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



Enormously great frequency brings us to the formulae of the 

 non-conducting dielectric, with a difference, thus : n x and n 2 

 become 



w 1 = 27T^ v, n 2 = n/v, .... (202) 



when 4:7rk/cn is a small fraction. The attenuation due to con- 

 ductivity still exists, but is independent of the frequency. We 

 have now 



(out) H=!^e-.'(co S -^ S in)(^-» ( ), (203) 



differing *rom the case of no conductivity only in the presence 

 of the exponential factor. 



It is, however, easily seen by the form of n x in (202) that 

 in a good conductor the attenuation in a short distance is very 

 great, so that the disturbances are practically confined to the 

 vortex lines of the impressed force, where the H disturbance 

 is nearly the same as if the conductivity were zero, as before 

 concluded. It follows that the initial effect of the sudden 

 introduction of a steady impressed force in the conducting 

 dielectric is the emission from the seat of its vorticity of waves 

 in the same manner as if there were no conductivity, but atte- 

 nuated at their front to an extent represented by the factor 

 6 _n ' r , with the (202) value of n lf in addition to the attenuation 

 by spreading which would occur were the medium non-con- 

 ducting. This estimation of attenuation applies at the front 

 only. 



30. Current in Sphere constrained to be uniform. — Let us 

 complete the solution (200) of § 29 by means of a current of 

 uniform density parallel to the axis within the sphere of 

 radius a, beyond which (200) is to be the solution. This will 

 require a special distribution of impressed force, which we 

 shall find. Equation (200) gives us the normal component of 

 electric current at r=a, by differentiation. Let this be 

 r cos 6. Then T is the density of the internal current. The 

 corresponding magnetic field must have the boundary-value 

 according to (200), and vary in intensity as the distance from 

 the axis, its lines being circles centred upon it, and in planes 

 perpendicular to it. Thus the internal H is also known. The 

 internal E is fully known too, being & -i r in intensity and 

 parallel to the axis. It only remains to find e to satisfy 



curl (e-E)=/iH, (3) bis 



within the sphere, and at its boundary (with the suitable sur- 

 face interpretation), as it is already satisfied outside the sphere. 

 The simplest way appears to be to first introduce a uniform 



