510 PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
acts on a cylindrical wire of specific resistance g>, we have 
-n d¥ 
?i=?—dr 
where F is got from the equation 
d 12 F 1 d¥ 
dr 2 ' r dr 
= -4 vp-p, 
r being the distance from the axis of the cylinder. 
Let one term of the value of F be of the form T r n , where T is a function of the time, 
then the term of p which produced it is of the form 
— -t— n?Tr n - 2 . 
47 T[& 
Hence if we write 
*= t +7 (- p +f r+TTir** w r ‘+ ** 
n~- 
' dt ' " r 
j 2 1 d s T 
dt 2 ‘ 
r 4 — &c. 
q I I 2 . 2 2 dt S 
point is 
CfP \ 7 , 1 rp [X.7T dT /A 2 1 d 2 T 
Jli - ^; <B= i :T+ 7 ^ + ™ w r + &c - 
The total counter current of self-induction at any point is 
At 2 1 d*T 
from t— 0 to t — co . 
When t= 0, j>=0, =P, =0, &c. 
When t=oo , w = s 
• = 0 . (S), 
= 0, &c. 
a ' /P \ 7 l m „ 1 LOT 2 dT , f* 2 7T 3 1 fi? 2 T - 
25r (j -p)rdrdt= -W+ 2Y~di r + l r TVFTs &c - 
from t=0 to =oo . 
When £=0, p= 0 throughout the section, .\ =P, = 0, & c - 
When t= co , p=0 throughout \ ) = 0 5 =0, &c. 
Also if l be the length of the wire, and R its resistance, 
k=4; 
and if C be the current when established in the wire, C= -yp 
The total counter current may be written 
B(T--T.)-|4c=-^by§(35). 
