STABILITY 4/16 



(2) Which way an expansion of the capsule moves the lever. 



(3) Which way a movement of the lever moves the gas-tap. 



(4) Whether a given movement of the gas-tap makes the 



velocity of gas-flow increase or decrease. 



(5) Whether an increase of gas-flow makes the size of the gas- 



flame increase or decrease. 



(6) How an increase in size of the gas-flame will affect the tem- 



perature of the capsule. 



Some of the answers are obvious, but they must none the less 

 be included. When the six answers are known, the designer can 

 ensure stability only by arranging the components (chiefly by 

 manipulating (2), (3) and (5) ) so that as a whole they form an 

 appropriate combination. Thus five of the effects may be decided, 

 yet the stability will still depend on how the sixth is related to 

 them. The stability belongs only to the combination ; it cannot 

 be related to the parts considered separately. 



In order to emphasise that the stability of a system is inde- 

 pendent of any conditions which may hold over the parts which 

 compose the whole, some further examples will be given. (Proofs 

 of the statements will be found in S. 21/5-7.) 



(a) Two systems may be joined so that they act and interact 

 on one another to form a single system : to know that the two 

 systems when separate were both stable is to know nothing about 

 the stability of the system formed by their junction : it may be 

 stable or unstable. 



(b) Two systems, both unstable, may join to form a whole which 

 is stable. 



(c) Two systems may form a stable whole if joined in one way, 

 and may form an unstable whole if joined in another way. 



(d) In a stable system the effect of fixing a variable may be to 

 render the remainder unstable. 



Such examples could be multiplied almost indefinitely. They 

 illustrate the rule that the stability (or instability) of a dynamic 

 system depends on the parts and their interrelations as a whole. 



4/16. The fact that the stability of a system is a property of the 

 system as a whole is related to the fact that the presence of stability 

 (as contrasted with instability) always implies some co-ordination 

 of the actions between the parts. In the thermostat the necessity 

 for co-ordination is clear, for if the components were assembled 



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