492 Prof. Skinner on Conditions controlling the Drop of 



The time U elapsing between the first and second impacts 

 maybe readily obtained by combining the equation of uniformly 

 accelerated motion «*««■« 



(where .^==0%, and t 1 /2 the time required to pass over that 

 space) with that of energy, 



s 



which gives 



-[(=)■* 



m 2 ~\i 



V 2 "*" e VJ 



Likewise we obtain the interval t 2 between the second and 

 third impacts, 



between the third and fourth, 





^= 2 *[(7)v» + 7vJ*' 



and so forth. 



The time T required for the particle to come to rest at the 

 electrode is given by the infinite series 



T=f, +#,+**;+ .... 

 =Hl7)v + 7vJ {*+* 2 +* 3 + • • •}» 



which, the series for 0<&<1 being convergent and equal 

 to jig, give, 



T _ 2sk, r/m\ 2 u 2 m 2 "l ± 



i T^LW V 3+ * VJ . 



Since T must be positive, 0</c<l, and the other quantities 

 chosen positive, the quantity in brackets [ ]i must be positive. 

 Assuming this latter has a finite value we have 



for k=0, T=0, 



and for k = l, T=cc, 



as we should expect — there being no elastic reaction, the 

 particle by first impact sticks to the electrode, while, on the 



