IN CYLINDRICAL CONDUCTORS, ETC. 
61 
A„J„(Xq) = B n q”+C n /q n 1 
A n XaJ'„(\a) = n (B n a n —CJa n )) 
A 0 J 0 (Xq) = B 0 log, a + C 0 
AA^J'o (Xa) = B 0 
or, expressing A„, C n in terms of B„ and making use of the properties of the Bessel 
functions, 
A„ = 2nB n a n /\aJ n _ x (\a) 
C n = B M q 2n J n+1 (Xa)/J„_! (Xa) 
A 0 = Bo/XaJ'o (Xa) 
C 0 = B u {J 0 (Xa)/XaJ' 0 (Xa)-log, a} J 
The general solution of (2) is the sum of the normal solutions of the type (3), so that 
the electric force may be expressed as a Fourier series, whose form inside the 
cylinder is 
Ei = B 0 
Jp(^) 
nB, i q"J n (Xr) 
+ 22 
XaJ'o (Xq) i Xq J„_j (Xq) 
cos (n6 + a n ), 
( 8 ) 
and outside the cylinder is 
X'qJ'o (Xq)/ 
+ 2 B J( ? ,n 
«\ 2n J B+ i (xq) 
r) J B _ x (Xq) 
cos (nO + a.,,). 
. (8a) 
The corresponding series for P and Q follow by differentiation using the relation (1). 
The combination of the cosine and sine terms into the form cos (nO + a n ) is permissible, 
since the ratios of the arbitrary constants are the same for both the sine and cosine 
series. The values of B„ and a n may be determined when the form of the undisturbed 
field is given. 
(3) Energy Dissipation in the Cylinder .—-From (8a) and (1) the values of E and Q 
at the surface of the cylinder are 
E = B oXo + 2 B„q" (1 +x») cos [n0 + «„) 
1 
( 9 ) 
Q = |b o + 2nB„q” (l — x„) cos (n6 + a. n ) j-.(10) 
coq L i J 
in which 
Xn (Xq)/J B _i (Xq) 
2 
Xo = J o (Xq)/Xq J' 0 (Xq) = i(l+Xa)-ri75 
a a 
If e, q represent the instantaneous values of E and Q, the rate at which energy flows 
