270 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. U, NO. 12 



tribution of bacterial counts C as would be guessed from "common 



sense." 



The frequency distribution (6) is mathematically very complicated. 

 Its graph, represented in figure 1 for the values 2 = 10 and 100 bac- 

 teria per cc, shows it to be nearly symmetrical about the mode, the 



1 1^ i. 





c 



H««i>*r »\ dacter'to. 



Fig. 1. — Graph of frequency distribution. 



maximum becoming very accentuated as z increases. This is obvious 

 from the variability of the curve, computed by Pearson's method of 

 moments, and given in table 2 together with the other constants. 

 Thus the curve possesses the remarkable property that although 

 it is unsymmetrical, the mode and the arithmetic mean coincide 

 within the errors of the computation. The geometric mean is of course 

 slightly smaller, but either mean is quite close enough for practical use. 

 Replacing the mode in (17) by the arithmetic mean (C), we have 



X = DC (18) 



so that the number of bacteria per cc. is calculated simply. 



