Forms of the Lines of Elect nc Force. 313 



(14) when?a=£=45°. In the actual case the lines of force 

 are almost' parallel to the surface. This is seen from (21) 



when we remember that h is by hypothesis very large. Ac- 

 cordingly we have to imagine the straight lines of force in 

 the diagram twisted round so as to meet the boundary at a 

 very small angle instead of at 45°. 



(b) Case of ha very small the current diffused through 

 the whole wire. Here we may put unity for J (k 2 r) aR d 

 \k 2 r for Ji(/t 2 r)- 



Further, as we have seen in § 3 ; the argument of m 

 approaches 45°, so we may write 



m= 2 £(l + i) 



So we have 



-2n~ 



Z = e~ 



-2nz 



an- 



2ttz 



.r . sin 



/ 2tTZ 7T\ 



(24) 



It is remarkable that h disappears from the expressions, or 

 iu other words, as we approach this limit the properties of 

 the wire cease to have an effect on the distribution of the 

 field inside. 



Phil Mag. S. 6. Vol. 4. No. 21. Sept. 1902. Y 



