210 Mr. R. H. M. Bosanquet on 



case reduced to ■£§ of its amount — i. e. to *08 ampere say. 

 Then M = 100, and >L6=S3. This points to a value between 

 the third and fourth steps of the table, where each of these 

 functions would be about 1250. 



Let us now suppose the ends of the solenoid separated, and 

 apply the analogue of the law which regulates the E.M.F. 

 between the terminals of a battery. 



If R be the internal resistance of the battery, 

 r the external resistance, 

 E total E.M.F., 

 e E.M.F. between terminals; 

 then 



R + r 



Similarly let X be the internal resistance of a magnetic 



solenoid, 



x the external resistance, 



M the total magnetomotive force of the circuit, 



m the magnetomotive force between the ends of the solenoid ; 



then x 



m= ^— — M. 



A. + x 



Here we assume that the whole magnetomotive force acts 

 within the solenoid. This is not strictly true; for every part 

 of the circuit is subject to some portion of it ; but it is nearly 

 enough true for approximate purposes. 



This is generally in accordance with fact (see Faraday, 

 Exp. Res. iii. p. 428, par. 3283). The case of the soft-iron 

 horseshoe surrounded by one or more coils of wire may now 

 be considered. X will be small, and x, the air-resistance, 

 great; .'. m nearly = M, as was observed in Speaking of the 

 unit magnetomotive force. If, on the other hand, an arma- 

 ture be applied having a resistance x much less than X, the 

 free magnetomotive force at the terminals is reduced, or m 

 becomes a small fraction of M. Other cases can be discussed 

 in the light of the analogy of the voltaic circuit. The solenoid 

 without iron corresponds to a battery of high internal resist- 

 ance ; it may be regarded as joined up through the compara- 

 tively small resistances at the end, and presents but little free 

 magnetomotive force. 



Let us now consider the case of a body of great conductivity 

 exposed to a uniform magnetic field, such as that of the earth's 

 horizontal magnetism. It is clear that, in consequence of the 

 conductivity, the potential at the ends of the conductor tends 

 to be equalized; and if the conductivity were infinite it would 

 be equalized throughout the body. The whole of the body 

 must therefore be regarded as being at the potential which in 



