approximately the Self-induction of a Coil. 227 



It is evident that if for any coil whatever we calculate ^ 

 on the assumption that there is no space occupied by insula- 

 tion, we have only to multiply this by =— ^ to obtain r— } taking 



W 2 -ti 



taking insulation into account. Another way of putting our 

 result is 



L_ V'-=-1000 m 



where V' is the volume, in centimetres, of copper in the coil. 

 For a coil of given volume wound with given wire, to dimi- 

 nish the ratio of ^, increasing c is nearly of the same import- 

 ance as increasing b ; whereas these are about twice as im- 

 portant as increasing a. In fact ^ is nearly proportional to 



7m ri and of course it is less as the wire is finer, 



a + 2{b + c)' ' 



because the volume of the insulation is relatively greater. 

 It may be noted that the empirical formula given in this 



b c 



paper, although seemingly truer when - and - are smaller, 



o c 



is not true when - and - are zero. The inductance of one 

 a a 



spire of wire whose section is infinitely small is infinite ; and 



it would have been possible to get an empirical formula, fairly 



correct for ordinary values of a, b, and c, which w ould give 



b c 



an infinite value for L when - and - are zero, based on the 



a a 



expression given by Maxwell, 

 L 



--KF-0 



where R is a function of b and c. Such a formula would, 

 however, be much less useful for ordinary purposes than the 

 one I have given. 



