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STATE BOARD OF AGRICULTURE. 



amount of acid a will be produced. The second generation consists of 

 twice as many cells which will, in the same time, produce twice as much 

 acid as the original number, and this is added to the first acid, making 

 the total quantity Sa. The third generation consisting of four times as 

 many cells as the original, will produce four times as much acid, making 

 the total 4a -}- 3fl = la. The fourth generation produces eight times as 

 much acid, etc. The resulting curve is shown in Figure 4. There is 

 evidently, in the beginning, a tendency in the curve to become gradually 

 parallel to the ordinate. This is, however, naturally limited by the re- 

 striction in the multiplication of the bacteria. After a certain time, 

 the growth of the acid producers will become slower and slower and 

 finally will cease. As soon as this takes place, the active mass is con- 

 stant, and when the active mass is constant, we have an enzymic curve. 

 The enzymic curves have the tendency to run gradually parallel to the 

 base line, and this combination of the two curves, the "curve of growth" 

 with the enzymic curve, gives rise to the typical "fermentation curve." 

 If the number of bacteria decreased soon after reaching the maximum, 

 the resulting curve from this moment would correspond to the law of 

 Guldberg and VVaage, giving practically the same path of curve. 



It is not necessary, however, for a typical fermentation curve that 

 the multiplication of micro-organisms follow the geometrical progres- 

 sion as in the example mentioned above. Any increase of active mass 

 will cause an increase in the rate of fermentation, or an increasing 

 angle of elevation, and we obtain fermentation curves with yeasts and 

 moulds as well as with bacteria, though their laws of multiplication are 

 different. Even growing animals and growing green plants must give 

 similar curves for their products. It is, of course, understood that the 

 factors influencing growth and fermentation, as e. g., temperature. 



Fig. 4. The Theoretical Fermentation Curve. 



