1903.] Thermal Relations of Energy of Magnetisation. 231 



If we compare this result with the customary magnetic vectors of 

 Kelvin and Maxwell, it appears that (a, /3, y) must represent the 

 "induction," and so will hereafter be denoted, after Maxwell, by 

 (a, b, c). The new vector, which has a potential cyclic with respect 

 to the finite currents only, represents the " force," and will hereafter be 

 denoted by (a, /5, y), whose significance is thus changed from henceforth. 

 The " induction " on the other hand has not necessarily a potential, 

 but is, by the constitution of the free aether, always circuital ; that 

 is, it satisfies the condition of streaming flow 



da cb dc 



— + — + — = 0. 



dx dy c.z 



The expression for the energy now includes terms 



J(tiNi 4-t 2 N 2 + . . .) 



for the ordinary currents i v l 2 , . . ., where Ni, N 2 , . . . are the fluxes, of 

 magnetic induction, through their circuits ; this transforms as usual into 



l-^^V(la + mb + nc)dS 



over both faces of each barrier, which by Green's theorem is equal to 



L^(a* + bp + cy)dT (i) 



extended throughout all space. But there are also terms 



H t i'N 1 ' + t2 / N. 2 / + . . .) 



for the molecular currents ; now taking N' to be the cross-section 

 of the circuit multiplied by the component of the averaged induction 

 normal to its plane, and remembering that i multiplied by this cross- 

 section is the magnetic moment of this molecular current, it appears 

 that t'W is equal to the magnetic induction multiplied by the com- 

 ponent of the magnetic moment in its direction, and therefore 

 J2t'N' is equal to 



|- ^(Aa + Bb + Cc)dr. 

 Thus the magnetic circuits add to the energy the amount* 



together with 



-!-j(Aa + B/3 + C r )tfr (ii) 



2- j^ + B^ + C 2 )^ (iii) 



# [These energies as here determined are kinetic ; if they are (as is customary) to 

 be considered as potential, their signs must be changed. Cf. 'Phil. Trans..' A, 

 1894, p. 806.] 



VOL. LXXI. S 



