54(5 



Mr. A. Schuster. 



The quantity ejm thus obtained can be directly compared with the 

 known electro- chemical equivalents. The assumption that in the 

 passage of the particles, the whole work done appears as accelera- 

 tion can never be perfectly realised, and experiments only can decide 

 how nearly we may approach it. In the dark space surrounding the 

 kathode the dissipation of energy is probably small, and we have 

 every reason to believe that there the velocities are very high. I need 

 not enter here into the many experimental difficulties which I have 

 encountered, and which I hope soon to overcome more completely 

 than I have yet been able to do. In the experiments hitherto carried 

 on equation (2) cannot be assumed to hold. The equation (3) may 

 be used, however, to fix an upper limit for ejm. A lower limit can 

 be calculated as follows : — As long as the effect of the magnet on the 

 particles projected from the kathode shows any directional preponde- 

 rance, we may take it that the velocities of the particles must be 

 greater than the mean velocity in their normal state. For it is clear 

 that, if distribution of velocities was symmetrical in all directions, the 

 magnet would have equal and opposite effects on the charges which 

 move in opposite directions ; and if by mutual impacts the velocity is 

 reduced to its normal value, it will also have lost any directional 

 inequality. We may obtain a lower limit for ejm if in equation (1) 

 we calculate 



m JVlr 



by putting for r the smallest radius of curvature which can with 

 certainty be traced in the glow, and for v the mean velocity of the 

 particle, according to the kinetic theory of gases. 



In an actual experiment M was 200 ; r diminished with increasing 

 distance from the kathode. The greatest value which could with 

 certainty be measured was about 1 cm. V was 225 volts at the same 

 place. Taking these numbers, we get for the upper limit 



- < 11 x 10 5 . 



m 



In the glow the radius of curvature is quickly reduced to about 

 % cm., showing that the luminosity is directly due to a conversion of 

 directional into thermal motion. The gas in the actual experiment 

 was nitrogen much contaminated with hydrocarbons. The value of 

 the mean velocity in the state of equilibrium will depend on the 

 supposition we make as to the nature of the particle which carrier 

 the charge. 



It will be sufficient to consider the cases indicated in the following 

 table : — 



