312 
PROFESSOR C. NIVEN OX THE INDUCTION OF ELECTRIC 
F = F', G = G', II =H' 
d^_dT clG _cK¥ dR _dW >■ 
f/N — f/N 5 d¥~ dN ’ 
(4) 
F', G', H' being the components of the electro-magnetic momentum in the second 
substance, and e/N an element of the normal drawn from the first into the second. 
The other boundary conditions are more difficult to recognise. Let us first confine 
our attention to the common surface of separation of two substances at rest. In the 
first the equations of electromotive force are 
11 =- 
dt dx 
dG_df 
dt dy 
(7H ddr 
dt dz 
V 
I 
( 5 ) 
with similar equations for the second. Let l, m, n be the direction cosines of the 
normal (N) at any point, and let ^f = /F-|-mG-j-; then, since 
M =( C +?J) P ’ &0 " 
h + mv + nw- 
and, for the second substance, 
lu -\-mv -\-nw’ 
The condition of “ continuity” at the surface requires that 
( 6 ) 
lu -f- mv nw = lu'+mv -\-n w', 
and therefore 
C-C' + 
K-K' 
47r / dt] dt 
47r dt) cZN 
47r dt dN 
( C , K d \ d $_ [CJ- K . 
\ Utt dt) dt V " r 47T dt) tfN ’ 
/ . K' d\ d§_( rA J^_ <£\ &¥_ 
\ " 1 "4tt dt) dt \ "^tt dt) fQT 
The free electricity e at the surface is given by 
