440 Mr. 0. Heaviside on Electromagnetic Waves, and the 



the manner of the settling down. We may commence to 

 change the nature of the medium immediately at the outer 

 boundary of the tube. We cannot, however, have those 

 abrupt assumptions of the steady or simply periodic state 

 which characterize spherical waves, owing to the geometrical 

 conditions of a cylinder. 



53. Case of two Coaxial Tubes. — If there be a conducting 

 tube anywhere outside the first tube, there is no current in 

 it, except initially. From this we may conclude that if we 

 transfer the impressed force to the outer tube, there will be 

 no current in the inner. Thus, let there be an outer tube at 

 r=x, of conductance K^ per unit area, containing the im- 

 pressed force ei» We have 



B * = Y.-Y.-lwK,' (322) 



where Y 3 and Y 2 are the H/E operators just outside and inside 

 the tube, whilst E z is the E at x, on either side of the tube, 

 resulting from e\. We have 



Y _cp J lx -yiGi x y _cp Ji a — yGr la> ,^$\ 



3 * J *-*/i<V 2 « Jo^-yCW 



where y A is settled by some external and y by some internal 

 condition. In the present case the inner tube at r = a, if it 

 contains no impressed force, produces the condition 



Y 2 -Y 1 = 47rKat7'=a, .... (324) 

 where Y x is the internal H/E operator. Or 



S \Voa—y\XQa "Oa/ 



giving 



47rKJ 2 0ffl „ 



irsa s 

 Now, using (323) in (322) brings it to 

 -p ( Jo* —y ftpx) ( Jo* — y 1 Gr 03; )47rK 1 g 1 (%2G) 



- (tt-y) — ~ 4flrK 1 (Jax-yG- «)(Jo#-yiG-o#) 

 s irsx 



in which y is given by (325), and from (326) the whole state 

 due to e x follows, as modified by the inner tube. 

 Now Joa=0 makes y = 0; this reduces (326) to 



