CH. xiv.] AT HIGH SPEEDS 141 



where ki is a constant depending on the relative 

 effective strengths of the fields applied. 



In so far, therefore, as the particles which reach 

 the plate are all emitted with nearly the same velo- 

 city, the photographic trace will be an approximate 

 straight line, whose slope is a measure of that 

 velocity. 



But to get the electrochemical equivalent we must 

 also write, from the above equations, 



r y ( } 



~ 2 '' 



e~ u*~ E 



where k is another constant expressive of experi- 

 mental conditions ; so in so far as the masses of the 

 particles are all the same, the photographic trace or 

 spectrum will be a parabola. 



But at the highest speeds mfe is not a constant, 

 but a function of u, such a function as is given on 

 page 133, with u = v sin 0. 



So calling; this function = 0(- 1 = </>( -| we 



m T \vj T \v y) 



arrive at the conclusion that the actual equation to 

 the photographic curve should be 



y \o y 



with k 2 another constant. 



At the highest speeds, when u approaches v the 

 velocity of light, u cannot vary much, since it 

 is approaching a limit, and accordingly the curve 

 to be expected will be approximately a straight line ; 

 the only rapid variable will then be the mass, which is 

 getting near to its asymptotic approach to infinity, 

 and therefore varies much more rapidly than u. 



The determination consists therefore in getting as 



