84 MAINTENANCE OF BLBCTBIC CUBBBNT8 BY MECHANICAL WORK. 



If p and q be the number of windings in the first and second coils respec- 

 tively, the ratio r becomes 



" 



which is greater than 1, provided 2lmp is greater than (ln + m')q. When 



we have for the maximum value of r, 



m 



r=l 



_ 



2 T 



n \i n -i- + n - m 



Vm' + ^7 *^ + m / 



In the experiment of Professor Wheatetone, in which the ends of the 

 primary coil were put in permanent connexion by a short wire, the equations 

 are more complicated, as we have three currents instead of two to consider. 

 The equations are 



*-Kz ............ (17), 



(18), 



where Q, K, and z are the resistance, self-induction, and current in the short 

 wire. The resultant equations are of the second degree ; but as they are only 

 true when the magnetism of the cores is considered rigidly connected with the 

 currents in the coils, an elaborate discussion of them would be out of place 

 in what professes to be only a rough explanation of the theory of the experi- 

 ments. 



Such a rough explanation appears to me to be as follows : 



Without the shunt, the current in the secondary coil is always in rigid 

 connexion with that in the primary coil, except when the commutator is 

 changing. With the shunt, the two currents are in some degree independent; 

 and the secondary coil, whose electric inertia is small compared with that of 

 the primary, can have its current reversed and varied without being clogged 

 by the sluggish primary coil. 



