304 Prof. W. B. Morton on the 



Write the common periodic factor in the form e i{ - mz ~ vt) r 

 then ??i= — -\-i/c, where X is the wave-length and k the 



A. 



attenuation-constant. 



^-v-x ' (2) 



where X is the wave-length for the same frequency in free 

 space, Y the velocity of radiation, 



h={1 + l)X /^, ..... (3 > 



'-v— ,;a © , -(r +fa ) t -- • • w 



Then the equations are satisfied by the following scheme, 

 omitting the periodic factor. 



Inside. Outside. 



Z... rfJo(V), DK„(«-) >, 



B -d-^-Uhr), -D^K.Cc,) I _ (5) 



H - d }k Hh r), -D|L Kl(cr) ! 



The J's and K's are the cylinder functions, vanishing for 

 zero and infinite arguments respectively, d and D are con- 

 stants. The argument of the J's should strictly be ^k 2 2 — m*. r, 

 but, as Thomson and Sommerfeld have shown, m is in actual 

 cases negligible in comparison with h 2 . Further,, c is a very 

 small quantity, so we can put for the K's the approximate 

 values 



where y is Euler's constant 1*781. 2 



In the case of two icires at distance b apart, if 7^ can be 



neglected in comparison with unity, then, as I have shown 

 in a former paper *, the state of affairs inside each wire is 

 unaltered, and, outside, we get the approximate values by 

 superposing two single wire solutions. 



* Phil. Mag. I. p. 605. Wrong signs appear in the values given for 

 m, k 2 , R, and H in this paper, but the results arrived at are not affected.: 



