284 
PROFESSOR J. H. POYNTING ON ELECTRIC CURRENT AND THE 
are. But the line integral of the magnetic intensity round the tubes diminishes as 
GV 2 
they approach the axis, being 47 t — round that at distance r. The number of unit cells 
diminishes, and, therefore, the energy per tube is less, the decrease being due to that 
4ttCE 
dissipated. Thus the energy entering in the E tubes at the outer boundary is 
C7T 
CE . . . 4vr Cr 2 
or —. That crossing m E tubes at a distance r is --r 
2 & 87 r a~ 
E = 
CE ?- 2 
Z Ob 
The difference 
CE / r 3 \ , .. . 
-y-(l— ,) being dissipated. 
Hence it appears that the energy dissipated per second may be represented as half 
electric half magnetic, the electric energy being dissipated by the breaking up of the 
tubes, and their disappearance while the magnetic energy is dissipated by the 
shortening of the tubes, and their final disappearance by contraction to infinitely small 
dimensions of the diameters of the rings by which we may represent them. At all 
points therefore outside and inside the energy crossing any surface may be represented 
as equally divided between the two kinds. 
As we know the value of the induction at any point, or the number of tubes passing 
through unit area, and as we also know the number of tubes cutting the boundary it 
is easy, on the assumption that the tubes move on unchanged, to calculate their velocity. 
Of course this velocity is purely hypothetical, as we cannot examine minutely into the 
medium and observe what goes on there. Probably, if we could observe with sufficient 
minuteness w r e should find unevennesses in the induction. If the velocity of the tubes 
has any physical meaning it is that these unevennesses are carried forward with that 
velocity. To illustrate this let us suppose that we have water flowing through a glass 
tube at a steady rate. We have nothing to show that the water is moving past any 
point in the tube beyond its disappearance at the entrance and its appearance at the 
exit, but knowing the cross section of the tube, i.e., the quantity of water in any part 
of it, and the quantity entering and leaving it is easy to assign a velocity to the water 
in the tube which shall account for the observed amount entering and leaving’. This 
velocity is to a certain extent hypothetical. But if we examine the tube with a 
sufficient magnifying power to show particles of dust in the water the existence of the 
velocity receives a more direct proof. I do not know whether we should have any 
right to expect a similar proof of the motion of induction even if we had the means of 
observation. 
To find the hypothetical velocity of the electric induction tubes let us calculate the 
number of tubes passing through a circular band with radii r and r-\-dr and centre in 
the axis of the wire, and lying in a plane perpendicular to the axis. The intensity 
IvE 
being E the induction is , and therefore the area of cross section of each tube is 
7r ~, since area X induction is unity. The number passing through the circular band 
KE 
KE 
is therefore Zirrclr- , — - 
*± 7 T 
IvE rdr 
9 
