R A. Fisher, H. G, Thornton, and W. A. Mackenzie 357 



difficult to imagine that this cause could be responsible for any such 

 bias as is observed, in view of the fact that a probable error is calculated 

 separately from each set. Severe competition between colonies on the 

 plate is admittedly a possible cause of diminished variabihty, but we 

 cannot imagine it acting with such severity as would be necessary to 

 explain these results, especially as in the 38 cases in w'hicli x" is less than 

 one, the mean number of colonies per plate is always less than 100, and 

 in 15 cases is less than 10. 



In more than one instance all the six plates have an equal number of 

 colonies; in samples from a Poisson Series, this would occur but very 

 rarely. For 13 colonies on each plate for example, as is recorded in one 

 instance, the most favourable assumptions will only allow such a coin- 

 cidence once in some 25,000 trials. Since in the majority of these counts 

 we clearly are not dealing with undisturbed conditions of random 

 samphng, the point cannot be pressed further. We do not agree, however, 

 with the statement that, when such a coincidence occurs, the probable 

 error is zero. 



In reviewing the foregoing data, it seems probable that the action of 

 liquefying bacteria, and the development of rapidly growing organisms, 

 unchecked by the medium employed, were the main causes of excessive 

 variance between parallel platings in the work of Buddin and Engberding 

 respectively. 



It appears, however, that the conditions of accuracy, such that the 

 development of colonies on parallel platings will form a Poisson Series, 

 can be fulfilled in deahng with a simplified bacterial flora (Breed and 

 Stocking), and have been approached in dealing with the mixed micro- 

 flora of soil, where the medium used has been so devised as to check 

 the excessive development of spreading organisms, as in the case of 

 Thornton's medium. It is possible that these conditions of accuracy 

 would be fulfilled with greater certainty in the case of a mixed micro-flora, 

 if the medium could be further improved so that it checked the growth of 

 such harmful organisms as that found in the Leeds soil (p. 345). 



Conclusions 



(1) Under ideal conditions the bacterial counts on parallel plates wnll 

 vary in the same manner as samples from a Poisson Series. When these 

 conditions are fulfilled the mean count of a number of plates is a direct 

 measure of the density of the bacterial population considered (though 

 not, of course, of the total bacterial flora); and the accuracy of such an 

 estimate is known with precision. 



