Bumstead — Reflection of ElectTiG Waves, etc. 359 



Art. XXXI Y. — On the Reflection of Electric Waves at the 

 Free End of a Parallel Wire System; by Henry A. 

 Bumstead. 



When electrical waves are sent along two straight parallel 

 wires, and a series of standing waves is formed bj reflection 

 from the unconnected ends of the wires, it is found that the 

 distance from the ends (where one would expect to find a loop 

 for electric force and a node for current) to the first node for 

 electric force is less than a quarter wave-length as determined 

 elsewhere along the wires ; and the discrepancy always appears 

 whether the measurements are made by means of a resonator 

 or by the sliding bridge method of Lecher. This apparently 

 anomalous behavior excited considerable attention among the 

 earlier experimenters and writers upon this subject, and sev- 

 eral attempts at an explanation, by means of special assump- 

 tions, have been made."^ A more careful consideration of the 

 question, however, shows that even with perfectly conducting 

 wires, and without any modification of Maxwell's theory, or 

 any assumption of the escape of charge into the air, a displace- 

 ment of the current node beyond the end of the wires is to be 

 expected theoretically and that its magnitude should be of the 

 same order as that which is found experimentally. 



The cause of the phenomenon is perhaps most easily seen 

 by using Mr. Heaviside's ingenious device of considering elec- 

 trical resistance in tlie guiding wires as approximately equiva- 

 lent to a fictitious magnetic conductivity in the dielectric. Thus 

 if the vectors E and H are the electric and magnetic forces at 

 any point and C the total current, the fundamental equations 

 of the field, in the form used by Heaviside and Hertz, are 

 curl H = 47rC (1) 



-curl E = AtH (2) 



C is the sum of the displacement and conduction current in 

 the dielectric, so that 



C=;^E+/E 



where K and f are respectively the dielectric constant and 

 conductivity of the medium. Equation (1) thus becomes 



curlH = KE + 47r/E (1') 



If we assume that the medium possesses also a magnetic con- 

 ductivity, g, then (2) takes the entirely analogous form 



-curlE^/xH + 47r^H (2') 



* See Poinear^, Les Oscillations Electriques, arts. 110 and 125. 



Am. Jour. Sci.— Fourth Series, Yol., XIV, No. 83. — November, 1902. 

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