STABILITY 



4/5 



4/4. This preliminary remark begins to justify the emphasis 

 placed on absoluteness. Since stability is a feature of a field, 

 and since only regular systems have unchanging fields (S. 19/16) 

 it follows that to discuss stability in a system we must suppose 

 that the system is regular : we cannot test the stability of a 

 thermostat if some arbitrary interference continually upsets it. 

 But regularity in the system is not sufficient. If a field had 

 lines criss-crossing like those of Figure 2/15/2 we could not make 

 any simple statement about them. Only when the lines have a 

 smooth flow like those of Figures 4/5/1, 4/5/2 or 4/10/1 can a 

 simple statement be made about them. And this property 

 implies (S. 19/12) that the system must be absolute. 



4/5. To illustrate that the concept of stability belongs to a 

 field, let us examine the fields of the previous examples. 



The cube resting on one face yields an absolute system which 

 has two variables : 



(cc) the angle which the face makes with the horizontal, and 



(y) the rate at which this angle changes. 

 (This system allows for the momentum of the cube.) If the cube 

 does not bounce when the face meets the table, the field is similar 



O O o a 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. 



45 



