296 On Self-regulating Dynamo-electric Machines. 



Equating to zero the coefficient of the highest power of 

 each variable, we find the following asymptotes : — 

 av 2 — c=0, v 2 = 0, 



ap 2 + d=0. 



With respect to av 2 — c=0, it would seem that we cannot have 

 an infinite value of p corresponding to a finite value of v; 

 .-. c = 0. 



This gives the condition 



RN 2 +p 



=5 is the current which would be produced through the arma- 

 ture, if not excited, by the given difference of potential. 

 — will generally be small. Neglecting its square, we have 



E 



n~UK ± 2 P J- R ' 



a value very close upon the boundary of stable arrangements, 

 as we see from the investigations under the head of E = con- 

 stant. 



Then all the asymptotes parallel to v=0 coincide with it. 



With respect to ap 2 + d = 0, these asymptotes may have real 

 values if they can ; then d is necessarily negative. 



P J \ p. 



or, as— is small, practically v>n, which is in conformity with 



P 

 practice and with the above condition. 



Then for high velocities p would require to have the con- 

 stant value \/(d/a). 



The governing function of the type p = constant is stable 

 for most cases. It is intermediate in character between p — kv 

 and pv = k. It obviously requires that the pressure on the 

 piston should vary inversely as the velocity. 



,( 1 + f)>„( I + 5); 



In partially discussing these cases it has been more my 

 object to throw light upon the general theory than to obtain 

 practical results. The great value of theoretical investigation 

 lies in the suggestion of new ideas ; and if the above only serves 

 to point out the importance of the construction of governors 

 in accordance with definite laws, it will not be without use. 



