1093 



electron between two succeeding impacts. Let v be the velocity of 

 the electron, I the mean free path, then the mean value of the 



interval between two succeeding impacts will be t = — sec. During 



V 



this time the electric lield X gives to the electron the acceleration 



e 

 X—. As after each impact the electron begins again with the mean 

 m 



velocity zero in the direction of the electric field, it will travel over 



e /A \' 

 a distance .r= i X— ( — J in this direction M. The mean value of the 

 m \v J 



increase T of the energy between two impacts will therefore be 



7n\v 



Evidently this increase becomes smallest when the energy ^ mv^ 



itself is as great as possible. Then the loss of energy r by the 



V 

 impact is however also maximal and therefore also the ratio ij = — . 



Let us now suppose, what probably will be the ease, namely that 

 ionisation will occur, as soon as an electron receives enough energy 

 to be ionised. Then ^ becomes a maximum for 4 ''^v" = ^ Vi, where 

 Vi is written for the ionisation potential 



ke Vi f V\ 



Now the free path of an electron in argon is 4r2 times that of 



an aigon molecule. From the data on internal friction, we can easily 



deduce, that P. in argon for 17° C. and a gas pressure of p mm. 



0,028 

 IS equal io ^ = cm. 



P 



The ionisation potential for argon is 12 Volt. Introducing this into 



the above formula we find : 



In the measurements with constant field p was about 2 mm. and 



e X 

 1) The mean velocity in the direction of the field becomes therefore Vx = i X — , 



m V 



while Hertz finds double the value. This must be ascribed to the integration 



used by H, in which the rare very long paths liave a great influence, hi reality. 



when the number of the impacts between two ionising impulses is not exceedingly 



great, an intermediate value will be the right one. 



