130 THE STRUGGLE FOR EXISTENCE 



rate the deaths are not uniformly distributed in time, nor do they 

 occur in a purely random fashion. They are grouped in a series of 

 waves, each wave showing minor fluctuation. The equilibrium 

 between parasite and host seems to be a shifting one. As the result 

 of some series of changes, the parasite appears to obtain a temporary 

 mastery, so that a considerable proportion of the mice at risk fall 

 victims to a fatal infection. This is followed by a phase in which 

 there is a decreased tendency for the occurrence of fatal infection, and 

 the death-rate falls. As fresh susceptibles accumulate this succession 

 of events is repeated, and the deaths increase to a fresh maximum, 

 only to fall again when this maximum is passed." But if only "no 

 such immigration occur the epidemic gradually dies down, leaving a 

 varying number of survivors." 



We can conclude that the process of elementary interaction between 

 the homogeneous hosts and the homogeneous bacterial population possesses 

 no "classical" periodic variations. Without wishing to adopt at once 

 the preconceived opinion that such a phenomenon is generally im- 

 possible, we ought in any case require a clear demonstration of its 

 possibility. This demonstration will be really given below. 



IV 



(1) Turning back again from empirical observations to the general 

 principles let us note that there can exist two different types of innate 

 periodic oscillations in the systems, as Hill ('33) has noted recently in 

 connection with physiological problems. One of them which was 

 assumed by Lotka-Volterra and which we have searched above must 

 be called a "classical" fluctuation and it is entirely analogous to well- 

 known oscillations in physics arising as the consequence of the reac- 

 tion with one another of properties analogous to inertia and elasticity. 

 A changing system tends, on one hand, to maintain its state of mo- 

 tion because it possesses mass, whilst on the other the force of elastic- 

 ity increases according to the removal from equilibrium and ulti- 

 mately reverses the motion or change. In the classical theory of 

 biological population the predator tends to multiply indefinitely, but 

 by a removal in this way from an equilibrium with the prey the change 

 in the predator population becomes reversed, later again replaced by 

 an increase, and so on (equation 21a). 



There is, however, another type of oscillation with which physiolo- 

 gists are concerned and to which apparently belong the spread of 



