Currents along a Number of Parallel Wires. 571 



9. In the case o£ the last mode o£ an even number of wires, 

 as discussed in § 6, we have the 2nd, 4th, 6th . . . wires acting as 



returns to the 1st, 3rd, 5th The inductance L can then 



be obtained directly by the method used by Maxwell (Treatise, 

 vol. ii. p. 318). Also the capacity can be found on the lines 

 followed in Heaviside's paper on the Capacity of Suspended 

 Wires (Electrical Papers, vol. i. p. 42). The analysis used 

 will be found to lead to equations similar to those used in the 

 present paper. 



10. Numerical results for a particular case. — To obtain 

 an idea of the effect produced by the variation in the mag- 

 nitude of r} on the circumstances of propagation, I have 



worked out numericallv the case of — = 100. The attenua- 

 te 



tion alone was considered. The results are shown on fig. 2, 



where the ordinates give the ratios of the attenuations 



caused by the different arrangements to that for two wires, 



the wires being supposed spaced round a circle of constant 



size. The value L was used for the inductance, applying to 



slow alternations. 



If we keep to a given mode and increase the number of 

 wires, the attenuation first increases slightly and then steadily 

 diminishes. For example, the attenuation for three wires with 

 phase-difference 120° is greater than for two wires, that for four 

 wires with difference 90° is equal to the two-wire value, that for 

 five with difference 72° is less. 



The smallest values of the attenuation are got when the 

 phase-difference is the least possible. For six wires the ratio of 

 greatest attenuation (phase-difference it) to least (phase-differ- 

 ence 60°) is about 1'3 : 0*8. For twelve wires it is 1*58 : 0*64. 



If, instead of the low-frequency limit for L, the high-fre- 

 quency limit had been used, the only difference would have 

 been a slight widening of the extreme values, leaving the 

 general form of the curves unchanged. For example, the end 

 values for twelve wires now come out 1*61 and 0*63 for the 

 6th and 1st modes respectively. 



2r 

 Increasing the ratio — has the opposite effect, bringing 



9 > 

 the values slightly closer together. For — =500 the values 



for twelve wires are 1*38 and 0*70. 



Queen's College, Belfast. 

 22nd February, 1901. 



2P2 



a 



