Popular Science Monthly 



465 



this, or 0.000373 henry. One micro- 

 farad is one-milHonth of a farad ; hence 

 the capacity in farads is one-milHonth of 

 0.0012 microfarad, or 0.0000000012 fa- 

 rad. Taking up the rule for compuHng 

 the time period, the first step is to mul- 

 tiply the capacity in farads by the in- 

 ductance in henrvs (0.0000000012 times 

 0.000373 = O.OOOObOOOOOOO-147 ) . The sec- 

 ond step is to take the square root of 

 this number, which is found to be 

 0.000000669. The third step is to mul- 

 tiply this by 6.28, which gives 0.0000042 

 second as the time period. Thus it ap- 

 pears that the alternating current passes 

 through a complete cycle in only 42 ten- 

 millionths of one second, and that the 

 frequency (which is the reciprocal of 

 this) is a little over 236,000 cycles per 

 second. This agrees with the result se- 

 cured from the first calculation above. 



If several other sets of capacity and 

 inductance values 



are worked out by i r 



both the above J 



rules, the same 

 agreement will be 

 found. It thus be- 

 comes clear that ^'^- ^- ^^"P'^^ 

 the resonant fre- 

 quency at which any conden .e* -circuit 

 will oscillate most strongly, i^ practi- 

 cally identical with the frequency of the 

 free alternating current which will be 

 produced if that circuit is ^tt into vibra- 

 tion by a sudden discharge within itself. 

 Referring to Fig. 1, if the capacity of the 

 antenna is charged by a gradually rising 

 voltage supplied from the secondary of 

 a transformer through terminals T, T, a 

 j)oint will be reached beyond which no 

 energy can be forced in, because the air 

 between the spark-balls at 6" will break 

 down. The spark which then occurs 

 completes the oscillating circuit from the 

 earth E through the inductance L to the 

 antenna A, and the stored electrical en- 

 ergy rushes to the ground. By the over- 

 shooting action which alwa)'s takes place, 

 if the circuit resistance is not too great, 

 the current surges back and forth. The 

 frequency of the alternations thus pro- 

 duced is that which may be computed as 

 in the paragraph above. This frequency 

 is practically the same as that which 

 would produce the greatest current in 

 the antemia, if the transfomier were dis- 



connected and the spark-gap replaced by 

 a '^igh-frequency alternator in such a 

 way that the total inductance and ca- 

 pacity remained the same. 



An entirely similar condition exists for 

 the closed circuit of Fig. 2. Here a con- 

 denser C, a spark-gap S, an inductance 

 L and a resistance R are connected in 

 series. The terminals of a high voltage 

 transformer, to charge the condenser, 

 are connected at T, T. If the potential 

 applied across the condenser is gradually 

 increased, a charge will be stored in it 

 by virtue of its electrical capacity. When 

 the voltage becomes so high that the 

 spark-gap breaks down and a spark 

 passes, the con- 

 denser discharges 

 through the induc- 

 tance and resis- 

 tance. If the re- 

 sistance is not too 

 high, the discharge 

 will be oscillatory, 

 and the frequency 

 of the oscillations 

 (and their time - 

 period)canbecalcu- 

 "lated according to 

 the three steps of the same rule given 

 for antennas. Thus the number of 

 cycles per second of the free alternat- 

 ing-current discharge in the circuit can 

 be found, if its inductance and capacity 

 are known. The wavelength which 

 would be set up by currents of this fre- 

 quency may also be determined easily, 

 as has been shown. 



If the transformer is disconnected and 

 a high-frequency alternator substituted 

 for the spark-gap, the circuit will have 

 in it forced alternating currents of the 

 frequency at which the alternator gene- 

 rates. As was shown in January, the 

 greatest current will flow when the fre- 

 quency of minimum impedance (or zero 

 reactance) is reached. This is the re- 

 sonant frequency and has practically the 

 .same numerical value as that of the free 

 oscillations discussed in the paragraph 

 immediately preceding. 



The foregoing descriptions should 

 give a clear indication of the difference 

 between free and forced alternating cur- 

 rents in oscillation-circuits. If a sus- 

 tained, alternating voltage is applied to 



