6/4 



PARAMETERS 



from the vertical, in degrees; y is the angular velocity, in degrees 

 per second; the time is in seconds. 



The first two Lines show that the lines of behaviour following 

 the state x = 14, y = 129 are equal, so the system, as far as 

 it has been tested, is state-determined. The line of behaviour is 

 shown solid in Figure 6/3/1. In these swings the length of the 

 pendulum was 40 cm. This parameter was then changed to 60 cm. 

 and two further lines of behaviour were observed. On these two, 

 the lines of behaviour following 

 the state x = 21, y = 121 are 

 equal, so the system is again 

 state-determined. The line of 

 behaviour is shown dotted in the 

 same figure. But the change of 

 parameter-value has caused the 

 line of behaviour from x = 0, 

 y = 147 to change. 



The relationship which the para- 

 meter bears to the two variables 

 is therefore as follows : 



(1) So long as the parameter is constant, the system of x and 

 y is state-determined, and has a definite field. 



(2) After the parameter changes from one constant value to 

 another, the system of x and y becomes again state-determined, and 

 has a definite field, but this field is not the same as the previous one. 



The relation is general. A change in the value of an effective 

 parameter changes the line of behaviour from each state. From 

 this follows at once : a change in the value of an effective parameter 

 changes the field. 



From this follows the important quantitative relation : a system 

 can, in general, show as many fields as its parameters can show 

 combinations of values. 



Figure 6/3/1, 



6/4. The importance of distinguishing between change of a 

 variable and change of a parameter, that is, between change of 

 state and change of field, can hardly be over-estimated. It is this 

 distinction that will enable us to avoid the confusion threatened 

 in S. 2/1 between those changes that are behaviour and changes 

 that occur from one behaviour to another. In order to make the 

 distinction clear I will give some examples. 



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