﻿Effective Adjustment of an Induction- Coil. 11 



peaked at the summits, and more flattened at the zeroes, 

 than the calculated carve, which indicates that the calcu- 

 lated damping factor of the shorter wave is rather too great 

 in comparison with that of the slower oscillation. This may 

 possibly be due to the existence of an appreciable difference 

 (arising from various causes) between the values of the- 

 effective resistances of the circuits when oscillating sepa- 

 rately, and their values when the circuits are oscillating as a 

 coupled system. 



Turning now to the primary circuit, Dibbern's formula 

 allows the potential wave in the primary condenser to be 

 calculated *. Using the values given above for the con- 

 stants of the circuits, and taking i , the primary current 

 interrupted, as 10 amperes, Dibbern's expression becomes in 

 the present case 



V l f - - 5020 e" 266 * sin (149000 1 + 8'02)° 



- 4940 e~ lU0t sin (435000? -9-07)°, . . (4) 



where Y x is the primary potential in volts. 



The amplitudes of the two oscillations in the primary 

 circuit are thus nearly equal, as required by condition (2). 



The two oscillations represented by (4) are shown in 

 fig. 5 (A), the result of their superposition in fig. 5 (B). It 

 will be seen that the negative potential J of the primary con- 

 denser reaches a maximum of 6800 volts at about '00025 sec, 

 and a minimum of 2250 volts at about '00005 sec. after the 

 interruption. Thus, at the moment at which the secondary 

 potential reaches its greatest value the primary condenser, 

 instead of being uncharged as would be the c;ise in an ideal 

 induction-coil, is still charged to about 2250 volts, and this 

 is due almost entirely to the difference in the damping factors 

 of the two oscillations. 



The effective resistances of the circuits therefore act in 

 two ways in reducing the efficiency of the arrangement. 

 First, they give rise to dissipation of energy and consequent 

 decay of the amplitudes of both oscillations. Second, owing 

 to the difference between the damping factors of the two 

 oscillations, there is some energy stored in the primary con- 

 denser at the moment when the secondary potential is at its 

 maximum. 



* The existence of the two oscillations in the primary circuit after the 

 interruption is well shown by a current oscillogram taken by "Wertheim- 

 Salomonson, Physik. Zeitschr. xi. p. 539, fig-, i (1910). 



t As explained in the footnote on p. 9 above, Y L here means E+ the 

 potential of the condenser. E is here 80 volts. 



% The potential of the primary condenser is taken negative when it 

 opposes the battery E.M.F. 



