106 



will show that it is extremely difficult to estimate the number of colon 

 forms present from the result obtained. Perhaps the point can best be 

 illustrated by considering a specific example. 



Suppose a sample of water was examined and gave the following re- 

 sult for colon types: 1 c. c.+ ; O.I c. c.+ ; and 0.01 c. c. . What was the 

 incidence of the colon group per unit volume? Should 10 colon bacilli 

 present per c. c. be recorded? It might be said, as is commonly stated, 

 that there were more than 10 but less than 100 colon forms, and yet it is 

 conceivable that there might be less than 10. Assume that there were five 

 Bact. coli per c. c. In that case, in taking out a 0.1 c. c. sample the analyst 

 would be just as likely to catch a Bact. coli as to miss one. The mere 

 detection of the organism in a sample is not necessarily a safe criterion 

 for regarding the organism constantly present in that quantity of water. 

 On the other hand, the absence of colon forms in 0.01 c. c. is no justi- 

 fication for stating that such organisms would be absent if another 0.01 

 c. c. sample were taken, for if there were 50 colon bacilli present per c. c., 

 the analyst would be just as likely to catch an organism as to miss one 

 in a single 0.01 c. c. sample. It is apparent, therefore, that from the an- 

 alysis presented it is extremely difficult to express by a single figure, the 

 number of colon types present per unit volume. If, however, instead of 

 having taken one portion of each dilution ten had been employed, a very 

 much closer approximation to the actual number of organisms could be 

 made. Similarly if the dilutions indicated were taken on ten different 

 days a reasonably close estimate could then be made of the average num- 

 ber of colon bacilli present during that period. 



In water works operation, and for comparison of the efficiencies of 

 different plants, we are not concerned with a single analysis but with a 

 series of analyses extending over a long period, perhaps a month or a 

 year. A number of methods have been suggested for calculating the in- 

 cidence of the colon group or what is known as the "Colon Index." . 



The most commonly employed method, and the one recommended by 

 the A. P. H. A. is that of Phelps. More complicated but probably more 

 accurate methods are described by McCrady, Wolman and Weaver, and 

 Stein. 



The Phelps method is based on the assumption that the most probable 

 number of organisms present in any specimen is the reciprocal of the 

 highest positive dilution; thus in the above example (1 c. c.-f ; 0.1 c. c.+ ; 

 0.01 c. c. ) 10 colon forms per cubic centimeter would be considered 

 the most probable number. To obtain the colon index for a month or a 

 year it is merely necessary to add the reciprocals of the highest positive 

 dilutions for the individual (daily or otherwise) tests and divide by the 

 total number of tests; this will give the average, but not necessarily the 

 most probable, number for the period under consideration. An example 

 follows: 



