INDUCTANCE AND CAPACITY 429 



the center of the shaft if the motion of the weight in that direc- 

 tion were not limited. This may be called the critical value of 

 the tension, since if it is exceeded, the weight will suddenly fly 

 outward. 



While the device may be operated with any one of the three 

 adjustments implied above, it is most sensitive and regulates 

 best when the tension is near its critical value. Referring to the 

 equation of equilibrium, 



C(r - a'} + 7\ 



If Ca f = Ti or, what is equivalent, if a' e' y 



M 



'his may be called the critical speed, since for any higher speed 

 ie equilibrium is unstable. 



Why the apparatus regulates most satisfactorily in the neighbor- 

 lood of the critical speed becomes evident if values of co and r be 

 lotted; this has been done in Fig. 252, two values of e' being 

 ised. 



It has been assumed in Fig. '252 that the construction of the 

 ^gulator is such that the center of gravity of the weight can never 

 nearer the axis than 3 cm. or more distant than 6 cm. It is 

 that as the critical speed is approached the change in the 

 sition of the weight for a given increase in the angular velocity 

 icomes vastly increased. This means a corresponding increase 

 the sensitiveness of the apparatus. 

 If a' > e' the weight arrives at its ultimate position slowly and 

 :he contact of KI and Kz may be uncertain. If a' < e' the motion 

 sudden and the pressure between the contacts considerable. 

 r the best results e' should be slightly larger than a', that is, 

 the initial tension on the springs should be such that the weight is 

 in unstable equilibrium at the speed which it is desired to 

 maintain. 



Any given regulator has only one speed at which it works with 



\~C 

 entire satisfaction, that is, at co = <\/T7* 



\ M 



