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LIV. On the Propagation of Polyphase Currents along a 

 Number of Parallel Wires. By W. B. Morton, M.A., 



Prof essor of Natural Philosophy, Queens College, Belfast*. 



1. TN a paper f published in the Philosophical Magazine 

 JL for December 1900, I gave a method for finding 

 approximately the speed of propagation and the attenuation 

 of electric oscillations guided along certain arrangements of 

 parallel wires. One of the cases worked out was that of an 

 even number of similar wires arranged in a regular polygon, 

 the currents at corresponding points of consecutive wires 

 being opposite in phase. I owe to Mr. J. Larmor the sug- 

 gestion that the method might be capable of application to 

 the case of parallel wires carrying alternating currents with 

 a constant phase-difference between consecutive wires, as in 

 the ordinary three-phase transmission of power. This appli- 

 cation I have made in the present note. It will be seen that 

 the case above referred to is included in the more general 

 problem here discussed. 



2. Results obtained. — Let there be n similar wires arranged 

 in a regular polygon. Then the phase-difference between 



. 2tt 



consecutive wires must be a multiple of — , and by taking- 

 different multiples we obtain, for each value of n, differen 

 possible modes. It is easily seen that the number of mode s 

 will be \n if n is even, \{n — V\ if n is odd. A formula is 

 found which gives the speed and attenuation for any number 

 of wires and any mode, on the same simplifying assumption 

 as was introduced in the former paper, viz., that the radii 

 of the wires are small compared with their mutual distances. 

 The results are expressible in two ways. The analysis leads 

 directly to the distance apart of the equivalent pair of wires. 

 Further, by comparison with lieaviside's well-known ex- 

 pression for the case of slow oscillations we deduce the 

 effective capacity, resistance, and inductance of each of the 

 leads. The second of these quantities comes out in agree- 

 ment with Lord Rayleigb/s formula, as was to be expected. 



* Communicated by the Author. 



f " On some cases of Propagation of Electric Oscillations along a 

 number of Parallel Wires/' Phil. Mag. [5] vol. 1. p. 605. The following 

 corrections have to be made in this paper : — 



Ln formula (2), value of k 2 , n is omitted in the numerator. 



In formula (81), the factor a should be inserted in the numerator of 



2 



the expression following the first ' log,' and a n in that following the 

 second. The value of the quantity called l y ' is~ — 



