Attenuation of Electric Warns along Parallel Wires. t>47 



or the curve at its lower end approximates to the form of a 

 rectangular hyperbola. 



It will be seen that in both cases log- - disappears from the 



equation, so that we get the same curve for all distances of 

 the wires apart. In other words we have, in the extreme 

 cases, a definite attenuation (as measured by the quantity f ) 

 associated with a given speed of propagation. The value of 



^ which gives a particular attenuation and speed is, at 



the upper, " skin-effect," part of the curve inversely as 



log- . In the opposite extreme region it is inversely as the 



square root of this logarithm. 



I have re-calculated the values of the speed and attenuation 



for the same values of as (01, 0*2, &c.) using - =200 and 



= 300 instead of =100. The points so found are marked 

 on the diagram with a circle and a cross respectively. It 

 will be seen that, even in the middle parts, they lie close to 



the curve drawn for - = 100. 

 a 



In former papers I have shown that a variety of more com- 

 plicated cases of propagation along a set of parallel wires 

 may be replaced, as regards attenuation and retardation of 

 the waves, by an equivalent pair of parallel wires. It would 

 seem therefore to be very generally true that — 



In syxtems which cause a given amount of retardation in the 

 speed of the ivaves, the attenuation-constant, k, is proportional 

 to the frequency ; or, there is a constant logarithmic decrement 

 in running a distance equal to the wave-length in free space 

 of oscillations of the same frequency. 



We can express in words the relations involved in equations 

 (1) and (6). The former is equivalent to 



k\ _ V-r 



27^-^^^~ , 



When the dissipation of energy in the icires is small the 



logarithmic decrement, on running the fraction ..— of a wave* 



length, is equal to the fractional decrease of the speed of pro* 

 paqation. 



2X2 



