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



that the arithmetic mean e in any actual case will be merely a cor- 

 rection to be applied to the "average log dilution negative" d. The 

 number of bacteria per cc, X, is therefore roughly equal to the geo- 

 metric mean Gd of the numbers of cc. (D) into which the sample 

 (Ice.) is diluted. Its precise value is given by (12) which is used 

 in the form (11). 



The computation of the "log count" (x) is very simple. The dilu- 

 tions are D = 10, 100, 1000, 10,000, etc., and the corresponding "log 

 dilutions" are d = \, 2, 3, 4, etc.; only those dilutions are chosen for 

 which the "per cent negative" (lOOPo) is between 5 and 90 per cent. 

 The values of e are taken from table 1, and the sum {d ■{- e) recorded. 

 The simple average of these figures gives x. The antilogarithm of 

 X is the number of bacteria per cc. (X). The following examples 

 illustrate the method. 



Example i 

 (20 samples, 3 negative in D = 10 cc, 13 in 100 cc, and all in 1000 cc.) 



d Per cent Neg. d -\- e 



1 20 1.21 



2 65 1.63 



.T = 1.42 



X = 26 bacteria per cc. 



