22 



appeared to be the Bact. aerogenes. This work of Rogers and his asso- 

 ciates aroused considerable interest in the possible different sanitary sig- 

 nificance of these bacteria and has stimulated considerable investigational 

 studies. 



Acid Production. Studies on acid production have been carried 

 out from two points of view. The earlier observations were restricted to 

 qualitative tests or to the determination of total titratable acid with phen- 

 olphthalein as an indicator but the more recent studies have concerned 

 themselves with actual or effective acidity (i. e. the H + ion concentration) ; 

 Evidence as to the differentiations of Bact. coli and Bact. aerogenes by 

 both of these methods will be considered briefly. 



Total or Titratable Acid. In considering total acidity, we are 

 struck with the fact that the titer is affected by the composition of the 

 medium as was indicated in the preceding chapter. Observations of 

 different investigators are therefore extremely difficult to compare as com- 

 parable data can be obtained only with the same medium. Furthermore 

 in order to avoid fallacies, it is necessary to observe considerable numbers 

 of strains and to treat the results statistically. A few extremely high or 

 low results will influence considerably the average acid production of a 

 collection of organisms. The use of unqualified averages may therefore 

 lead to a misconception of the acid producing properties of a group. To 

 supplement the arithmetic mean or numerical average some statement should 

 be made as to the distribution of the individual strains (variates) about 

 the average. This may be indicated by the probable error or by the 

 standard deviation. The coefficient of variability (the ratio of the stand- 

 ard deviation to the mean) is an excellent abstract measure of variability. 

 The modal acid production (the amount of acid most frequently formed) 

 is usually of greater significance than the average amount of acid formed. 



The standard deviation is the measure of variability most commonly 

 employed, particularly by mathematicians. It may be expressed mathe- 

 matically as 



where "n" is the number of variates or observations, "d" the deviation of 

 the individual variates from the mean, and "f" the frequency of a devia- 

 tion "d".The standard deviation serves to indicate whether the departures 

 from the mean are small or great. The closer the individual organisms 

 group themselves about the mean, or average, the smaller the standard 

 deviation. 



An example may make clear the meaning and significance of the 

 standard deviation. Suppose that the amounts of acid formed by a group 

 (A) of 4 organisms in glucose broth are 2.1, 2.2, 2.2, and 2.3 percent normal 

 acid, and that those formed by another group (B) of 4 organisms are 1.9, 

 2, 2.4, and 2.5 percent normal acid. The average for each group is 2.2, 

 but mere inspection shows that the organisms in Group A and those in 



