Dynamo- electric Machines. 

 (R resistance of armature, r remaining resistance), 



WvH 2 



281 



and 



P = 



U + r' 



r being constant; this is a parabola. As r varies, the para- 

 meter of the parabola varies, and we have a series of curves 

 such as those shown in fig. 6. 



Now draw any governing curve, or curve of supplied power 

 (fig. 6); it intersects the carves of absorbed power in points 



Fig. 6. 



£b$or~bccL 

 power 



Swpjjlied 

 jpower 



which represent equality between supplied and absorbed 

 power, and therefore defines the motion of the machine for 

 the values of r concerned. 



If the governing curve b e regarded as the assemblage of 

 such points, it defines the motion of the machine under the 

 action of a given engine as the resistance varies. 



We may invert and generalize the process. 



Take the function of absorbed power f(p.v.r) = 0. It is 

 required to define the motion so as to satisfy a given con- 

 dition. 



Between f(p.v.r) = and the given condition eliminate r. 

 There results an equation of the form F(^.y) = 0, which must 

 hold for all points defining the motion. This, if embodied in 

 a governor, will determine the motion so as to satisfy the con- 

 dition independently of r. 



There is one general condition which must be satisfied that 

 the motion may be stable. This is, the curve of absorbed 

 power must pass from below to above the curve of supplied 

 power at the intersection as v increases. 



For in this case, if the velocity be accidentally increased, 

 more power is absorbed than supplied, and the velocity is 

 checked. Similarly, if the velocity be accidentally diminished, 

 more power is supplied than absorbed, and the velocity is in- 

 creased and the motion is stable. 



If the curves coincided, the equilibrium of the motion would 

 be neutral. 



If the curve of absorbed power passed from above to 



