702 
MR. G. F. FITZGERALD ON THE ELECTROMAGNETIC THEORY 
or in Cartesian coordinates 
^($£+ 17817+£8 £) 
, _ c lL\ , 
77 I dd [dy dz) d0 [dz dx) dd [dx dy 
+^{S(f-S)+S(f-f)+S(S-?)} 
. I \m_ten\(dK _dv\,m_^\(dJ_dX\ 
K[\ dy dz )\dy dz) \ dz dx )[dz dx) 
/dS ?7 d&£\ !dy d£ 
[dx dy )[dx dy 
Integrating these now by parts relatively to x, y, z, and calling l: m : n the direction 
cosines of ill the normal to the surface of separation, and aZ+/3m+y??,=S311SR = e when 
9)1 is the vortex whose components are cl, (3, y, we get 
j j|{s. 4 ttC{V v 9i j +|V(SR.y v SR) J831jcfe 
+ |||S.j(^+ 8ttCV v ,] f e + | V v V v 9 1) 89 i | dxdydz 
dt=0 
or in Cartesian coordinates 
w 
\J d A_ c IP 
[ch dx, 
+ 47tC 
-I 
KKS-S) 
+{”<f-S)- ; (S-I)i s < 
rr ~*M(£ -S 8 ^@-f )) s 4 * 
- 477-C j j(7a + m/3 -f ny) j - ■ 
+ 11 \y(&g+r)%r) + i§C)dxdydz 
dy dz j dd \dz dx) 
'^(±L_d±\_d (dJ__JZ\ 
dy [dx dy I dz [dz dx J 
+sfff 
S^+ 
dd \dx dy J J 
d /dg dy\ d /dy dg \ 
_dz[dy dz) dx[dx dy )_ 
Sp 
+ 
'd_(dt _dX\_d fdX_ _ dy 
dx\dz dx) dy[dy dz)_ 
§C l dxdydz 
