R. A. Fisher, H. G. Thornton, and W. A. Mackenzie 337 



;^^ (> 11) among the higher values of x, but this on investigation proved 

 to be completely accounted for by the epidemic character of the occur- 

 rences of these large values, which we shall demonstrate below (see Fig. 2). 

 The longest and most severe epidemic occurred during a period (Oct.- 

 Dec.) when the bacterial numbers were generally high. Within this 

 period no sensible association is apparent. 



Confining attention therefore to the distribution of x'^, irrespective of 

 the mean number of colonies counted, it is clear that the sets with 

 exceptionally large variations, which interfered with the preliminary 

 reduction of the data, are now distinguishable as those with high values 

 of x^- If the sets were random samples of Poisson Series, it appears from 

 Elderton's Tables that only 3 per cent, of the observed values should 

 exceed 9. It is clear that there is here a group which must be excluded 

 in considering the agreement of the remainder with the theoretical 

 distribution. If this were the only irregularity in the observed numbers 

 we should therefore compare them with a theoretical series having the 

 same total below 9. As it is there is also some irregularity visible at the 

 beginning of the series, suggesting that there is also an excess of unduly 

 small values of x^- For this reason we shall base our comparison on the 

 total observed between 1 and 9, as is shown in Table VII. 



Table VII 

 Compariso7i of observed and expected distribution of x^, ^-plate data. 



Within the range from 1 to 9, the agreement of the observed with the 

 expected values is striking. When tested in eight groups, the probabiUty 

 of obtaining a worse fit by chance from perfectly normal data is -682, 



Ann. Biol, ix 22 



