354 STATE BOARD OF AGRICULTURE. 



AMOUNT OF GELATIN LIQUEFIED. 



Living culture. Dead culture. 



After 1 day 1 mm. 5 mm. 



2 days 5 mm. 



3 days 11 mm. 13 mm. 



4 days 16 mm. 16 mm. 



5 days 19 mm. 17 mm. 



6 days 20 mm. 17 mm. 



(I 



a 

 (I 



The difference between the two curves is plain, though the method of 

 analysis is vei'y inaccurate. The curve of the dead bacteria has from the 

 first moment a decreasing angle of elevation, while the cui^e of the 

 living bacteria becomes at first steeper, and only after the third day 

 does it resemble that of the dead bacteria of the first day. 



In the first three days, the angle of elevation or the rate of liquefac- 

 tion increases. This increase is due to an increase of the active mass, 

 namely, the bacteria or the enzymes secreted by these bacteria. During 

 the fourth day, the rate of liquefaction has decreased a little, the angle 

 of elevation being a little smaller. We must conclude that the active 

 mass has ceased to multiply and is possibly decreasing. The curve of 

 liquefaction, running at first more and more parallel to the ordinate, 

 after three days turns the other way, and has the tendency to become 

 parallel to the base line. The mathematician calls the point where a 

 line curving in one direction changes to another direction, the point of 

 inflection. This point is the characteristic point of the fermentation 

 cuiTe. The part beyond the point of inflection is in no way essentially 

 different from the enzymic curve, but the part before, indicating the 

 ''increase of active mass" is typical for changes brought about by grow- 



ing organisms. 



The point of inflection indicates the moment when the maximum num- 

 ber of bacteria is present. Ck)nsequently, we can recognize a curve as 

 a fermentation curve only when the analysis of the products is begun 

 before the maximum number is reached. At the point of inflection 

 begins the enzymic curve, characterized by no increase of active mass. 



If, instead of using the total products, we would plot the curve from 

 the daily or hourly increase, we get a maximum corresponding to the 

 point of inflection. This is a mathematical law; the curve of the in- 

 crease is the differential curve or derivative of the process itself, and 

 the point of inflection in any cui*ve is necessarily followed by a maximum 

 (or minimum) in the differential curve. 



As one of the simplest examples, we shall discuss first lactic 

 fermentation in pure culture. The following data are taken from a 

 paper by Schierbeck (Archiv fuer Hygiene, Bd. 38, p. 209). 



