542 Dr. W. F. G. Swarm on the Pulse 



whole X-ray tube emits about 10 6 ergs per second*, in order 

 that a shall correspond to the area of a hemisphere of sav 



20 cm. radius, we must, if y = 6 x 10 9 have — =10 10 . The 



number r might possibly, though not necessarily, be asso- 

 ciated with the frequency of oscillation in the discharge-tube, 

 so that if it is of the order 100 we have s = 10 12 . The s pulses 

 would take at least 10 ~ 7 second to pass an electron, and this 

 of course introduces the difficulty that during this time the 

 electron would suffer many collisions, and even if this were 

 not so, it would travel several metres while the pulses were 

 passing over it. 



Of course, the above is extremely speculative, and my 

 object in bringing it forward is not to suggest it as a theory 

 (indeed, I do not believe that it is the explanation of the 

 phenomenon at all), but rather to examine what can be done 

 in the way of explaining the origin of the /3 rays as arising 

 from the free electrons between the molecules. The main 

 points so far may thus be summarized as follows : — 



(a) It" the electrons are ejected by the pulses with velocities 

 of the order 6 X 10 9 they will certainly show a want of 

 symmetry, both in velocity and number, approaching the 

 amount experimentally found. 



(U) The energy required to eject the electrons with the 

 necessary velocity seems at first sight to be enormous, or 

 rather the energy-density appears to be enormous, so that it 

 would appear necessary to concentrate the energy iu thin 

 filaments in order to obtain a large energy-density in places 

 without a lar.Je total quantity. On examining the matter 

 more closely, however, it is found that the concentration of 

 the energy becomes no longer necessary when we imagine 

 the radiation to take place in a large series of pulses. Under 

 these conditions, even on the assumption of spherical pulses, 

 the velocities produced in the electrons are quite consistent 

 with the radiation of a reasonably small amount of energy 

 from the X-ray bulb, but difficulties are encountered in 

 this case owing to the movement of the electron during 

 the comparatively long time in which it is receiving its 

 velocity. The want of symmetry is just as pronounced 

 as if the velocity had been produced by a single pulse, 

 since, in the case of a free electron, no matter how y is 

 produced, so long as it is produced by electromagnetic 



waves we always have x= <r- y 2 . The concentration of the 

 * Rutherford and McClung-, Phil. Trans. A. vol. cxcvi. p. 25 (1901). 



