In reporting a single test, it is preferable merely to record results as observed, indicating the amounts tested and the result in each, rather than to attempt expression of the result in numbers of B. coli per cc. In summarizing the results of a series of tests, however, it is desirable, for the sake of simplicity, to express the results in terms of the numbers of B. coli per cc., or per 100 cc. To convert results of fermentation tests to this form, the result of each test is recorded as indicating a number of B. coli per cc. equal to the reciprocal of the smallest decimal or multiple fraction of a cubic centimeter giving a positive result. For example, the result: 10 cc. +; 1 cc. +; 0.1 cc. -; would be recorded as indicating one B. coli per cc. An exception should be made in the case where a negative result is obtained in an amount larger than the smallest portion giving a positive result; for example, in a result such as: 10 cc. +; 1 cc. -; 0.1 cc. +. In such case, the result should be recorded as indicating a number of B. coli per cc. equal to the reciprocal of the dilution next larger than the smallest one giving a positive test, this being a more probable result. Where tests are made in amounts larger than 1 cc., giving average results less than one B. coli per cc., it is more convenient to express results in terms of the numbers of B. coli per 100 cc. The following table illustrates the method of recording and averaging results of B. coli tests: Result of Tests in Amounts Designated. Indicated Number of B. coli. 10 cc. 1 cc. 0.1 cc. .01 cc. per cc. per 100 cc. + − − − 0.1 10. + + − − 1.0 100. + + + − 10.0 1,000. + + + + 100.0 10,000. + + − + 10.0 1,000. ————— ————— Totals (for estimating averages) 121.1 12,110. Average of 5 tests 24.0 2,422. The above method of expressing results is not mathematically altogether correct. The average number of B. coli per cc., as thus estimated, is not precisely the most probable number calculated by application of the theory of probability.[220] To apply this theory to a correct mathematical solution of any considerable series of results involves, however, mathematical calculations so complex as to be impracticable of application in general practice. The simpler method given is therefore considered preferable, since it is easily applied and the results so expressed are readily comprehensible.