304 
PROFESSOR J. H. POYNTING ON ELECTRIC CURRENT AND THE 
some parts than in others, while the magnetic intensity is not altered in a correspond¬ 
ing manner. For instance, the magnetic tubes will be continued through an insulated 
conductor in the field, while in the steady state no electric tubes pass through it. 
But each element adds to the line integral the quantity which, after Mr. Bosanquet, 
I have called the magnetomotive force, this being equal to 477 times the number of 
electric tubes passing through the element. But it only adds it on integrating round 
the whole of the closed curve. 
The intensity at any point will therefore be the resultant of the intensities produced 
by the magnetomotive forces in the various elements. Perhaps the simplest mode of 
finding it is as follows. 
The components of the magnetomotive force produced in a cube dx, dy, dz parallel 
to the three edges will be 
dA , dB , dC 7 
—ax, —ay, — dz. 
dt ’ dt dt 
for -y- — 77 , y— -y- —y, are by definition the rates at which electric tubes are 
47T dt 47T dt 47T dt J 
cutting unit lengths parallel to the axes. 
But these magnetomotive forces would be produced by currents round the cube in 
planes perpendicular to the axes respectively, and equal to 
1 d A ; 1 clB 
4tt dt dX> 4t r dt 
7 1 dC 7 
dy, - - -dz. 
J 47 t dt 
for the line integral of the intensity round a curve threading a current is 
477 X current. But the magnetic intensity at any point due to a current is equal 
to that of a magnetic shell of strength (i.e., intensity X thickness), equal numerically 
to the current bounding the shell. 
If we suppose the thickness of the shell equal to that of the cube, the effect is the 
same as if the cube were magnetised with intensity having components 
1 dA J_dB 1 dC 
477 dt ’ 477 dt ’ 477 dt 
The potential of such a distribution of magnetisation is (Maxwell, vol. ii., p. 29, 
equation (23)). 
y 1 rrr/rfA dp dB dp dC dp 
477J J J \ dt dx dt dy dt dz 
yaz 
where p=~, and the magnetic intensity is given by 
dV 
dx* 
fi= — 
dV 
dy’ 
7 = 
d\ 
' dz' 
