DESTRUCTION OF ONE SPECIES BY ANOTHER 125 



face a similar situation, and it may be of interest to quote their usual 

 remarks on this subject: "Chance does not confine itself here to in- 

 troducing small, practically vanishing corrections into the course of 

 the phenomenon; it entirely destroys the picture constructed upon 

 the theory and substitutes for it a new one subordinated to laws of 

 its own. In fact, if at a given moment an extremely small external 

 factor has caused a molecule to deviate very slightly from the way 

 planned for it theoretically, the fate of this molecule will be changed 

 in a most radical manner: our molecule will come on its way across 

 a great number of other molecules which should not encounter it, and 

 at the same time it will elude a series of collisions which should have 

 taken place theoretically. All these 'occasional' circumstances in 

 their essence are regular and determined, but as they do not enter 

 into our theory they have in respect to it the character of chance" 

 (Chinchin, '29, pp. 164-165). 



(4) If we take a microcosm without any refuge wherein an ele- 

 mentary process of interaction between Paramecium and Didinium is 

 realized, and if we introduce an artificial immigration of both predator 

 and prey at equal intervals of time, there will appear periodic oscilla- 

 tions in the numbers of both species. Such experiments were made 

 in glass dishes with a flat bottom into which 2 cm 3 of nutritive liquid 

 were poured. The latter consisted of Osterhout's medium with a 

 two-loop concentration of Bacillus pyocyaneus, which was changed 

 from time to time. The observations in every experiment were made 

 on the very same culture, without any interference from without (ex- 

 cept immigration) into the composition of its contents. At the 

 beginning of the experiment and every third day thereafter one Para- 

 mecium -f- one Didinium were introduced into the microcosm. The 

 predator was always taken when already considerably diminished in 

 size; if it did not find any prey within the next 12 hours, it usually 

 degenerated and perished. Figure 32 represents the results of one of 

 the experiments. Let us note the following peculiarities : (1) At the 

 first immigration into the microcosm containing but few Paramecia 

 the predator did not find any prey and perished. An intense growth 

 of the prey began. (2) At the time of the second immigration the 

 concentration of the prey is already rather high, and a growth of the 

 population of the predator begins. (3) The third immigration took 

 place at the moment of an intense destruction of the prey by the 

 predators, and it did not cause any essential changes. (4) Towards 



