G. F. Firzerranp.— Wave Disturbances in Ether by means of Electric Forces. 175 
to a current in the direction of x, and then the only component of the electro- 
magnetic potential at each point is F and 
U 
R=eR 
(I distinguish the points at which F exists by the suffix), Where - is the 
magnetic inductive capacity of the medium, and R is the distance of the point , from 
the current. The current at , produced by the acceleration of U is 
2 
ik = I Py 2 " 
Up= =F Fo - a : = writing U for U. 
Hence the vector potential at , due to this is 
Kp ty (din 
ae 19; / (Lee 
ae 4 rR 
Where dm, is the element of volume at ,, and 7. is the distance from , to ,. 
Similarly 
re Kp 2 uf we 
NGA Tr, @ Ta1ef 7 wR 
ee. 1 (By Uf <a a 
10 
u.nm—l 
1 hIMy,_ SI: 7% 
Pu (Aar)e ae 56000 0 0 Po 
: F,=(—1)"(Kp)"Up, 
and the relation connecting pn and Pn. is 
2 
A Pn—r1UMn—1 
a erent 
nn—1 
Before going further with this I may call attention to this, that if U were a 
simply periodic function of the time =a cos mt, we can see that the complete F 
and generally 
Hence, if we call 
we may write 
PSH. 
would necessarily be of the form 
cos mt X(Kp)"m?"p,=V», cos mt 
so that as F is to satisfy the equation 
AF + Ku: F=0 
we can see that V,, must be as before 
™m 
Weal Op mR) 
R 
for it can only be a function of R as is evident. 
We may get this otherwise by proceeding to determine p» from pr for we know 
that — We may do this with facility by observing that as pis a function of 
the co-ordinates of the point ,_, only we have 
[Na Ons 
