516 Mr. E. C. Rimington on Luminous 



8 will be less than y, if ~ be nearly equal to - ; so that the 



dc 

 maximum value of x will occur after the maximum of — , 



dt' 



but the value of x will not differ very much from its maximum 



dc . 



when — is a maximum*. This bears out the results obtained 

 dt 



in experiments 1 and 2, though, of course, the electric field in 

 the bulb will be that due to the P.D. between one of the 

 plates, C or D, and the opposite side of the turn of wire, and 

 this will only be about half that between the outer coatings 

 A and B. Moreover, the phase of the potential of C will 

 not be quite the same as that of A, on account of the 

 inductance of the connecting wire e. Experiments 1 and 2 

 were, however, tried with the plates C and D, and the con- 

 necting wires removed, the turn of wire ah being moved so 

 as to bring either a or b nearest to A or to B, and the results 

 obtained were practically the same as those of experiments 

 1 and 2. 



Effect of Size of Jars. 



When different-sized Leyden jars are employed w T ith the 

 same length of spark-gap the luminous ring is more brilliant 



* The above investigation into the value of the P.D. between the 

 outer coatings will only give correctly the state of things when a steady 

 swing has been set up in the circuit; as evidently when £ = the value 

 of x also equals zero, so that x must start in phase with the current ; it 

 will, however, rapidly get out of phase with the latter, and finally be 

 nearly in quadrature with it. This is due to an initial wave starting 

 from the spark-gap which runs round the circuit. Possibly the value of 

 x can be empirically represented by one of the two subjoined formulae : — 



Yeat , 



z= -^ >J l 2 b*+{r+laf sin {{bt+^)(l-e-pt)), 



or Ye a t / 



x= -j-j- V I* l>* + (r+ la) 2 sin \bt + ^ (l-e-pt)}, 



where \f— — — 77% andp some constant. Dr. Lodge, in his researches on 



the A and B sparks, approximately represents the initial values of x by 

 the current multiplied by the impedance of the conductor r, or makes 



#= -^VW+r 2 sinta. 



The initial maximum of x will consequently roughly coincide with the 

 maximum of the current, or be near the point M, of fig. 9, and will thus 

 come about a quarter of a period before the second maximum rate of 

 change of current, point \i x (fig. 9). 





