318 
PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
H=~(rP), V 2 P=0 
F=o, G= 
dP 
_TT , dV 
sin 9d(f> ' dd . 
. 
■ ■ ( 31 ) 
and may be readily verified by substitution and actual differentiation, as in the former 
cases, observing that v 2 P=0. They coincide with the expressions given by Maxwell 
(Pol. II., Art. 671), and before him by Jochmann ; they likewise satisfy the condition 
of no convergence, which in this case is 
1 d.FA 1 d. sin 9G dH 
r 3 dr r sin 9 d9 r sin 9dxf> 
(B.) The vector components of the electro-magnetic momentum give rise to the 
vector potential of the magnetic force in the space in which the currents themselves 
exist: we shall therefore enquire what distribution of currents must be assigned that 
the vector potentials due to them may be respectively of the foregoing types. 
(«.) Rectangular coordinates. 
The equations to be satisfied are 
If we take 
4 TTU = 
dy 
dy 
d/3 
dz’ ’ ' ‘ 
dG 
' dz 3 
dP dP 
dif ^~dx’ 
H = 0 
(22,) 
we find that the above equations are satisfied by 
where 
d 3 P d 3 P d 2 P d 2 P 
dxdz ’ ' J ~~dd j dd V-dx* + df 
d O 
v=-. , w— 0 
dx 
— V 2 P. 
( 22 s ) 
is here the current function, and V ~P is not now supposed to be equal to zero ; 
in fact, nothing is at present supposed to be known about it. 
( b .) Semi/polar coordinates. 
The x — and y — directions are variable and are supposed to be in the directions of 
