DYNAMIC SYSTEMS 2/7 



Some systems cannot be forced, for instance the astronomical, 

 the meteorological, and those biological systems that are accessible 

 to observation but not to experiment. Yet no change is neces- 

 sary in principle : the experimenter simply waits until the desired 

 set of values occurs during the natural changes of the system, 

 and he counts that instant as if it were the instant at which the 

 system were started. Thus, though we cannot create a thunder- 

 storm, we can observe how swallows react to one simply by 

 waiting till one occurs 4 spontaneously '. 



2/7. The 4 machine ' will be studied by applying the primary 

 operation, defined thus : The variables are brought to a selected 

 state (S. 2/9) by the experimenter's power of control (S. 2/6) ; 

 the experimenter decides which variables are to be released and 

 which are to be controlled ; at a given moment the selected 

 variables are released, so that their behaviour is controlled pri- 

 marily by the ' machine ', while the others are forced by the 

 experimenter to follow their prescribed courses (which often 

 includes their being held constant) ; the behaviours of the vari- 

 ables are then recorded. This operation is always used in the 

 practical investigation of dynamic systems. Here are some 

 examples. 



In chemical dynamics the variables are often the concen- 

 trations of substances. Selected concentrations are brought 

 together, and from a definite moment are allowed to interact 

 while the temperature is held constant. The experimenter records 

 the changes which the concentrations undergo with time. 



In a mechanical experiment the variables might be the posi- 

 tions and momenta of certain bodies. At a definite instant the 

 bodies, started with selected velocities from selected positions, 

 are allowed to interact. The experimenter records the changes 

 which the velocities and positions undergo with time. 



In studies of the conduction of heat, the variables are the 

 temperatures at various places in the heated body. A prescribed 

 distribution of temperatures is enforced, and, while the tempera- 

 tures of some places are held constant, the variations of the 

 other temperatures is observed after the initial moment. 



In physiology, the variables might be the rate of a rabbit's 

 heart-beat, the intensity of faradisation applied to the vagus 

 nerve, and the concentration of adrenaline in the circulating 



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