Resistance and Inductance of a Helical Coil. <s] 



electric force along these directions. Since the operation 

 3/3$ annuls any component, the solenoidal conditions 

 become. 



~° X + B - Y ■ = 0, ' 



"dpP2Ps d<f>PiPs J 



It is assumed also that (pij^p.i) are independent of 0, as is 



the case in all important applications. Functions % and i/r 

 may be introduced, where 



X = p 2 p 3 3%, 30, Y = Pl ^ a %% "dp, [ 

 « = PiPz 3^ y 30, P = Pip* o^, 3p 1 

 By Faraday's law, if /jl be the permeability, 



—a* 3v _ 3 v _ a x 



P1P3 3' 3/) pa 30 /'1 



_ 3. P1P2 3% + 3 p 9 pg "dx . (7) 



3p p% 3/3 36 />, 30 ' 

 and by Ampere's law, in a dielectric, 



1 ax_ 3 7 



whence, on reduction,^, andjsimilarly -^ satisfy the equation 



'dp Pi 3/> 3</> jPi 30 V-/,,,,. 3/"" 



where V is the velocity of propagation or* electromagnetic 

 disturbances. Thus any disturbance in which the vectors are 

 independent of" one coordinate of an orthogonal system mast 

 be made up of two typos, in which the electric and magnetic 

 forces along the direction of increase of thai coordinate are 

 respectively zero everywhere. 



If the wave-length of the oscillation, supposed simply 

 periodic, be 'IttJU, the equation for yfr becomes 



I / ' ,/ ''? + -^— X+ / '' V3 ^= ' -( 10 ) 



Op P2 Op 30 pi 00 /']/'■■ 



and For a conducting medium, it is only necessary to change 

 /.-. In the present problem the oscillation defined by yjr exist-, 

 Phil. Mag. S. (5. Vol. 10. Xo. 109. Jan. 1909. G 



