68 Mr. W. BvMell [Feb. 21, 



where ¥ is the caj^acity of the condenser or Leyden jar and L is 

 the self-induction of the circuit. So that the frequency of the oscil- 

 lations, or the number of complete swings which can take place in one 

 second, is the reciprocal of the above or 



Frequency = 



2 7r VL.F. 



Such a circuit in which the discharge of the condenser is oscillatory 

 I will refer to, in what follows, as an oscillatory circuit, and the 

 above periodic time as the periodic time of the circuit. 



If an unstable arc is made to form part of an oscillatory circuit 

 then any oscillations in this circuit, instead of dying away as they 

 would do were the arc not present, will persist indefinitely forming 

 an alternating current, the energy required being automatically con- 

 verted by the unstable arc into a suitable form to maintain 

 them. 



The electrical instability that is necessary for this purpose, is 



that if the current A through the arc be increased by any small 



quantity 8 A then the potential difference V between its terminals 



^ V 

 must decrease by an amount S V so that the ratio ___will be a nega- 



o A 



tive quantity. Messrs. Frith and Rodgers * determined the value of 



8 V 

 the ratio ^-r for a large number of arcs between carbon electrodes, 



and they found that whereas the ratio is always iiositive when both 

 cored carbons are used, it is negative for solid carbons. 



If a perfectly steady current direct arc between solid carbon elec- 

 trodes be shunted with an oscillatory circuit consisting of a suitable 

 condenser and self-induction in series, then alternating currents of 

 constant amplitude will be maintained in the circuit composed of the 

 condenser, the self-induction and the arc, these alternating currents 

 will cause the current through the arc to vary, and the arc will give 

 out a musical note. I have therefore called it the Musical Arc. This 

 will not occur if an arc between cored carbons be used, because such 

 an arc has not the requisite instability, or, if the resistance of the in- 

 ductive coil and connections exceeds a certain critical value. In a 

 previous paper I have shown f that the necessary conditions in order 

 to convert direct into alternating current by means of the arc 

 are : — 



(1) ^-r , must be negative. 



8 V 



(2) — , must be numerically greater than the resistance of the 

 o A. 



* Proceedings of the Physical Society, 1896, vol. 14, p. 307. 



t Proceedings of the Institution of Electrical Engineers, 1001, vol. 30, p. 262. 



