

Discharges in Electrodeless Vacuum- Tubes. 511 



is connected to D, as the strongest field is between b and D, 

 where the P.D. is greatest, it does not pass through the bulb ; 

 in fact the field in the bulb will simply be that due to the P.D. 

 between a and b, or the same as it is if the wires e and / are 

 disconnected. The results of Experiments 2, 3, 4, and 5 are 

 also obviously explained by this theory. 



To treat the subject mathematically. We have the well- 

 known equations for the discharge of a condenser : 



L — + Re = — y? ? where K is the capacity, 

 and _ dq 



Combining these, 



df 2 + Tdt + KL? : 



€ ~df 



d?q Bdq 1 



To obtain an oscillatory discharge 4L must be greater than 

 Putting a for — ^T and b for \/ _ _ 2 the solution 



19 



g = Qe<* ^ a2 + b \in(bt + 0), . . . (1) 

 b 



where 0=tan- J ( J and Q is the initial charge. 



This may be more conveniently written 



q=Qe« t <S a* + b * cos (bt- V \ 

 b 



where 



2 6 V 4L-KR* 



If the oscillations are to be rapid, ^j- must be large compared 



t0 n? 



Therefore r] will be some small angle. 



Instead of quantity we may write P.D. of the condenser, 

 or 



v = V e " ^ ' + y o 0a (&<-i y ). ... (2) 



