514 Mr. E. C. Rimington on Luminous 



and they are both very small angles, hence y = 2?7 approxi- 

 mately, or EF = 2AB. 

 When bt = 7r—y, 



dt h 



_ e KE3 



or if the oscillations are very rapid 



dc V - e? w? 



_ — _ *> 2 V T, 



If, however, £ = 0, 



d£ L 



dc __ V 

 d* ~ L' 



so that the greatest rate of change of current occurs at the 

 first instant of discharge, although this is not a mathematical 

 maximum. 



Equation (4) may also be written 



dc V sJa 2 4- b 2 , 



dt=- T- ""^^ • • • (5) 



?; being the same angle as before. 



It is now necessary to consider the values of the P.D. 

 between the outside coatings A and B of the Leyden jars. 



Let I and r be the inductance and resistance of the coil 

 connected to the outer coatings, and L and R the same for 

 the whole circuit. Let v l — v 2 = x be the P.D. between the 

 outer coatings at any instant t. Then 



V 



c=r rr e at sin bt. 

 oh ' 



and , -.dc 



x = v l — v 2 =cr + l-j- , 



y 



.-. # = -Y e at {{r + la) sin bt + lb cos bt} 



bh 



= %£*' VW + (r + /a) 2 cos(Jt-i/) . • (6) 

 where r , 



i + a 



tan rf — — j 



rf will be in general a small angle not very different from t\ ; 



