644 Prof. Morton on Speed of Propagation and 



papers* in this Journal, and proceed to investigate the rela- 

 tion between the real and imaginary parts for the limiting 



cases in which a\ / t-L has a very small or very large value. 

 V p 



The results are shown graphically, not only for these extreme 



cases, but also for intermediate values of the quantity ax/W 



V p ' 



The plotting of the complete curve is rendered possible by the 



use of Aldis's tables f of the functions J (# *Ji) and J x (a? \/i). 



In this case 



V P ■ 



The speed of the waves along the wires will be expressed as 

 a fraction of V, the speed of free radiation. For a measure 

 of the attenuation it will be found convenient to take, instead 



tcV tck 



of k, the quantity — - or ^-^-, where \ is the wave-length 



in free space. For good-conducting wires X is practically 

 equal to X, and our measure of attenuation is then the 

 logarithmic decrement of amplitude corresponding to a dis- 

 tance jr- along the wires. For cases of rapid attenuation 



when X is no longer nearly equal to X, we may suppose that 

 the frequency is kept constant, and that the alteration in the 

 state of atfairs is brought about by changing the properties 

 of the leads. 2 



For two wires at distance b, we have J, if ^ can be neglected, 



• • (i) 



and 



p- 



j — m 2 = 



VW 



-y 2 

 = 1- 



J U' Vz) 





\ : 



J (^ \/i) 



Wi 





f 



log-Ji(*i/f) . 



x sj l 



= I + UY 



Ym V/2tt 

 p\X 



Y + i* 



v p 



where v is the speed of the waves along the wires. 



* Phil. Mag. vol. 1. p. 605 (1900) ; i. p. 563 (1901). 

 t Aldis, Proc. Roy. Soc. vol. lxvi. pp. 42, 43 (1899). 

 t Phil. Mag. vol. 1. p. 610, equation (12). 



