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



not unusual. Occasionally very interesting streams of hori- 

 zontal discharge are seen running through the cloud-caps of 

 the Table Mountains just parallel with and above their flat 

 tops. He then becomes eloquent on the varied colours of the 

 lightning, and proceeds to say that "the end of the vast 

 storm-cloud is brought out in deep relief at each discharge by 

 glows of electric light bursting forth from behind its edge, 

 the foldings and twistings of which are rendered conspicuous 

 by lines and sheets of coloured fire. I have seen displays of 

 this character taking place simultaneously on six different 

 points of the horizon, and continuing for hours at a stretch, 

 and I have counted 56 flashes in a minute." Sometimes a 

 number of cattle huddled together are killed at once. " The 

 popular notion is that the discharge runs through the beasts 

 in succession. My own impression, derived from the appear- 

 ance of the ground where such accidents have taken place, is 

 that the discharge acts at one blow over the entire area 

 covered by the cattle, and divides itself among them.'" 



Highgate, N. 



LVI. On Electromagnetic Waves, especially in relation to the 

 Vorticity of the Impressed Forces ; and the Forced Vibra- 

 tions of Electromagnetic Syste?ns. By Oliver Heaviside. 



[Concluded from p. 449.] 



63. /CYLINDRICAL Surface of circular curl e in a Dielec- 

 tric. — Let the curl of the impressed electric force be 

 wholly situated on the surface of a cylinder of radius a in a 

 nonconducting dielectric. The impressed force e to correspond 

 may then be most conveniently imagined to be either longi- 

 tudinal, within or without the cylinder, uniformly distributed 

 in either case (though oppositely directed), and the density of 

 curl e will be e; or, the impressed force may be transferred to 

 the surface of the cylinder, by making e radial, but confined 

 to an infinitely thin layer. The measure of the surface-density 

 of curl e will now be 



de 

 /=^7= E (out)— E (in) , .... (356) 



where e is the total impressed force (its line-integral through 

 the layer). The second form of this equation shows the effect 

 produced on the electric force E of the flux, outside and inside 

 the surface. This E is, as it happens, also the force of the 

 field ; but in the other case, when e is uniformly distributed 



