510 Transactions. — Miscellaneous. 



(1.) The spark-gap offered resistance to the discharge, and 

 energy has been dissipated in the air-space according to 

 Joule's law. 



(2.) The wires and connections of the discharge circuit 

 have also dissipated part of the energy into heat. It must be 

 remembered in this connection that the resistance of wires 

 for ley den- jar discharges is often much greater than for steady 

 currents. 



(3.) Part also has been radiated away into space as electro- 

 magnetic waves. The amount of this radiation varies greatly 

 with the type of condenser used. An ordinary leyden-jar is a 

 poor radiator, but Hertz's dumb-bell vibrator is a good radiator 

 and the oscillations are rapidly damped down. 



(4.) Part also has been absorbed in the dielectric, due to 

 molecular hysteresis in the glass. The amount of this is not 

 known with certainty, and it most probably varies greatly 

 with the kind of glass used. 



For the ordinary leyden-jar most of the energy is wasted 

 in heat in the spark-gap, and the number of complete oscil- 

 lations that occur depends almost entirely on the length of 

 spark-gap. Indirect evidence of the rapid damping-down of 

 vibrations is afforded by experiments on resonators. If the dis- 

 charge circuits of two equal condensers be exactly equal and 

 facing one another, a few feet apart, when one jar is discharged 

 oscillations are set up in the neighbouring circuit, and since 

 the periods of the two systems are the same the well-timed 

 impulses due to the vibrator will cause sparking in the 

 resonator. 



The distance to which this sparking may be detected de- 

 pends almost entirely on the length of the spark-gap in the 

 circuit of the vibrator. When the spark-gap is long, although 

 the first oscillation is very vigorous no sparks can be detected 

 in the resonator more than a few feet away. As the spark- 

 gap is shortened the oscillations of the vibrator diminish in 

 amplitude, but are more persistent on account of the lower re- 

 sistance in the spark-gap, and, as the resonator responds more 

 readily to a succession of small impulses than to one vigorous 

 impulse, sparking may be detected to a much greater distance. 

 For spark-gaps greater than j^in. in length an ordinary 

 discharge is damped down extremely rapidly, and the ampli- 

 tude of the second swing is generally less than a fifth of the 

 first. 



When a discharge occurs in currents of known inductance 

 and capacity the theoretical law of decay is known. The 

 current J at any instant t is given by 



T CV e-fi;-' • t 

 J = -PF-Pir- sin. 



(LC)J olu - (LC)i 



