generated in a High-tension Magneto. 

 Hence the solutions for Y 2 and V x are 



151 



V,= 



A, 



A-i — A,< 



sin (2irnit + $i) 



\i — X< 



sm(27Ttt 2 £ + S 2 ), (22) 



V x = r^-sin(27rM + S 1 )--^-sin (2W + S 2 ). (23) 



A-2 — Aj A^ — A-i 



The coefficients A l5 A 2 , and the phase angles 8 ly S 2 , are to 

 be determined from the initial conditions. These express 

 that at the moment of break 



(1) the P.D. of the plates of the condenser is zero, 



(2) the potential at the free secondary terminal is ^E, 



(3) the current in the primary coil is i Q , 



(4) the current entering the secondary coil at J is zero. 



The last depends of course upon the assumption already 

 made, that during the period considered the E.M.F. due 

 to the rotation may, owing to its comparative smallness and 

 slow rate of variation, be regarded as constant. 



dVJ dVJ 



Thus, at t=0, V^O, Y 2 ' = qE, 0*1*-=%^ a 



in terms of Vi and V 2 , 



dt 



0, or, 



V x = -E, ' 









Yi=-E, 









dY 1 i . 

 dt IV J 







~^ 2 =0. 1 

 dt J 







Substituting in (21) we find 







A 1 sinS 1 = -E(l + A!), 



1 





A 2 sinS 2 = — E(l+\ 2 ), 

 27rn 1 A l cos Si = io/Ci, 



1 

 | 



• • 



27rn 2 A 2 cos B 2 = i /Ci. 



1 



J 





Consequently, 







^-s6s?+-»ci+^ 







f 2 



A 2 — ° I "R 2 



(i+x 2 ) 2 







(24) 



(25) 



