432 Prof. A. Gray : Notes on 



force is i{a 2 — a' 2 )H&). The current is Io)/27rR, and is 

 constant. 



2. The conclusion (see Lord Kelvin's £ Electrostatics and 

 Magnetism,' § 571, note) that the "mechanical value " of a 

 current in a closed conductor is not affected by steel magnets 

 in the neighbourhood, has always seemed to me remarkable 

 and significant. For it would appear that we must, if we 

 assume the Amperean hypothesis that a permanent magnet is 

 made up of a congeries of circuits of molecular dimensions, 

 in which currents of electricity circulate, introduce a term 

 of the form My '7, or rather a sum y£(M.y') of such terms, to 

 express the mutual energy of the circuit carrying the current y 

 and the multitude of molecular currents typified by y'. Thus- 

 if we write for the total kinetic energy (electrokinetic and 

 ordinary kinetic energy, taken together) 



T = i{Ly* + ZL r r ,2 + 2yS(My')+2{mv*)} } \ (1) 



we should obtain from this and the molar potential energy, 

 by the Lagrangian method, the equations of motion, as we 

 may call them, both of electricity and of molar matter. 



Thus for the rails and slider we should get, bringing in 

 the dissipation function, JR/y 2 , the equations 



-J{L 7 +2(M 7 ')}=E 7 ,1 .... (2> 



mvv ~-~Ly =0, * 



since we suppose y to be constant. 



Here we identify — XM-y' with ~H.lv and obtain 



H/i>-L7=Ry, (3) 



and so far there is no difficulty about the mutual term 

 7 2(M 7 '). 



Let us now consider any number of battery circuits in the 

 field of a system of permanent magnets. Let E l5 R 1? L t , y ly 

 be the electromotive force, the resistance, the self-inductance,, 

 and the current for one battery circuit, E 2 , R 2 , L 2 , y 2 those 

 for another, and so on. Considering the magnets as assem- 

 blages of molecular circuits, and denoting by T as before 

 the whole kinetic energy (that is T e + T TO the sum of the 

 electrokinetic energy and the molar kinetic energy of moving 

 conductors), and by x lf # 2 > • •- coordinates determining the 

 configuration of the conductors, we can write the equations 



