176 G. F. Frrzceratp.— Wave Disturbances in Ether by means of Electric Forces. 
or as pn and Pn are all functions of R only we have that this reduces to 
d Pn 
m2 pe) ar Ro, ;=0 
or what is the same integrated 
dR <2 
P2= fF Rp, dR 
From this we obtain neglecting the constants introduced by integration which do 
not affect the form of the result 
1 R R3 (-1)" R» 
3 ee Se? ip. 
so that we evidently have 
(Kp)” 2n R22 
ee ° U [27° 
Now in order to sum the results we must, as before, split up U im its components 
by expanding it in a series of sines and cosines, as before, when we may evidently 
take 
5 
COs Int R22 
F,=DA,, Te +( = 1) Ky)” m2n. [2m 
so that R= PF, 
cos mV KR 
R 
which is of the same form as before, as we saw it ought to come out. 
There are some obvious objections to the latter part of this enumeration, in 
which several of the terms are infinite if the space be infinite. 
The only assumption I seem here to have made is that the initial disturbance is 
the sum of all the initial induced currents, and this seems the only natural and an 
almost necessary assumption. 
“.L=SA .cosmt. 
ty 42 , A aut 3 . 
As VKp 1s the velocity of hight, WKpz 1s very small, so that with currents varying 
at the rate they usually do cosmyK,R=! for any not very large value of R and F, 
and so has the same value as if there were no induced displacement currents at all. 
Dustin: Printed by AutEex. Tom & Co., 87, 88, & 89, Abbey-street, 
The Queen’s Printing Office. 
For Her Majesty’s Stationery Office. 
[1627. 950. 7. 80.] 
