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XXIV. Note on a Paper on Electromagnetic Waves. 

 By Oliver Heaviside*. 



AN editorial query, the purport of which I did not at first 

 understand, has directed my attention to Prof. J. J. 

 Thomson's paper " On Electrical Oscillations in Cylindrical 

 Conductors" (Proc. Math. Soc. vol. xvii. Nos. 272, 273), a copy 

 of which the author has been so good as to send me. His results, 

 for example, that an iron wire of ^ centim. radius, of inductivity 

 500, carries a wave of frequency 100 per second about 100,000 

 miles before attenuating it from 1 to e -1 , and similar results, 

 summed up in his conclusion that the carrying-power of an 

 iron wire cable is very much greater than that of a copper 

 one of similar dimensions, are so surprisingly different from 

 my own, deduced from my developed sinusoidal solutions, in 

 the accuracy of which I have perfect confidence (having had 

 occasion last winter to make numerous practical applications 

 of them in connexion with a paper which was to have been 

 read at the S. T. E. and E.), that I felt sure there must be 

 some serious error of a fundamental nature running through 

 his investigations. On examination I find this is the case, 

 being the use of an erroneous boundary condition in the 

 beginning, which wholly vitiates the subsequent results. It 

 is equivalent to assuming that the tangential component of 

 the flux magnetic induction is continuous at the surface of 

 separation of the wire and dielectric, where the inductivity 

 changes value, from a large value to unity, when the wire is 

 of iron. The true conditions are continuity of tangential 

 force and of normal Jinx. 



As regards my own results, and how increasing the induc- 

 tance is favourable, the matter really lies almost in a nutshell; 

 thus. In order to reduce the full expression of Maxwell's 

 connexions to a practical working form I make two assump- 

 tions. First, that the longitudinal component of current 

 (parallel to the wires) in the dielectric is negligible, in com- 

 parison with the total current in the conductors, which makes 

 C one of ihe variables, C being the current in either conductor; 

 and next, what is equivalent to supposing that the wave-length 

 of disturbances transmitted along the wires is a large multiple 

 of their distance apart. The result is that the equations 

 connecting V and C become 



* Communicated by the Author. This Note may ho regarded as a 

 continuation of Note 13 to " Electromagnetic Waves," Phil. Mag. February 



1888. 



