4/5 



STABILITY 



o O O D o o o 



Figure 4/5/1 : Field of the two-variable system described in the text. 

 Below is shown the cube as it would appear in elevation when its main 

 face, shown by a heavier line, is tilted through the angle x. 



consideration, and this departure correspond^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 quantities because they are rigidly 

 connected). If, now, a disturbance 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 



47 



Figure 4/5/2. 



