232 



Dr. J. Larmor. On the Electrodynamic and [Jan. 2, 



The formula (i) is usually taken, after Maxwell's example, to 

 represent the energy of the electrokinetic field. It here appears that 

 it represents only the part of the energy that is concerned with the 

 currents, arising from their mutual interactions and the interactions of 

 the magnets with them : that there exists in addition a quantity (ii) 

 which is that taken by Maxwell as the energy of magnetisation in 

 the field («, /3, y), and also a quantity (jii), which is purely local and 

 constitutive, of the same general type as energy of crystallisation. 

 The question arises whether (iii) is a part of the intrinsic energy of 

 magnetisation of different kind from (ii), in that it cannot even 

 partially emerge as mechanical work, or on the contrary the usual 

 formula (ii) must be amended. See §§ 5, 8. In any case the 

 dynamics of the field of currents (when there are no irreversible 

 features) involves only that part of the energy function in which the 

 currents operate, thus excluding both (ii) and (iii). 



3. The simplest example is that of a coil of n turns carrying a 

 current i, wound uniformly on a narrow iron ring-core, of cross- 

 section S and length I. On the present basis the energy is made up 

 of an electrodynamic part -Jt?i<38S and a magnetic part -J3j§5S/ ; as 

 47r?u = pZ by the Amperean circuital law, these parts are 



and m%y, 



when v is the volume of the core ; they make up in all §} 2 /87r per unit 

 volume instead of the usual J/8tt. The former part is mechanically 

 available. The question has been raised by Lord Kayleigh* whether 

 the latter part, which includes the very large term (iii) above, namely 

 27r|%, in the case of iron, has any considerable mechanical effective- 

 ness ; the question can only arise when it belongs in part to permanent 

 magnetism whose ultimate annulment can induce a current, — when the 

 current vanishes the energy of permanent magnetism, in the present 

 case represented by (iii) alone, is the only part of the energy of the 

 system that remains. The conclusion reached by him is that it 

 cannot be annulled quick enough, when the ring carries a coil, to 

 develope any considerable available electric energy by induction. 



4. We may form a rough illustration of the mechanical role of this 

 purely magnetic energy by considering, as the analogy of the currents, 

 a branching system or network of pipes carrying liquids, in one of 

 which a turbine is located, to be driven by the stream, which will be 

 supposed to be an alternating one. The flow will be directed more 

 fully into this particular pipe, and higher pressure will also be 

 attained, after the manner of the hydraulic ram, if it communicates at 

 the side with an expansible reservoir into which the liquid can readily 



* ' Phil. Mag.,' 1885 : also ' Archives neerlandaises, vol. 2, 1891, p. 6, reprinted 

 in ' Phil. Mag./ 1902, and in ( Scientific Papers,' vol. 4, No. 272. 



