DESIGN FOR A BRAIN 4/18 



extensive and complex, movements. The stable system is re- 

 stricted only in that it doe£ not show the unrestricted divergencies 

 of instability. 



Stability and the whole 



4/18. An important feature of a system's stability (or instability) 

 is that it is a property of the whole system and can be assigned to 

 no part of it. The statement may be illustrated by a consideration 

 of the first diagram of S. 4/14 as it is related to the practical 

 construction of the thermostat. In order to ensure the stability 

 of the final assembly, the designer must consider: 



(1) The effect of the temperature on the diameter of the cap- 



sule, i.e. whether a rise in temperature makes the capsule 

 expand or shrink. 



(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 Ss. 20/9 and 21 /12.) 



(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. 



56 



