492 Mr. 0. Heaviside on Resistance 



electric energy on the whole journey ; the electric energy in 

 the shell is greater, but ultimately becomes the same.] In 

 practical cases this energy would be mostly, perhaps wholly 

 dissipated in conductors. 



(/) If a uniformly distributed impressed force act alter- 

 natingly longitudinally within an infinitely long circular 

 cylindrical portion of a dielectric, the axis is the place of 

 reflexion of the primary wave inward, and the reflected wave 

 cancels the outward primary wave when 



J^na/v) = ; 



so that there is no external disturbance, except at first. 



(g) There is a similar result when the vorticity of impressed 

 force takes the place of impressed force in (/). 



(A) If the alternating impressed force act uniformly and 

 longitudinally in a thin conducting-tube of radius a, with air 

 within and without, then 



J (na/u) = 



destroys the external field and makes the conduction-current 

 depend upon the impressed force only. And if we put a 

 barrier at distance x to serve as a perfect reflector, that is, a 

 tube of infinite conductivity, 



J Q (nx/v) = 



makes the electric force of the field in the inner tube to be 

 the exact negative of the impressed force ; so that there is no 

 conduction-current. The electromagnetic field is in sta- 

 tionary vibration. If the inner tube be situated at one of 

 the nodal surfaces of electric force, the vibrations mount up 

 infinitely. 



(i) If, in case (A), the impressed force act circularly about 

 the axis of the inner tube (which may be replaced by a 

 solenoid of small depth), 



J^na/v) = 



destroys the external field, and 



J^nx/v) = 



makes the electric force of the field the negative of the 

 impressed force, and so destroys the conduction-current. 



(J) We can also destroy the longitudinal force of the field 

 in a conductor without destroying the external field. Let it 

 be a wire of steady resistance in a dielectric, and the impressed 

 force in it be 



e = e cos mx cos nt 



per unit length. Then m = n/v makes e be the force of the 



