The Effect of the Spark on the Oscillations of an Electric Circuit

The Thompson or "logarithmic decrement" theory of oscillatory circuits is contrasted with the linear decrement theory. Both are limiting cases of the more general theory which considers circuits containing both conductor and spark resistance. It is this last and most general theory which is fully developed in the present paper. It is found that the effect of the spark is to introduce a simple harmonic counter E. M. F. of constant amplitude during the oscillations and having the same frequency as these oscillations. The mathematical expressions for the current and voltage, under practical working conditions, are found to be simple, and to reduce to the older expressions in the limiting cases. The new theory gives the value of the spark resistance at any time and determines the quenching time. A new resonance analysis method of studying the law governing the dependence of spark or arc resistance on current is given. A novel method of producing "quenching" in gaps is the following. There are shunted around the gaps several circuits of different frequencies so proportioned that the total current remains appreciably zero for a considerable portion of each cycle (of the fundamental frequency). The practical applications of this method to radio telegraphy are described in detail. Finally, a parallel spark gap method for obtaining oscillations of any desired phase difference is given.