454 Mr. W. E. Sumpner on the Variation 



force passing through the coil, T is its kinetic energy, and L 

 its coefficient of self-induction. 



2. If the magnetic medium is air, L 1? L 2 , and L 3 are identical. 

 If the medium be wholly or partially composed of iron, this is 

 no longer the case. The values of L differ from each other, 

 and vary with C. The value of h l can easily be found in 

 terms of L 2 from the equation 



L 1 = L 2 +C-7T7, 



which is an immediate consequence of the first two equations 

 of definition. 



We see that L X = L 2 only when C=0 or when -yp=0, 



and that L, is greater than L 2 for small currents where L 2 is 

 increasing with C. 



Since .£), the magnetizing force, is proportional to C ; and 

 since N is a measure of 33, the average value of the flux of 

 induction per unit area, w T e see that L 2 is directly propor- 

 tional to fju, the average value of the coefficient of magnetic 

 permeability for the magnetizing force represented by the 

 current C. 



If, therefore, the medium be wholly of one kind, L 2 will be 

 a measure of the permeability of that medium. In any case, 

 however, if we know the relation connecting 33 with .£>, we 

 shall be able to determine the way in which the coefficients 

 vary with the magnetizing force. 



If OPKP' (see fig. 1) be the curve connecting 33 with $ 

 (or N with C), the value of L 2 for any point P, on it corre- 

 sponding with the current O0 r and the flux of induction ONj 

 will be represented by the tangent of the angle which the 

 line OPi makes with the line OC^ 



Since 



T dC_ _ d{L 2 Q) _ rfN 

 iJl dt ~ e ~ dt ~ ~dt' 

 we have 



T _rfN d¥> 



and L x will consequently be represented by the tangent of the 

 angle PiQiC^ which the tangent to the curve at P, makes with 

 the line OOp 

 Moreover, 



afCWN f^33 

 L 3 = ^- a J 



