252 The " Hunting" of Alternatiny-Curft '/if. Mm-h-'mr*. [June 10, 

 Hence /xS is unaltered and the damping term 



/- 



becomes ny', assuming that corresponding values of the current are as 

 ti 2 : 1. As a fact corresponding values of the current (that is, values 

 which are the same fraction of the maximum rated output) are in a 

 somewhat less ratio than ii' 2 : 1, so that y' increases but very little 

 with n. 



It appears, therefore, that the coefficient of instability decreases 

 very rapidly with increasing size, while the damping coefficient y' 

 increases somewhat. At the same time, owing to the rapid decrease 

 of p/Ijp, the critical value of the load at which y' becomes negative, 

 rapidly becomes smaller in relation to tlje output of the machine. It 

 may be inferred that a machine similar to that experimented with and 

 but very little larger, would run stably at practically all loads. 



In actual practice the dimensions of a pair of adjacent poles and 

 of a corresponding piece of armature in a section perpendicular to the 

 axis are rarely more than t\vo or three times those on the machine 

 here experimented with even in big alternators ; the increased output 

 is obtained by increasing the number of poles and by increasing the 

 length of the machine. The number of poles and the length of the 

 machine, provided the peripheral speed remains the same, have but 

 little effect on the quantities y, y' and 8. In other words the per- 

 formance of a machine as regards hunting is determined almost 

 wholly by the form and dimensions, in a section perpendicular to the 

 axis, of a pair of poles and the corresponding bit of armature. The 

 weight of a corresponding bit of fly-wheel (if there is one) must, of 

 course, be added to that of the bit of armature. Thus it is quite con- 

 ceivable that machines of large size, but with small armature reaction 

 and self-induction, might be constructed in which the quantity y 

 would be important and the running unstable, at any rate at low 

 loads, though if the magnetic circuit of the machine were similar to 

 that of the one experimented on (in which the self-induction and 

 armature reaction are pretty high), and of double its linear dimensions 

 or more, the motion would undoubtedly be stable. 



