Rays of Positice Electricity. 245 



difference not smaller than the' value just found, this gives 

 a minimum value for the potential difference required to 

 produce the secondary radiation. There will, however, be a 

 maximum as well as a minimum value, for the uncharged 

 Canalstrahlen are produced by the combination of a posi- 

 tively charged particle and a negatively charged corpuscle, 

 and in consequence of the small mass of the corpuscle the 

 velocity of the uncharged system will practically be that of 

 the positively charged particle before it combined with the 

 corpuscle. If, however, the velocity of the particle exceeded 

 a certain limit, it could not combine with a corpuscle even 

 though it passed quite close to it, its velocity would be 

 sufficient to cany it far away from the corpuscle, and it 

 would not retain it as a satellite. If A and B represent 

 respectively the particle and the corpuscle, then if when 

 they are at a distance r apart their relative velocity is v, they 



will separate to an infinite distance of v 2 >2.~ -, where 



m r 



e is the charge in electrostatic measure and m the mass of a 

 corpuscle. Even with the smallest admissible value of r a 

 corpuscle would acquire a velocity great enough to satisfy 

 the preceding inequality by the fall through a potential 

 difference of two or three volts ; hence it is only exceedingly 

 close to the cathode, perhaps only inside the hole through 

 which the rays pass, that the corpuscles are still enough to 

 allow of any combination with a positive particle to take 

 place. Let us take as the case most favourable to recombi- 

 nation the one where the corpuscles are at rest and the 

 relative motion is entirely due to the positive particles, then 

 if v is the velocity of the positive particle for combination 



to take place, v 2 <2.~ .-. The smallest value of r nermis- 

 i m r r 



sible will depend upon the size of the particle : it will be of 

 atomic dimensions. Let it equal b x 10~" 8 cm. 



Putting e/m=l'7 x 10 7 x 3 x 10 10 , e = ±'5 x 10" 1 



we find u 2 <^- 6 xl0 16 . 



o 



If the velocity is due to the fall of the charged body through 

 V volts, then if to is the electric atomic weight of the 

 particle, the preceding relation is equivalent to 



i?<2-3rxl0\ 



b 



