Dynamo-electric Machines. 279 



power at increasing speeds by the governor or otherwise, by a 

 hyperbolic curve. 



(1) Common rectangular hyperbola pv = K 2 (fig. 3). 



(2) pv 2 =K d (fig. 4). 



(n) 



pv 7 



E> 



+i 



Fig. 4. 



Fig. 3. 



p=av. pv=K 2 . p = av pv 2 = K 3 . 



W dv" v 2 > 



.*. at the vertex, where^9=v=K, =— 1 ; 



and at this point, on the bisector of the axes, the curve is 

 inclined downwards at 45°. 



(2) 



dp K 3 



~r- = — 2— 5-= —2 sit vertex : 



dv v 3 



curve at vertex is inclined downwards at 634°. 



Similarly the inclination downwards at the vertex increases 



rapidly ; and for 



dp K> +1 



(n) 



dv 



'\n+- 



the tangent of the downward-pointing angle is n. 



"We can approximately represent most governing relations 

 by a straight line meeting such a hyperbolic curve. The 

 part which represents the state of things where the governor 

 is in action is on the curve beyond the point of junction with 

 the straight line. 



Consider first the straight line from 0; p = av. The 

 power is proportional to the velocity. This will be the case 

 so long as the steam is supplied at constant pressure. For 

 power is pressure on piston x velocity. But pressure on 

 piston is constant ; .*. power varies as velocity. The hyper- 

 bolic curves represent governors which are sharper and 

 sharper as n increases. In the case of an infinitely sharp 

 governor the governing function, or curve of supplied power, 



X 2 



