470 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



electric current, and includes the steady state as a particular case, 

 for if the currents do not vary with the time, and there is no 

 motion of any circuit, every p s is constant, and we have for each 

 circuit, 



the usual form of Ohm's Law. The statement is frequently made 

 that Ohm's Law does not hold for induced currents this is a mis- 

 conception, for in the statement of Ohm's Law we should include 

 electromotive forces of all kinds, including those due to in- 

 duction. 



If permanent magnets are present there will be terms in T 

 where each current is multiplied by the flux through it due to 

 magnets. These terms will be of the first order in the currents, 

 so that Twill not be homogeneous, and we have the case mentioned 

 in 66 each magnet acting like a concealed current. We have 

 in the previous chapter considered the possible replacement of a 

 magnet by currents, so that we may consider magnets replaced by 

 " concealed " or " apparent " currents of unchangeable strength. 



236. Isocyclic and Adiabatic Changes. An adiabatic 

 variation, being defined by the constancy of cyclic momenta, will 

 take place when in each circuit the electromotive force E s is just 

 large enough to maintain the current in the circuit steady, namely 

 E s = Rglg. If the current is varying, this necessitates the va'ria- 

 tion of E s . Such changes seldom occur in practice. Isocyclic 

 motions are such that all the currents remain unchanged. The 

 electrokinetic momenta may be varied by motion or deformation 

 of the circuits, involving change of the values of the parameters 

 q s , or by motion of permanent magnets. The simplest phenomena 

 to observe experimentally, and those first discovered, are of this 

 class. 



We may now apply to a system of currents the theorems which 

 have been demonstrated in 69, 70. In particular may be 

 noticed the two theorems of 70, which may be thus stated. 



I. In any motion of currents or magnets during which the 

 strengths of all the currents are unchanged, the work done by the im- 

 pressed electromotive forces E s is equal to twice the work done 



