256 Dr. J. W. Nicholson on the 



first and second wires respectively. If the first wire were 

 not disturbed by the presence of the second, the electric and 



magnetic vectors would be derivable from a vector potential 

 H parallel to the axis, independent o£ 0, and proportional to 

 a time factor e l ?\ if 2ir/p be the frequency of alternation. 



The electric force in the general case is axial, and will be 

 denoted by R. There is no axial magnetic component. Let 

 the magnetic components radial and .transversal with respect 

 to an origin in the axis of the first wire be (a'fi'). 



Then in a medium of permeability p, 



, 1 9H l BH 



a= ^-w p-'^- ■ ■ - • (2) 



All vectors are independent of z. The current is parallel to 

 the axis, and of magnitude 



IV 



1 fb , ok ^ a "\ 



1 r^H 1BH 1 yH-) 

 ~ 4*^1 3r* + r -dr + r 2 M A J ' 



If the medium have specific inductive capacity K, and 

 specific resistance a, 



r + 4:7T I 



1 iKp 



W ~ a + 4tt 3* 



-e + ^)» 



for the periodic vibration. 



Moreover, so far as inductive action is concerned, 



*=-!?' ( 3 > 



and thus, H being entirely due to inductive agency, 



■dm i9H u 2 h . ri tK P -\ n A ,,. 



■^-s +- ^- + -0-S7T2-— 4:77 /U/^ -+ --£ ^H = 0. (4) 



3r 2T r ^r r 2 dfl 2 ri \_a ^ 47r J w 



