the Induction- Coil. 707 



General Description of the Method. 



In a former communication one of us * arrived at the 

 following expression for the difference of potential at the 

 terminals of the secondary of an induction-coil at any time 

 t seconds after a current i is interrupted in the primary : — 



2V- m ° T ~®\*^~ p hj* x\ 



t /0,4-G., , o\ 



m; t' ~^\r^ + n .ft s ,\ n > 



"(T^T^o^* sm^-SJ, . . (1) 



where M is the mutual inductance of the primary and 

 secondary coils, 



l/27rT and 1j2ttT' are the frequencies of the two oscillations 

 calculated from the well-known expression for coupled circuits 



8 2 2_ _i_ r x x / ft x x v 4P n 



n ~ 1 -*■ La + LA ± V 1 U A " LA/ + LALA / J ' 



, _ • • • • ( 2 ) 



k being the coupling coefficient M/ V /L 1 L 2 . 



The quantity /?, and the phase-angles S, 8', are to he 

 calculated from the constants of the circuits as described in 

 the former pnper above referred to. R L , K 2 , (-'is C! 2 , L x , L 2 are 

 the primary and secondary resistances, capacities, and self- 

 inductances. 



In the paper referred to the above expression (1) was 

 worked out for an air-core induction-coil with various 

 condensers in the primary and secondary circuits, and the 

 curve of secondary potential plotted from the results. The 

 curve was also obtained photographically in each ca&e by 

 means of an electrostatic oscillograph, and was found to 

 agree closely in its general form with the curve calculated 

 from (1). The differences were mainly in the damping 

 factors, and these discrepances probably arose from losses 

 in the primary condensers". 



Strictly speaking, the expression (1) is not applicable to a 

 coil with an iron core, owing to the variable permeability of 

 iron ; all that can be expected is that suitable mean values 



* E. T. Jones, Phil. Mag-. January 1909, p. 28. This expression for 

 the secondary potential was obtained by an application of Urude's 

 1 Theory of the Oscillation Transformer," Ann. der Physik, xiii. p. 512, 

 1904. 



