R. A. Fisher, H. G. Thornton, and W. A. iMackenzie 331 



distribution, and that when this is the case the accuracy of the count 

 is known with precision and depends only on the number of cells counted^. 

 The ideal conditions for bacterial counts made by the dilution 

 method, are closely parallel to those found necessary in the case of the 

 haemocytometer. The chief practical difference lies in the fact that 

 instead of 400 squares with only a few yeast cells in each, we have some 

 five plates with perhaps 200 colonies apiece. The agreement of the 

 results with the theoretical distribution cannot, therefore, be demon- 

 strated from a single count. Under ideal conditions the data would 

 consist of a number of small samples from different Poisson series. For 

 this reason as soon as it was suspected that this ideal condition might 

 have been realized in practice, a special investigation of the nature of 

 such samples was undertaken, owing to the importance of demonstrating 

 the substantial fulfilment of the severe conditions laid down in the 

 previous section. 



4. Preliminary Reduction of Cutler's Data 



When the question of the accuracy of the bacterial counting technique 

 was discussed between the present authors in the spring of 1921, it was 

 decided that the daily observations of bacterial numbers then being 

 carried out at Rothamsted by Cutler would afford a valuable opportunity 

 of studying the variance between parallel plates and its causes. In this 

 choice our investigation was more than fortunate, for no other series of 

 bacterial counts known to us, of which many have been examined, would 

 have gone so far in clearing up the obscurities of the subject. 



In conjunction with daily estimations of soil protozoa carried out at 

 Rothamsted from July 1920, daily counts of bacteria were also made in 

 the protozoological laboratory (Cutler(i7)). The dilution technique used in 

 this work has been described above. Plates were incubated at 18° C, 

 and counted after five and seven days, the seven day counts only are 

 considered here. Throughout the work the agar medium recently 

 elaborated by Thornton (ii) was used. The data thus supply an extensive 

 test of this medium under routine conditions. 



When the statistical examination of these data was commenced it 

 was not anticipated that any clear relationship with the Poisson dis- 

 tribution would be obtained; the reduction was designed to determine 

 empirically the relation between the mean bacterial number calculated 

 from any set of plates, and the variability of that set about the mean. 

 Knowing this relation, a probable error could be assigned to each value. 



* Valuable tables of the Toisison Series liave been prepared by H. K. ,Soper(7). 



