402 HERMANN VON HELMHOLTZ 



of individual parts, and which on the contrary are alterations 

 in velocity of unknown internal motions, or even possibly of 

 changes in momentum. And in this case we find ourselves in 

 the region of electrodynamics; here we have to deal with 

 electrification and magnetization of individual bodies and 

 substances, both which conditions may persist permanently. 

 Electrical currents evoke magnetic forces, magnetic alterations 

 evoke electrical forces. And here, unless we depend upon 

 that relation between energy and the kinetic potential, and can 

 establish the principle of least action by calculation of the 

 latter, we are compelled to see whether the empirical laws of 

 electrodynamics, as expressed in Maxwell's equations, can be 

 brought under the form of a minimal law, and what analogy this 

 form has with that established for ponderable bodies. 



Helmholtz now set out from the consideration that if we 

 want to form conceptions as to the mode of electrical and 

 magnetic forces, and the nature of the material substratum 

 that carries them, we only know in the first place that both 

 come under the law of the conservation of energy. But we 

 cannot separate the two forms of energy from one another 

 for certain, and, further, we do not know if they participate in 

 the other general properties of all the conservative motive 

 forces of ponderable substances, which find their briefest 

 expression in the principle of least action, and, as Helmholtz 

 pointed out in the mechanical papers previously alluded to, are 

 the expression of a series of special laws of reciprocity between 

 the forces of different origin in a system of ponderable masses. 

 The principle of least action holds good (as Helmholtz had 

 already pointed out) in so far as the laws of potential 

 determined by Neumann and extended by Helmholtz apply 

 to closed currents, in which the intervening spaces are free 

 from magnetic and electrical substance. The further question 

 remained, whether the principle could also cover the more 

 complete equations of electrodynamics, as proposed by 

 Clerk Maxwell, and completed by Hertz, with explicit develop- 

 ment of the terms which depend upon the motion of the 

 medium. 



Apart from theoretical questions as to the nature of the 

 fundamental forces, there were other problems relating to the 

 observed phenomena. The values of the pondero-motive forces 



