1921-22.] The Faraday-Tube Theory of Electro-Magnetism. 233 
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 And the convective flux we require to localise the energy 
in a manner rather difficult to justify. The whole energy per unit volume 
may be written 
iNB + iED 
(37) 
Then we may suppose the part — Vq„^B) of the energy to be 
moving with velocity , and so on. The total convection of energy will 
therefore be 
|2d„,(E- Vq^B). (38) 
To find the stress-activity flux from (35), consider first the term 
(E-fVq^B).d^ ; the appropriate velocity is clearly q^ , and the flux (by 
Heaviside’s method) 
~ Qm(^-l-^qm^) • dm— “ Qm® • d^^ • 
Again, we may write the second term 
- ^ED + iHB = - i{(Sd,JE - (SVq,,d JB} 
^.-iSd^(E + Vq^B), 
and it seems permissible to write the activity flux due to the term 
-id^(E + Vq^B) as + Jq„j . d„(E + Vq„B). Hence the total activity flux 
will be 
-i;{q„E.d„-|d„(E + Vq„,B)}, , . . . (39) 
and the whole flux, adding (38) and (39), 
W = i2d„(E- Vq„,B) . q„ - 2q„E . d,„ + iSd™(E + Vq„B)q„ 
“ ^(d„jE . q„( — q^E • ^m) 
= VESVq„d„ 
= VEH (40) 
8. Since we have shown that this theory leads to the ordinary 
equations of the electro-magnetic field, it is unnecessary to give a separate 
proof of the uniform propagation of disturbances with velocity 1/ J yotK. It 
is perhaps as well, however, to examine shortly the mechanism of pro- 
pagation, particularly since the mental picture of electro-magnetic radiation 
afforded by the theory is in many respects very satisfactory. 
N. Campbell gives a short discussion of the question, and shows that a 
tube at rest may be compared to a flexible cord of linear density /uD under 
a tension D/K ; the square of the velocity of propagation of transverse 
disturbances being then l//xK by the elementary dynamics of cords. To 
extend this result to the case of a tube having a general velocity v per- 
pendicular to its own direction, we have only to remember that, by 
