312 Prof. W. B. Morton on the 



Write 



**=(l + *}«, so that h = A S J^ M E ) . . (19 ) 



and let y denote the distance of a point below the surface of 

 the wire or (a — r). After a little reduction we find for the 

 ^components of electric force 



7 e~ hy . (2itz , 7 \ 



^P {X J ... (20) 



-P ttV-2, e- ky . y-2-TTZ , , 7T\ i 



The attenuation constant /c is here neglected in comparison 



with — . 

 A, 



Therefore for lines of force 



. /2ttZ , 7T\ 



-Sill (_—+/«/— - 



sm(— +%) 



leading to 



htj= log sin (-^- -f% + I j + const. . . (22) 



and for lines of flow we get 



my(W+,w?)-hz(2h? + m 2 ) = hmlog {(27**4- m 2 ) sin (mz + Jiy) 

 — m 2 cos (mz + %)} + const (23) 



In tlie last equation m is written for — - . 



In fig. 3 these two families of curves are plotted for the 

 simple case m = h=l. It will be seen that all the curves of 

 either family can be got by moving one of them in a direction 

 making an angle of 45° with the negative direction of z. 



The angles marked on the diagram give the phase-angles 

 of the lengthwise electric force. The magnetic force being 

 45° in advance of the lengthwise electric vanishes at all 

 points of the straight line of electric force which meets the 

 -surface at 135°. The flow of energy is therefore oppositely 

 directed on the two sides of this line, as shown by the arrows 

 on the lines of flow. An inspection of the figure shows that 

 the flow of energy at the surface is backward and inward 

 from 0° to 45°, forward and inward from 45° to 135°, and 

 -backward and outward from 135° to 180°, agreeing with 



