400 LOUIS J. GILLESPIE 



mation point (at pair 4), then pairs 3, 4, and 5 will be substafi- 

 tially correct as calculated by the plan in question, but pairs 2 

 and 6 will be in error by nearly 0.10 pH, and pairs 1 and 7 by 

 about 0.25. The mass action equation is, however, in accord 

 over the useful interval of pH with the measurements of Tizard 

 (1910) for methyl red, of Barnett and Chapman (1918) for phenol 

 red,- and of the present writer for all indicators studied by 

 Medalia, except the acid range of thymol blue, which was not 

 studied. 



We do not need to assume the applicability of the mass action 

 equation in order to show that the proposed tables are in dis- 

 agreement wdth these measurements. It is only necessary to 

 plot the results to be compared on one diagram in any uniform 

 manner,^ and the discordance wall be apparent. The proposed 

 tables must therefore be considered incorrect, since the plan on 

 which they are mainly based lacks a solid foundation, and is not 

 supported by enough data to put into question the conflicting 

 measurements. 



In the article, mention is made of measurement of acid produc- 

 tion of bacteria by means of pH determinations. A word of 

 warning seems justified by the fact that the idea is apparent 

 in the writings of others. The definition of acid production in 

 terms of a difference between initial and final pH values is decid- 

 edly not superior to definition in terms of titration, but rather 

 false, or at least of slender and involved significance. To measure 

 how much acid is produced we must titrated If the composition of 

 the culture medium makes impossible a true titration on the 

 direct culture, then we may distil the volatile acids and titrate 



2 This has been shown by me (Gillespie, 1920). 



^ For instance, the percentage of indicator placed in the alkaline solution 

 may be plotted against the pH pertaining to it, or better, the logarithm of the 

 ratio between the quantities of indicator as distributed between the alkaline 

 and the acid tubes of the color standards may be plotted against pH. By the 

 second procedure a straight line is required by the mass action equation. Mathe- 

 matically, the plan of Medalia consists of a pure guess as to the form of the curve 

 obtained by such plotting of the data. 



^ Measurement of change of pH may, in some cases, give us the acid produc- 

 tion, if we have already incorporated the results of titration in a titration curve. 



