107 



Total (for estimating averages) 151 



Average of 7 tests 21.6 per c. c. 



In 1915 McCrady proposed a method for the calculation of the most 

 probable number of colon bacilli from a series of fermentation results 

 but his methods have not been employed because of the cumbersome cal- 

 culations involved. Wolman and Weaver, in 1917, simplified the McCrady 

 formula and presented some graphs by means of which the tedious com- 

 putations are almost entirely removed. 



If A=total number of tubes inoculated with 10 c. c. 



B=total number of tubes inoculated with 1 c. c. 



C=total number of tubes inoculated with 0.1 c. c. 



a=number of 10 c. c. tubes positive 



b= number of 1 c. c. tubes positive 



c= number of 0.1 c. c. tubes positive 



then x the most probable number of colon bacilli per 100 c. c. may 

 be obtained by trial substitutions of values for x in the following equation. 



lOOa lOb Ic 



100A - 10B - 1C=- 



.99 X 1 ,999 X 



From the charts accompanying Wolman and Weaver's paper, the 

 values for x corresponding to any proportion of positive tests may be 

 read off directly when dealing with a single dilution. When concerned 

 with several dilutions the above formula must be employed, but the val- 

 ues of (1 .9 X ), (1 .99 X ), and (1 .999 X ) for any assumed value of 

 x are also given on these charts so that the actual mathematics involved 

 is reduced to merely simple arithmetic. 



Stein in 1918, from a consideration of the laws of probability, evolved 

 a curve from which the colon index, together with its reliability could be 

 read directly if (1) the number of observations (2) the proportion of 

 positive tests, and (3) the size of the test samples, were known. 



For further details the reader is referred to the original papers by 

 Stein, M. F. Journal of Bacteriology, IV, 1919, p. 243, and Wolman and 

 Weaver, Journal of Infectious Diseases, XXL, 1917, p. 287. In the Pub- 

 lic Health Journal (Canadian) IX., 1918, p. 201, McCrady presents a set 

 of tables for the interpretation of fermentation-tube results, which almost 

 completely relieve the analyst of mathematical calculations. 



