﻿Faraday-Tvbe Theory of Electro-Magnetism. 603 



the stress is 



4> = ^ + 2(Yd m B.q,„) (35) ; 



= E . D + H . B-pD-^HB + XYq^B . d m -SVq m d m . B 



+ 2(Yq m dJB 

 = E . D + H . B-pD-iHB + 2\ r q Wi B . d w -H . B + HB 



= 2{E + Vq m B.cU -iED + iHB (35) 



From (35)' we see that the stress coincides with Maxwell's 

 stress when there is no convection of momentum relative to 

 the (so-called) fixed reference frame ; and from (35) that it 

 consists in general of a quasi-tension equal to E-f-Yq m B per 

 tube of the mth set together with a hydrostatic pressure 

 ^(ED — HB). The torque per unit volume is seen to be 



- <// = S = - 2V(E 4- Vq ?H B) cU 

 = + 2Yd m Yq 7n B 



= +2Yq„,Yd w B, (36) 



the last expression being the rate of change of moment of 

 momentum about a fixed point due to component of velocity 

 perpendicular to the momentum, familiar in the hydro- 

 dynamics of the motion of bodies in a fluid. 



7. The flux of energy also consists of two parts : the 

 convective flux due to the motion of the tubes, and the flux 

 due to the activity of the stress. To find the convective flux 

 we require to localize the energy in a manner rather difficult 

 to justify. The whole energy per unit volume may be 

 written 



iNB + pD 



= i2d JB (E-Vq m B) (37) 



Then we may suppose the part d m (E — Vq m B) of the energy 

 to be moving with velocity q m , and so on. The total con- 

 vection of energy will therefore be 



i2d m (E-Vq TO B).q w (38) 



To find the stress-activity flux from (35), consider first 

 the term (E-f-Vq Hl B) . d ??l ; the appropriate velocity is clearly 

 q m , and the flax (by Heaviside's method) 



- q m (E + Vq m B) . d„ z = - q M E . d w . 

 Again, we may write the second term 



- iED + iHB = - i { (ScL)E - (2 Yq TO d m ) B} 

 --±2d.(E + VqJB), 

 and it seems permissible to write the activity flux due to the 

 term — id m (E -f- Yq,„B) as + iq, n . d m (E + Yq,„B). Hence the 



