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XXXIII. On the Forms of the Lines of Electric Force and of 

 Energy Flux in the neighbourhood of Wires leading Electric 

 Waves. By W. B. Morton, M.A., Professor of Natural 

 Philosophy, Queen's College, Belfast *. 



§ 1. Contents of the Paper. 



IN the case of electromagnetic waves which are guided 

 through a dielectric by imperfectly conducting leads, it 

 is generally stated f that the flow of energy, as defined by 

 the Poynting vector, is nearly parallel to the conductor, but 

 converges slowly upon it, the lines of flow striking the surface 

 of the wire at a small angle, and part of the energy being 

 turned into heat in the wire. Since the magnetic force is in 

 planes perpendicular to the wire the above statement implies 

 that the lines of electric force leave the wire with a slight 

 forward tilt ; there is a large radial and a small longitudinal 

 component. 



Now an examination of the periodic vectors as worked out 

 in detail by J. J. Thomson J, Sommerfeld §, and Mie || 

 brings to light the fact that there is a certain difference of 

 phase between the radial and longitudinal components of the 

 electric force. Therefore these components do not change 

 sign together, and for a part of each wave-length the lines of 

 force will be tilted backwards. In this region the flow of 

 energy instead of being, as elsewhere, onward and inward, 

 must be either onward and outward or backward and inward. 

 The direction of the magnetic force decides between these 

 alternatives. A flux of energy outwards across an element 

 of surface of the wire indicates that, at this section, the 

 energy of the magnetic field in the wire is being drawn 

 upon, not only for the energy dissipated, but also to increase 

 the magnetic energy in the adjoining dielectric. 



It seemed of interest to examine the state of affairs in this 

 eddy of the energy-flow. In what follows I have worked 

 out in some detail the case of two parallel similar wires, 

 which in some respects is simpler than that of a single wire. 

 I have used the first approximation to Mie's complete solution 

 for this case, which, as I have shown in former papers ^f , can 

 be very simply deduced from the single-wire solution, and 

 can be readily applied to more complicated cases. The main 



* Communicated by the Author. 



t Of. Heaviside, ' Electromagnetic Theory,' vol. i. p. 79. 



% J. J. Thomson, Recent Researches, p. 262. 



§ Sommerfeld, Wied. Ann. lxvii. p. 233 (1899). 



I! Mie, Ann. d. Phys. ii. p. 202 (19 0). 



f Phil. Mag. [5] vol. 1. p. 605 (1900), and [6] vol. i. p. 563 (1901). 



