ELECTRIC AND MAGNETIC INDUCTIONS IN THE SURROUNDING FIELD. 283 
if we regard the field as caused by the inward flowing of the energy rather than by 
something propagated out from the wire. 
Assuming that the induction tubes bring in their energy, the quantity is easily 
found. The number of unit cells per unit length is equal to the difference of potential 
E 
per unit length, or E. Hence the energy per unit length of each tube is -, since each 
cell contains a half unit. If C tubes disappear in the wire per second they yield 
CE 
up — of energy per unit length. How the total energy dissipated per unit length 
is CE per second. Or the movement inwards of the electric induction will only 
account for half of the energy. The other half must be accounted for by the move¬ 
ment inwards of the magnetic induction. This movement of the magnetic induction 
is suggested by the existence of electric induction, which cannot be ascribed to statical 
charges. 
The electric intensity is E. Hence E tubes of magnetic induction must move in per 
second, cutting unit length parallel to the axis of the wire, in accordance with the 
second principle, and it will easily be seen that the inward motion gives the right 
direction of the electric intensity. The line integral of the magnetic intensity round a 
tube is 47 tC, the tubes being closed rings. Hence there are 47 tC unit cells in the length. 
1 . 47tC C 
Since each of these contains — of energy the quantity per tube= ^ =-. E tubes 
CE 
entering the wire per second will carry in 0 of energy, the other half to be accounted for. 
We can in a similar manner trace the dissipation of the energy, which we must 
suppose taking place within the wire. The line integral of the magnetic intensity 
round a circle, with its centre in the axis of the wire, is constant up to the wire, 
and equal to 47 tC. Within the wire it gradually diminishes as the circle contracts. 
o 
V* 
At a distance r from the centre it is AnC.—z when a is the radius of the wire, If we 
a z 
assume this intensity to he still due to the passage inwards of the tubes of electric 
induction only, — cross inwards per second at a distance r, the difference between 
this number and the C tubes entering the outer boundary being destroyed and their 
energy dissipated. The energy thus dissipated per unit length between the outer 
per second. If r=:0 
the whole of the electric energy is dissipated. It would appear, then, that we may 
represent the dissipation of the electric energy by the total destruction of the tubes 
all through their length. 
The value of the electric intensity being E throughout the wire the number of tubes 
of magnetic induction cutting unit length parallel to the axis is the same at all parts, 
viz., E per second. Hence, the magnetic tubes are not destroyed as the electric tubes 
EC 
boundary and a coaxal cylinder of radius r will be — (1 — 
