496 
PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
Hence f^=A.^e , / 2 = A 2 <?~ , &c. ; and by referring to the values of e 2 , &c., 
we find 
a r, ¥ 
1_ r ak' 
7" « 2 a: 2 ak 
&c. ; 
(57) 
so that we find for the difference of extreme potentials at any time, 
. . (58) 
(89) It appears from this result that if all the layers are made of the same sub- 
stance, T - ' will be zero always. If they are of different substances, the order in which 
they are placed is indifferent, and the effect will be the same whether each substance 
consists of one layer, or is divided into any number of thin layers and arranged in any 
order among thin layers of the other substances. Any substance, therefore, the parts 
of which are not mathematically homogeneous, though they may he apparently so, may 
exhibit phenomena of absorption. Also, since the order of magnitude of the coefficients 
is the same as that of the indices, the value of W can never change sign, but must start 
from zero, become positive, and finally disappear. 
(90) Let us next consider the total amount of electricity which would pass from the 
first surface to the second, if the condenser, after being thoroughly saturated by the 
current and then discharged, has its extreme surfaces connected by a conductor of 
resistance R. Let p be the current in this conductor ; then, during the discharge, 
''¥'=p l r l -\-p 2 r 2 +&c.=p'R (59) 
Integrating with respect to the time, and calling q l , q 2 , q the quantities of electricity 
which traverse the different conductors, 
5 , 1 7'i+5' 2 r 2 +&c.=5 , R. 
The quantities of electricity on the several surfaces will be 
4 — ? — ?i> 
0 2 +?.— ? 2 , 
&c. ; 
and since at last all these quantities vanish, we find 
(60) 
?. =0.-?, 
?2 = 0 r ,+ 02 — ?; 
whence 
¥r 
ak ’ 
»b=?( 4+4+&C.)-: 
r Va,*, a 2 k 9 / 
( 61 ) 
