the High-Tension Magneto. 285 



than in the indnction-coil, and the lamination of the iron is 

 in general much less complete, it is possible that a source 

 of error which is inappreciable in one instrument might be- 

 very serious in the other. Prof. Jones's experiments on the 

 magneto are hardly sufficient to indicate how far the theory 

 may be employed in the design of the magneto ; for the 

 methods of determining the periods of the oscillations set up 

 in the circuits which he had developed in his work on the 

 induction-coil were much less well suited to the more rapid 

 and more highly damped oscillations of the magneto. It was 

 thought that experimental methods which had already been 

 developed for other purposes would enable some of the diffi- 

 culties which Prof. Jones had encountered to be overcome, 

 and accordingly an attempt was made by the use of these 

 methods to investigate more nearly the applicability of the 

 theory to the magneto. 



Theory of the Experiments. 



2. The general principles of the investigation were the 

 same as those of Prof. Jones's work on the induction-coil, 

 but in order to indicate clearly the bearing of the expe- 

 riments which were made, it will be convenient to transform 

 slightly some of the equations given by Prof. Jones. 

 Adopting his notation with slight modifications, we shall 

 write: — 



Li, C 1? R x the self-inductance, capacity, and resistance of 

 the primary circuit; L 2 , C 2 , R 2 the corresponding quantities 

 for the secondary circuit. 



L 2 i, L 12 the two mutual inductances, which become equal 

 when the current is uniform throughout the secondary. 



P the coupling; s= (L 2 -f- L 2l 4- L 12 + Li)/L 2 , c=(l — P)/s. 

 (Prof. Jones puts c = l — P). 



The values which L 2 , k, c, s assume when a condenser 

 of large capacity is inserted in the secondary, so that the 

 current in it becomes uniform, will be denoted by L 2 ', k\ c , s'. 



TY^a-LA, T 2 2 =4tt 5 L 2 C 2 , N^l/T,, N 2 = l/T ? ; 



t, t' the periods of the two components of the oscillation, 

 t being greater than t'; ?i = 1/t, n' = l/T'. 



r = n'/n i; u = T 1 2 /T 2 2 . 



X, \' the damping coefficients of the two components of the 

 oscillation; and //, = A,t, fjb' = \'r / , their logarithmic decrements. 



Then from Prof. Jones's pnper it is easy to show that 



T 2 + T '2 =Tl 2 +T 2 2 (1) 



n 2 + n /2 = - (N! 2 + N 2 2 ) (2) 



Phil. Mag. S. 6. Vol. 37. No. 219. March 1919. X 



