442 Prof. A. Gray on the Dynamical 



When the circuits are separated again by external forces 

 applied to overcome the electromagnetic forces, the intrinsic 

 energy is diminished by the same amount, and the battery is 

 saved just as much energy in the reverse displacement as it 

 supplied in the direct. 



If the displacement do not take place infinitely slowly, we 

 have to take into account the change in the intrinsic energy 

 due to the change of the current in each circuit. 



Thus the change in the intrinsic energy is here very 

 important. 



Again, when we consider two magnets which are displaced 

 by their mutual forces, we find the change in the intrinsic 

 energy, expressed in terms of the configuration of the system, 

 the only thing to be taken into account. The mutual forces 

 set the magnets into motion, or displace them against external 

 resistance, and thus do work. This work can be obtained 

 from no other source than the intrinsic or configuration 

 energy of the system. 



Thus in the case of two circuits and in that of two magnets, 

 change of intrinsic energy plays a part ; in the case of a mag- 

 net and a circuit it apparently does not ; and I have never 

 seen the reason of the apparent exception anywhere clearly 

 stated. I think that the treatment of the intrinsic energy in 

 the presentation of this part of the theory of electromagnetic 

 action is a source of difficulty to many, and prevents clearness 

 of ideas regarding what is certainly not found an easy subject 

 when an attempt is made to master it in all its bearings. 



This difficulty is met with in the perusal of the writings of 

 even the greatest masters of the science of Electricity. Thus 

 Clerk-Maxwell, in his i Electricity and Magnetism'' (vol. ii. 

 p. 179), has given a treatment of the problem of two cir- 

 cuits, in which the change of intrinsic energy is left out of 

 account, and a correct result is obtained only by what seems 

 an inadmissible process*. This passage is a pretty close 

 rendering of one in HelmhohVs famous essay, Die Erhaltung 

 der Kraft, in which the same treatment occurs. It is evident 

 that here the change of intrinsic energy has not been present 

 to the minds of the writers, and the result is a statement 

 of theory which may have caused thoughtful students con- 

 siderable embarrassment. 



Again, I have observed what seem to me traces of this 

 want of clearness in attempts to deduce directly from the 

 expressions for the intrinsic energy of a magnetic field due 

 to any distribution of currents, the energy dissipated per 

 unit of volume of the medium, in carrying the substance 

 round a closed cycle of magnetization. The correct way of 



* See McConnel, ' Nature/ vol. xxxv. p. 172. 



