402 



On the Maintenance of Electric Currents, [March 14^ 



we have for the maximum value of 



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

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

 tions are more complicated, as We have three currents instead of two to 

 consider. The equations are 



R^+^(L^+My)=Sy+|(M^^+%) = Q^ + llU . (17) 



x^tj-^z={) (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 con- 

 nected 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 experiments. 



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 indepen- 

 dent ; 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. 



On the other hand, the primary coil loses that part of the total current 

 which passes through the shunt ; but we know that an iron core, when 

 highly magnetized, requires a great increase of current to increase its mag- 

 netism, whereas its magnetism can be maintained at a considerable value by 

 a current much less powerful. In this way the diminution in resistance 

 and self-induction due to the shunt may more than counterbalance the di- 

 minution of strength in the primary magnet. 



Also, since the self-induction of the shunt is very small, all instantaneous 

 currents will run through it rather than through the electromagnetic coils, 

 and therefore it will receive more of the Jieating effect of variable currents 

 than a comparison of the resistances alone would lead us to expect. 



