226 Prof. J. J. Thomson on the Electrical 



Comparing this with (12) we see that 



47TV 



x a 



_b 



must be of the form e a<>, where b is a constant and inde- 

 pendent of the radiating substance. Thus a, the time occupied 

 by the collision of a corpuscle with an atom of the substance, 

 must at the same temperature, i. e. with the same average 

 velocity of the corpuscle, be the same for all substances, and 

 when the temperature varies must be inversely proportional 

 to the temperature, i. e. to the square of the average velocity 

 of the corpuscles. The measurements which have been made 

 of the radiation at different temperatures enable us to find 

 the duration of the collision for any velocity of the corpuscle. 

 We see from equation (12) that for a given value of d\ Ea. is 

 a maximum when 



47rVa = 4\, 



or 1 . . 



a = —(time of vibration of the light of maximum radiation). 



Now at 0° C, the radiation is a maximum for light whose 

 wave-length is about 10~ 3 cm., and the time of vibration of 

 this light is 3-3 X 10~ 14 sec. 



Hence the time of collision at 0° C. when the corpuscles 

 are moving with a velocity about 10 7 cm./sec. is 1*1 X 10~ 14 

 seconds. In this time light would travel through 3*3 X 10~ 4 cm. 



If the time of a collision varies inversely as the square of 

 the velocity, this time for cathode rays moving at the rate of 

 10 9 cm./sec. would be 2*1 X 10~ 18 sec.,and the distance travelled 

 by light in this time, i. e. the thickness of the Rontgen pulse, 

 would be 3*3 x 10~ 8 cm. For cathode rays moving at the rate of 

 10 10 cm./sec, the thickness of the pulse would be 3*3 x 10~ 10 cm. 

 In an ordinary Rontgen-ray tube the velocities of the 

 cathode rays, and therefore the thickness of the pulse 

 of Rontgen radiation, are probably between these limits. 

 Sommerfeld, from a discussion of the results of experiments 

 by Wind and Haga, estimates the thickness of the pulses used 

 by these physicists as 2*5 x 10~ 8 , a value which is within the 

 preceding limits. 



Radiation produced by the impact of Cathode rays. — An 

 interesting application of the preceding results is to the effect 

 produced when a stream of cathode rays impinge on a solid 

 body, without any ordered connexion between the time at 

 which the impacts occur. In this case we see that the energy 

 corresponding to a frequency between q and q + dq radiated 



