Yule, the probability is still -232. There is therefore no 

 significant deviation of those values from expectation. 



Of those above 9, we may anticipate that some three or four will be 

 normal values and the remainder exceptions. It is of course impossible 

 to separate these with absolute certainty. In discussing the evidence for 

 epidemics we shall assume that the four values below 11 are normal and 

 that the remainder are exceptions. When, however, the fact of the 

 epidemic incidence of those exceptional values is taken into account, it 

 appears that the two between 10 and 11 are among the relatively few 

 '■ normal" sets occurring in an epidemic period and are therefore probably 

 exceptions, while the two between 9 and 10, and possibly also the value 

 at 11-4, are for the same reason probably normal. 



It is thus possible to separate this class of exceptions from the 

 remaining data with some degree of certainty and to study them 

 individually, but this is not possible for the exceptionally invariable sets. 

 All that we can do here is to show that the evidence for their real 

 existence is stronger than appears in Table VII. If we subdivide the 

 region of the first two groups of that table somewhat more closely we 

 obtain 



Table VIII. 



the excess of numbers is most clearly marked in the group of smallest 

 values, and is possibly though not certainly confined to the region. 



These conclusions are independently confirmed by the sets of five 

 parallel plates. In Table IX is shown a comparison of the observed 

 distribution with that expected, on the basis of the total observed 

 between 2 and 11. 



The agreement with expectation in the range from 2 to 1 1 is perfectly 

 satisfactory ; when tested in the 9 unit groups, the possibility of obtaining 



