﻿Straight Wire on Electric Waves. 53 



of wares by wires with which it deals. On the contrary it 

 omits the most interesting parts of the discussion, namely, 

 the substitution of numerical values for the physical constants 

 with a view to ascertaining what quantities in the formula? 

 are negligibly small, and the interpretation of results such as 

 formulae (8) and (10) ; these are to be found in the works to 

 which reference has been made above. It is only to the 

 preliminary mathematical analysis that our attention is now 

 directed. 



5. The Scattering of Waves by a Perfectly 

 Conducting Wire. 



Let the axis of the wire be the axis of r, and a the radius. 

 Consider first the case in which the incident wave, propagated 

 in a direction perpendicular to the wire, has its electric- 

 intensity perpendicular to the wire and therefore its mag- 

 netic force parallel to the wire. Taking the direction of 

 propagation as axis of #, we have for the magnetic force in 

 the incident wave an expression of the form 7 = H <?<O^ *•*'). 



In cylindrical coordinates the space exponential is 

 e -iKr cos0 5 an J niay be expanded by Fourier's method in a 

 series of cosines of multiples of 6 ; no sines occur because 

 the function is an even function. Let the expansion be 



e k»-«*0=2./»cos*0 (11) 



Xow as 



I dr- r dr \ r- /' J 



it follows that 



whence for each value of s 

 <Pfs ■ ldf t 



-£ s+ (^h)f°=°- • • ■ m 



dr 2 ? 



Put /s(r) =g s (tcr) =g s (p) say, and we get 

 d 2 o s lda s 



d-<i s , \dq s , /„ s 2 \ 



^ + ^ + ( l -^> =0 - • • • (14) 



Clearly g s (p) is not infinite for p = Q; we may assume that 

 there is another solution h f (p) of equation (14), which is not 

 infinite -for values of p other than zero, -and is zero for p = y?. 



