110 PHYSIOLOGY OF BACTERIA 



The rate of fermentation can be written in its mathematical form: 

 dx J ^/ alcohoK 



ax , ,,/. aiconoix 



which means that the rate with which the sugar is decreased, is 

 proportional to the amount of yeast Y, and is independent of the 

 sugar concentration which, therefore, does not enter the equation 

 at all, and is retarded by alcohol in the manner discussed above. 

 Since one gm. of sugar yields practically one-half gm. of alcohol, 

 we can substitute: 



alcohol = one-half of sugar, or 



X 



alcohol = X 



because x was the amount of sugar decomposed. Thus we get 

 the equation 



= ^y(2L-x) 



Y, the amount of yeast, is constant in Rubner's experiments because 

 more yeast was added than would normally grow in such a solution. 



k 

 Therefore, the entire expression • F is constant, and may be sub- 



stituted by another constant, K. The equation 

 -J = K{2L - X) 



gives upon integration 



2L 



Kt = In 



2L -X 



The accuracy of this equation can be tested by com- 

 puting the X-values for all the above data. The 

 fermentation constants in the right section of Table 15 

 have been computed with the value L = 10.2 % alcohol. 



