(parts per hundred mg/liter) and may be considered constant during this 

 time period. The dependence described in the experiments y on N may be 

 approximated by the linear function y = 0.023 N as shown in Figure 11, 

 i.e., k 2 = 0.023. The quantity of the consumed phenol, according to the 

 data given above, is approximately twice as great as the growth of bac- 

 teria; therefore, we accepted k ; = 2 k 2 . The coefficient kj was chosen so 

 that model (4) would most closely simulate the experimental data; it was 

 taken to be 0.0028. The values of coefficients k 2 and k 3 of model (4) do 

 not suit model (5). The coefficients k 2 , k 2 , k 3 , and k 4 for model (5) were 

 chosen, preserving their ratios, as in model (4), in such a way that mathe- 

 matical model (5) would most closely approach the results of experiment 6; 

 in this case, coefficients k 5 and k 6 were taken as equal to k„ and k 5 of 

 model (2). They were accepted to be ki = 0.0055, k 2 » 0.0438, k 3 = 0.0876, 

 k 4 = 0.0025, k 5 = 0.0510, and k 6 = 0.0240. 



After determining or while choosing the coefficients, the processes de- 

 scribed by the models were computed on a "^insk-22" digital computer to com- 

 pare the calculated and experimental curves. The calculated and experi- 

 mental curves correspond quite well, that is the mathematical models given 

 above describe rather correctly the processes taking place in the experi- 

 ments. An analysis of the models allows us to obtain quantitative data on 

 the growth and feeding rates of the living components and on the character 

 of their interrelationships in the process of organic matter decomposition. 

 The product k 4 H in model (2) is the rate of bacteria consumption by unit 

 dry weight of infusoria. Its calculation and conversion for the number of 

 cells show that one infusorian P. caudatum consumes about 50 thousand bac- 

 terial cells per hour at D = 0.04 hrs -1 , and 25 thousand at D = 0.02 hr" 1 

 at the steady state in the reactor. 



Analysis of models (4) and (5) renders it possible to understand why 

 the destruction of organic matter by bacteria accelerates in the presence 

 of infusoria given a nitrogen deficiency. The necessity to make the coeffi- 

 cients k 2 and k 3 in model (5) almost twice as great as those in model (4) 

 indicates that in the former case nitrogen was more easily assimilable as 

 present in the reactor, than nitrate nitrogen inflowing with the medium. 

 As is known, some of the substances excreted by infusoria are urea and uric 

 acid (Dogel, 1951). The infusoria apparently play a role in stimulating 

 the decomposition of organic matter by creating nitrogen circulation and 

 liberating it in a form more readily accepted by the bacteria in the envir- 

 onment. In model (3) the values of k 3 S and k^H are correspondingly the 

 values of glucose and bacteria consumption by zoof lagellates. Calculation 

 of them has shown that at steady state with a dilution rate of D = 0.06 

 hrs" 1 , 0.126 mg of dry weight of bacteria and 0.055 mg of glucose are con- 

 sumed per hour by 1 mg dry weight of zoof lagel lates . At a dilution rate of 

 D = 0.08 hrs" 1 these values are equal to 0.212 and 0.047 mg, respectively. 



In such a manner, in test conditions, from one-sixth to one-third of 

 the zoof lagel lates ' food consumption is satisfied by consumption of organic 

 matter. To verify the fact that the zooflagellate P_. jaculans feeds on dis- 

 solved organic matter, model (3) was calculated by computer, with coeffi- 

 cients k 3 and k 6 equal to zero, so that an exclusion of glucose from the 



138 



