PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
495 
_ n de i _ } 
e '~ /*> dt -? 1 ’ 
«.=/-/»»■ §=^1-^2, [ 
&c. &c. 
But by equations (E) and (F), 
'Fa 'F 3 = ajc^^ = — 
&c. &c. &c. 
(51) 
(52) 
After the electromotive force has been kept up for a sufficient time the current 
becomes the same in each layer, and 
q/ 
jp 1= p 2 =& c. =p = —i 
where 'F is the total difference of potentials between the extreme layers. We have then 
and 
■'P r x 
r CiAj’ 
'l 
akj’ 
&c. 
(53) 
These are the quantities of electricity on the different surfaces. 
(87) Now let the condenser be discharged by connecting the extreme surfaces 
through a perfect conductor so that their potentials are instantly rendered equal, then 
the electricity on the extreme surfaces will be altered, but that on the internal surfaces 
will not have time to escape. The total difference of potentials is now 
^ &c. = 0, (54) 
whence if e\ is what e x becomes at the instant of discharge, 
j ¥_r, T — 
1 r a l k ] ak ak 
(55) 
The instantaneous discharge is therefore or the quantity which would be dis- 
charged by a condenser of air of the equivalent thickness a, and it is unaffected by the 
want of perfect insulation. 
(88) Now let us suppose the connexion between the extreme surfaces broken, and the 
condenser left to itself, and let us consider the gradual dissipation of the internal charges. 
Let "V be the difference of potential of the extreme surfaces at any time t ; then 
^'■=ajc x f, + ajcj, ;+&c.; (56) 
dfi 
