﻿364 On the Velocity of the Cathode-Rays. 



velocity of the cathode-rays is 



6-7T x 10 6 cm./sec., 

 or about 



1*9 x 10 7 cm./sec. 



This velocity is small compared with that with which the 

 main discharge from the positive to the negative electrode 

 travels between the electrodes (see J. J. Thomson, Proc. 

 Roy. Soc. 1890). I verified this by inserting an electrode 

 into the far end of the tube used in the previous experiment, 

 and observing the images formed when a bright discharge 

 passed down from the electrode at the beginning to the elec- 

 trode at the end of the tube. The light from the luminous 

 gas shines through the places where the lampblack has been 

 scraped from the tube, and we get two images, which when 

 the mirror is at rest coincide in position with the images of 

 the two phosphorescent patches in the previous experiment. 

 These images, however, unlike the phosphorescent one, re- 

 mained in the same straight line when the mirror was rotating 

 rapidly, thus proving that the velocity of the main discharge 

 is very large indeed compared with that of the cathode-rays. 



The velocity of the cathode-rays is very much greater than 

 the velocit} r of mean square of the molecules of gases at the 

 temperature 0° C. Thus, for example, at 0° C. the velocity of 

 mean square of the molecules of hydrogen is about 1*8 x 10 5 

 centimetres per second : the velocity of the cathode-rays is 

 about one hundred times as great. The velocity of the 

 cathode-rays found from the preceding experiments agrees 

 very nearly with the velocity which a negatively electrified 

 atom of hydrogen would acquire under the influence of the 

 potential fall which occurs at the cathode. For, let v be the 

 velocity acquired by the hydrogen atom under these circum- 

 stances, m the mass of the hydrogen atom, V the fall in 

 potential at the cathode, e the charge on the atom; then we 

 have, by the conservation of energy, 



mv 2 = 2Ye. 



Now e has the same value as in electrolytic phenomena, so 

 that e/m = l0\ 



Warburg's experiments show that V is about 200 volts, or 

 2 x 10 10 in absolute measure. Substituting this value, w T e find 



«*=4xlO u , 



or 



v = 2 x 10 7 cm./sec. 



A value almost identical with that found by experiment, 



