Induction" Coil Potentials. 



575 



Y] is the difference of potential at the terminals of the 

 primary condenser which, for the reasons stated above, was 

 connected directly across the primary coil. 



The expression for Y 2 was accordingly worked out afresh 

 for these new initial conditions, and the results show that 

 the values of 8 L and 8 2 are considerably modified by the 

 change in the conditions. The expressions arrived at are 



tan 8 



, = 2n h J2/3 



n£±n£ 



2 2 



n 2 — H]f 



[9,-29, 



■'«)}. 



tan 8 2 = — . tan 81. 



These reduce to the expressions used in the former papers if 

 $i is made equal to # , «, £. B^ to R . 



In arriving at the above expressions the squares and 

 product of 0i, 6 2 are neglected. The fuller expressions for 

 tan£ p tan 8 2 , including these second order terms, were also, 

 however, worked out for each of the three cases, and found 

 to give values not differing greatly from those calculated 

 from the above formulae. The difference in 8 1 was in each 

 case quite negligible, and in 8 2 less than 1° except in 

 Case II., where it amounted to 2°'5. The values of 8 l9 8 2 

 given in Table Y. are those given by the more exact formulae. 

 This table contains the values of the eight constants of the 

 formula (1) for each of the three cases, the amplitudes being 

 given in volts for i = 10 amperes. 



Table Y. 





n x . 



» 2 . 



A r 



A 2 . 



*,. 



k 2 . 



*!• 



d. 2 . 



Case I 



Case II 



Caselll. ... 



1943 

 2328 

 304-4 



1063 

 1102 

 1224 



258000 

 314G00 

 416500 



49420 



75270 



105400 



58 

 120 

 965 



728 

 1130 

 1210 



-3°-5 

 -7°-l 

 -3°-03 



-17°'7 

 -28°-8 

 -ll ? -4 



Values of the secondary potential were calculated from 

 these by (1) for various values of t, squared (for comparison 

 with the photographic curves), and plotted over one period 

 of the slower oscillation. The curves are shown in figs. 1, 2, 

 and 3, the maximum potentials indicated being in the three 

 cases 238700, 291400, and 419000 volts respectively. 



2Q2 



