296 
PROFESSOR J. H. POYXTIXG OX ELECTRIC CURREXT AXD THE 
Comparing these with Maxwell’s equations (vol. ii., p. 216) we see that 
dz dy dy dz 
with two similar equations, F, G, H being the components of the vector potential. 
We should obtain Maxwell’s equations if we defined F, G, H to be the number of 
tubes which would cut the axes per unit length if the system were to be allowed to 
return to its original unmagnetic condition, the tubes now moving in the opposite 
direction. According to Maxwell, the vector whose components are F, G, and H 
<£ represents the time integral of the electromotive force which a particle placed at the 
point [x, y, z) would experience if the primary current were suddenly stopped ” (vol. ii., 
2nd Ed., p. 215). If the electric intensity is produced by the motion of magnetic 
induction, then our definition of F, G, H will by the second fundamental principle 
agree with Maxwell’s statement. 
o 
If u, v, iv be the components of current—including, of course, under currents, growth 
of induction—w r e have from the third principle Maxwell’s equations E (vol. ii., 
p. 233), which on multiplying by y become when y is constant 
dc dh' 
Attixu— - -— 
dy dz 
da dc . 
>■ 
db da 
4777xw= ——— 
dx dy 
( 2 ) 
Combining these with equations (L) (as in Maxwell, vol. ii., pp. 236-7), and 
writing — V 2 for f 0 + 7v+ tv we obtain 
° ax- dy i clz - 
0T d (dh , dM , dN 
4ny a— — V L — da {^+ dy + dz 
dfdhdM. dlh\ 
4 ^ = _v 2 M--(-+- ¥ + -) F 
, 0AT d (dh , dM . dB\ 
inyir— V ~N d J^ + dy + dz J 
■ ( 3 ) 
These equations only differ in sign from Maxwell’s, and are therefore to be 
solved in the same way. 
It is easy to see by substitution that if we assume 
