Mr Campbell, The study of discontinuous phenomena. 125 



Since /(?'t) is a continuous function of r, we may, with certain 

 reservations to be considered later, replace the summations by 

 integrations. Putting t = dt we find 



-tre'T=d^T = N' r^dt f(t) [*~^dtf{t) + N\'' dtf'it)... (15), 

 V J «=o J t = o J t=^0 



or, remembering that 



(16). 



I 7. 6t is the deflection of the needle from its zero position, 

 but it will be found more convenient to express (16) in terms of 

 the deflections of the needle from its mean position 6j- If ^'t 

 denote the deflection from this mean position 



6^T=[{eT) + o'TY • an 



or since X6't=0 



WT=(dTY+0''^T (18). 



But, by an argument precisely similar to that given above, it can 

 be shown that 



Hence 



-(M-f) (-)• 



-s^ „ (A' P P^ 1AB , 2BP , 2PA\ ,„., 



We have found a relation between the unknown N (the number 

 of particles emitted per second) and the quantities 6''^t, -^i P, P, 

 a, y8, p, which are known, except so far as the charge E is 

 concerned. PJ may be eliminated by the device of Meyer and 

 Regener, who, by the use of their compensation method, measured 



not ^'V but (=1 = A^ The formula applicable to their experi- 



ments is 



^2 ^ p2 2AB IBP 2PA 



., 1 2^'^2^'^2p'^ a + /3'^ ^+p\ + a 



" =^- MTfT^y '''^- 



\a /3 pi 



Since £^ is a factor of J., jB, and P, it disappears in the ratio 

 on the right hand of (21). 



