Self-induction of Wires. 199 



of the core, of length 1, the same as that of the coil, n/2?r the 

 frequency, c the core's radius, and IN" the number of turns of 

 wire in the coil per unit length ; whilst 



L 1 =(2ttNc)V 



is that part of the steady inductance of the coil circuit which 

 is contributed by the core. 



The full expression for the increased resistance due to the 

 dissipation of energy in the core is to be got by multiplying 

 the above Ex by Y, which is given by * 



1 + O 2 V 1 + 2.10.12 2 K 1 + 3.14.16 2 ( * + 4.18.20 2 V 1 + ' ' ' 



1+ 2^ 2 ( 1+ %£& ( 1+ 3l032 2 ( 1 + 4.14.16 2 ( 1 + '-- 



where y = (ATr/ikne 2 ) 2 . The value of E' is therefore R + RjY. 

 The series being convergent, the formula is generally appli- 

 cable. The law of the coefficients is obvious. I have slightly 

 changed the arrangement of the figures in the original to show 

 it. We may easily make the core-heat a large multiple of the 

 coil-heat, especially in the case of iron, in which the induced 

 currents are so strong. When y is small enough, we may 

 use the series obtained by division of the numerator by the 

 denominator in (49c), which is 



16.24^ 15.16 3 .9 {0Uc) 



Corresponding to this, I find from my investigation f of 

 the phase- difference, that the decrease of the effective induc- 

 tance from the steady value is expressed by 



v&-ii?fa+SK + --.v> • • ■ < 5 "> 



When the same core is used as a wire with current longi- 

 tudinal, and again as core in a solenoid with induction longi- 

 tudinal, the effects are thus connected. Let L x be the above 

 steady inductance of the coil so far as is due to the core, and 

 L'x its value at frequency n/27r, when it also adds resistance 

 ~R\ to the coil. Also let R 2 be the steady resistance of the 

 same when used as a wire, and R' 2 and L' 2 its resistance and 

 inductance at frequency n/Zir, the latter being what \[i then 



* f Electrician/ Mav 10, 1884 p. 606. 

 t Ibid. May 14, 1884, p. 103. 



,(49c) 



