Figure 4/5/2. 



4/5 DESIGN FOR A BRAIN 



to that sketched in Figure 4/5/1. The stability of the cube 

 when resting on a face corresponds in the field to the convergence 

 of the lines of behaviour to the centre. 



The square card balanced on its edge can be represented approxi- 

 mately by two variables which measure displacements at right 



angles (x) and parallel (y) to the lower 

 edge. The field will resemble that 

 sketched in Figure 4/5/2. Displace- 

 ment from the origin to A is followed 

 by a return of the representative point 

 to 0, and this return corresponds to the 

 stability. Displacement from to B is 

 followed by a departure from the region 

 under consideration, and this departure 

 corresponds to the instability. The 

 uncertainty of the movements near O 

 corresponds to the uncertainty in the behaviour of the card when 

 released from the vertical position. 



The Watt's governor has a more complicated field, but an 

 approximation may be obtained without difficulty. The system 

 may be specified to an approximation sufficient for our purpose 

 by three variables : 



(x) the speed of the engine and 



governor (r.p.m.), 

 (y) the distance between the 

 weights, or the position 

 of the throttle, and 

 (z) the velocity of flow of the 

 steam. 

 (y represents either of two quan- 

 tities because they are rigidly 

 connected). If, now, a disturb- 

 ance suddenly accelerates the 

 engine, increasing x, the increase 

 in x will increase y ; this increase 

 in y will be followed by a decrease 

 of z, and then by a decrease of x. 

 As the changes occur not in 

 jumps but continuously, the line 

 of behaviour must resemble that 



46 



Figure 4/5/3 : One line of behav- 

 iour in the field of the Watt's 

 governor. For clarity, the resting 

 state of the system has been used 

 as origin. The system has been 

 displaced to A and then released, 



