ELECTRIC AND MAGNETIC INDUCTIONS IN THE SURROUNDING FIELD. 503 
=°Jt*+ 
= C / a+ 
K da 
47T dt 
K da 
4 : 77 " dt 
from (13) 
with two similar equations. 
Finding the values of the left hand from (12) we obtain 
4nC,a+K^= 
' dt 
4„Ci+Kf = 
4ttCc + Kv = 
' 1 dt 
„. d [dA c£B . dC 
“ V ~ A “^flfe 
0T) d (dA d\) dC 
-vB “-U + -+ 
dy\ 
dy dz 
0 p d fdA d£> dQ 
^~Jz\dx'^"dy^"dz 
If we assume 
A --sUI( 4 ^ a+K l)7 1 ^ 
• • (14) 
with corresponding values for B' and O' and 
then 
A=A'- 
B = B' — 
C = C'- 
riM‘ 
dM 
% 
c/N 
d v. 
(15) 
are solutions of (13). 
We may obtain by substitution from (15) in (12) values for f, g', li' corresponding 
to the values of the magnetic induction in (9), viz. : 
, dC' d& 
~~ dy dz 
and two others; where A', B', C' are given in terms of the magnetic induction as 
above. 
It is only in special cases, such as that of a straight wire with a steady current, 
that the magnetic intensity will be equal to 47 t times the number of electric induction 
tubes passing through unit length per second. In all cases the line integral of the 
magnetic intensity round a closed curve is equal to 47 t times the number of electric 
tubes passing through the boundary, but the electric tubes may be more crowded in 
2 r 2 
