1903.] The " Hunting " of Alternating- Cur rent Machines. 241 



As a rule K/3 Q is small compared to (A - Xao), so that the criterion 

 of instability in this case is approximately (L + *) p>p, and i 

 generally fulfilled. The value of (L + K), which will not vary greatly 

 with load, may be determined by observing the current given by the 

 machine when short-circuited, including, of course, in its circuit all 

 resistances and self-induction up to the constant source of E.M.F., 

 which has been postulated. The apparent resistance under these 

 circumstances is approximately */( [L + *] %2 p 2 + p 2 ). On the other hand, 

 the value of L may be approximately obtained by observing the 

 current when the machine is at rest, and connected to the mains, the 

 field coils being short-circuited. The apparent resistance of the whole 

 circuit under these circumstances is x/([Ly + p 2 ]). If the motor be 

 under-excited a is positive. /? is positive for a motor and negative 

 for a generator. The E.M.F. Ap cos pt is equal to the impressed 

 E.M.F. less that required to drive the current through the self- 

 induction and resistance of the circuit ; hence, unless Lp, or p, or the 

 current, be large, Ap/ */(2) is not much different from the applied 

 E.M.F. [ ^/(mean 2 )]. By reducing the exciting current Ap is somewhat 

 reduced, owing to the increased armature current ; but the reduction 

 is far from being in proportion to the decrease in exciting current. 

 On machines with large armature reaction and small self-induction, Ap 

 is practically constant, and equal to ^(2) times the impressed E.M.F. 

 " 



Damping Coils. 



In practice there are, of course, many causes unconsidered in the 

 above investigation which tend to damp out the oscillations, and 

 which in all but exceptional cases overpower the forces making for 

 instability, and render the motion stable. Air resistance and local 

 currents in the armature give rise to forces of this nature, which 

 increase roughly in proportion to the velocity and so appear in the 

 equations of motion as true viscous terms. The most important damp- 

 ing effect, however, is that due to the variations of the field of the 

 motor, which, as stated in the last paragraph, are generally produced 

 by the oscillation. These variations give rise to periodically varying 

 electric forces in the substance of the magnets and in the field 

 coils, which cause currents in the former and variations of the 

 current in the latter. These induced currents re-act on the armature, 

 producing changes in the torque which tend to damp out the oscilla- 

 tions. In many machines the effect is intensified by putting addi- 

 tional damping coils of copper or " Amortisseurs," as they are called, 

 round the field magnets. I propose shortly to investigate this damping 

 effect. 



The general effect of the induced currents in the magnets and in 



