282 Mr. R. H. M. Bosanquet on Self-regulating 



below the curve of supplied power with increasing v, the 

 motion would be unstable. 



The condition of stability may be thus expressed: if p a be 



power absorbed and p s power supplied, -4^ — ^A must be 

 positive. 



I will now apply the above rules to the case already men- 

 tioned of a constant field 33 normal to the armature surface ; 

 this includes magneto machines, machines with separate exci- 

 tation, and saturated magnets. 



23VZ 2 



(1) The equation of the machine is p = ^— — 



(2) Let the condition be E = constant. 



.•. v= constant, since E = 35^. 



This is already independent of r; so it is not necessary to 

 eliminate. Andv= constant is the ideal governor. It cannot 

 be realized by a function of v and p. 



(3) Regarded as a line of great steepness directed down- 

 wards, this (v = const.) satisfies the condition of stable motion; 

 but if the line be absolutely upright, the equilibrium is neutral; 

 for if it were turned over in the least, the equilibrium would 

 be unstable, except for the greatest value of p. 



I will now take the same case subject to the condition of 

 constant current: — 



(1) is p— =- , as before. 



(2) C = const., 





.*. p = G$bvl, the required governing function. 



23VZ 2 

 (3) p = C$$vl is capable of governing p = - in stable 



motion. K + r 



A governing arrangement of the tjipep = kv can be realized, 

 as observed above. It is only necessary to supply steam at 

 constant pressure, by means of a reducing-valve or otherwise. 

 Then the power is pressure x velocity, and is proportional to 

 the velocity when the pressure is constant. 



We hear of self-regulating arrangements of dynamo 

 machines by which the current is supposed to be kept con- 

 stant under varying resistance. But since the electrical power 

 absorbed is C 2 (R + r), it is obvious that some arrangement 

 must be made to supply a power proportional to the resist- 



