236 Mr. B. Hopkinson. [June 16, 



aware) to the work of Kapp, and of others on similar lines,* who have 

 ascribed it to resonance. Take the case of a synchronous alternating 

 current motor driven from a source of alternating E.M.F. of constant 

 amplitude and periodicity. In all essentials this is the same problem 

 as that of one alternating machine running in parallel with a number 

 of others, but the results are simpler to express. The motor is 

 supposed to work against a constant resistance, and corresponding to 

 that resistance there will be a certain state of steady motion in which 

 the motor runs with a constant speed equal to that of the generators 

 supplying it and with a constant lag e behind them, and develops a 

 torque T corresponding to the external resistance. If the angle of 



fJT 



lag be increased to e + f , the torque will be increased to T + -=- , and 

 if the external work done by the machine remains the same there will 



7rp 



be a force r or c tending to accelerate the motor. Kapp's 



ment then is that the equation of motion of the motor is M + c = 0, 

 where M represents on a suitable scale the moment of inertia of the 

 motor, from which it follows that it executes simple harmonic oscilla- 

 tions of constant amplitude and period 27r v / (M/c) about the state of 

 steady motion. It is easy to calculate c approximately from a know- 

 ledge of the magnetic properties of the machine. Kapp worked out 

 the period and found it to agree fairly well with observation in certain 

 cases. He ascribed hunting to approximate equality between the 

 period of free oscillation and that of some variation in the turning 

 moment of the engine. Such equality would of course give rise to 

 forced oscillations quite out of proportion to the cause. It was stated 

 in support of this explanation that in certain cases an increase in the 

 fly-wheel effect of the machine viz., an increase in the period of oscil- 

 lation was found to aggravate the evil, contrary to what would at first 

 sight be expected. And indeed it is probable that some cases of hunting 

 are due to resonance. 



I believe, however, that there have been cases in which it has been 

 difficult or impossible to discover any external disturbing cause of 

 approximately the same period as that of the oscillation. One case of 

 the kind has come under my notice. A small single-phase synchronous 

 motor, to be presently described, hunted violently under certain con- 

 ditions when worked off the Wimbledon supply mains. The period of 

 the oscillations could be varied continuously from about 0'35 to 0'45 

 second by appropriate variation of the self-induction in series with the 

 motor. Furthermore, the hunting occurred equally, and with the 

 same period, with either of two different generators working in the 

 Power Station, one being three times the size of the other. It was 



* See ' Dynamomaschinen fur Gleich- und Wechselstrom,' von Gisbert Kapp, 

 p. 401 ; also a paper by Hans Gorges, ' Elektrotechnische Zeitechrift,' vol. 8, 1900. 



