Wave Propagation over Parallel Wires. 613 



are expressible as 



H t =£B„{^ + (-l)»^}, 



fCOS??^! . COS n# 2 



H y = X C„ -j — + 



h=1 v. 



y COsn& 2 • 

 V ; r a » J" 



The magnetic force in the dielectric is thus expressed in 

 terms of two symmetrical waves centred on the axes of 

 the two wires respectively. 



From the equation div. H = it follows that 



d x ^y 



differs from zero only by 7H., which is a very small 

 quantity since both 7 and JEL are small. With very small 

 error we may therefore write 



ox dy 



which determines the relation between the B and C co- 

 efficients of (11) and gives 



h. = sb:{=^ + (-i)-5^), . . (12, 



n=l \ r l ?2 J 



H y =-iB„{^ + (-l)» C ^}. . . (13) 



n=l *■ ? 1 '2 ) 



In the dielectric the electric forces satisfy the wave 

 equation II, and are therefore expressible as two Fourier- 

 Bessel expansions oriented on the axes of the two wires. 

 In accordance with our assumption, however, that y andp/v 

 are very small quantities, the Bessel functions are replaceable 

 in the neighbourhood of the wires by the limiting forms 

 which they assume for vanishingly small arguments. The 

 same result is arrived at if we take E x and E y as satisfying 

 the equations 



(d 2 /B* 2 + d 2 % 2 )E y = 0. 



Furthermore, from the relative magnitudes of E^ and the 

 electric force in the plane XY in the dielectric, the equation 

 div. E=0 may with very slight error be replaced by 



I E x + | E f = 0. 



0% oy 



Phil. Mag. S. 6. Vol. 41. No. 244. April 1921. 2 S 



