Middle of the Nineteenth Century. 247 



Discussing next the mutual energy due to the approach of a 

 permanent magnet and a circuit carrying a current, he arrived 

 at the remarkable conclusion that in this case there is no 

 electrokinetic energy which depends on the mutual action ; the 

 energy is simply the sum of that due to the permanent magnets 

 and that due to the currents. If a permanent magnet is 

 caused to approach a circuit carrying a current, the electromotive 

 force acting in the circuit is thereby temporarily increased ; the 

 amount of energy dissipated as Joulian heat, and the speed of 

 the chemical reactions in the cells, are temporarily increased also. 

 But the increase in the Joulian heat is exactly equal to the 

 increase in the energy derived from consumption of chemicals, 

 together with the mechanical work done on the magnet by the 

 operator who moves it ; so that the balance of energy is perfect, 

 and none needs to be added to or taken from the electrokinetic 

 form. It will now be evident why it was that Helmholtz 

 escaped in this case the errors into which he was led in other 

 cases by his neglect of electrokinetic energy ; for in this case 

 there was no electrokinetic energy to neglect. 



Two years later, in 1853, Thomson* gave a new form to the 

 expression for the energy of a system of permanent and 

 temporary magnets. 



We have seen that the energy of such a system is represented 



by 



where p denotes the density of Poisson's equivalent magnetiza- 

 tion for the permanent magnets, and <f> denotes the magnetic 

 potential, and where the integration may be extended over the 

 whole of space. Substituting for p n its value - div I ,f the 

 expression may be written in the form 



- J 



< div Io dx dydz ; 



*Proc. Glasgow Phil. Soc. iii (1853), p. 281; Kelvin's Math, and Phys. 

 Papers, i, p. 521. t Cf . p. fi4. 



