Self-induction of Wires. 137 



which make, if /=y* 



M 2 + N 2 = J (/^)Jo(/v / -0 = ^ 2 727r/ 7 ^ 



M /2 + N /2 = /e^V2^, \ . (44) 



MM' + NN' = ef^/27rr\/2. 



In the extreme, very high speed, or large retardation, or 

 both combined, making y very great, the amplitude of the 

 wire current C tends to be represented by 



e/L ln; (45) 



showing that the current is stronger than according to the 

 linear theory, and far stronger in the case of an iron wire, or 

 very close return. 



The amplitude of the current-density at the axis, under the 

 same circumstances, 



%E. ( 27m< * V 



Jl7ra^Jj cti \fefS* 



y, • . • . («) 



which is of course excessively small. On the other hand, the 

 boundary current-density amplitude is 



'RTra*Lo(4:7rp 1 k 1 n)i L Z% \ ^n ) ' 



which may be greater than the linear-theory amplitude. 



Analogous to this, the amplitude of the current in a coil 

 due to a S.H. impressed force in the coil-circuit is greatly 

 increased by allowing dissipation of energy by conduction in 

 a core placed in the coil, when the corresponding y is great, 

 a large core, high inductivity, &c. ; that is, the inertia or 

 retarding-power of the electromagnet is greatly reduced, so 

 far as the coil-current is concerned. This is, in a great mea- 

 sure, done away with by dividing the core to stop the electric 

 currents, when the linear theory is approximated to. 



If z/ = 1600, the axial is about one fourteenth of the boun- 

 dary-current amplitude. To get this in a thick copper wire 

 of 1 centim. radius, a speed of about 850 waves per second 

 would be required. But in an iron rod of the same size, if 

 we take ^ = 500, only about 8J waves per second would suffice. 



Returning to the former expressions, if we go only as far as 

 n 6 , the amplitude C of the wire current is given by C = efBf'l ; 

 where the square of W, which is the apparent resistance, or 

 the impedance, per unit length of wire, is given by 



