Unstriated Discharge and in the Are. 287 



We have further evidence that V 1 decreases with in- 

 creasing- current in the striated discharge. Thus Wehner * 

 found that the potential difference between consecutive 

 striations becomes less as the current becomes greater. 

 Again, the electric force in the arc where the current is 

 large is very much less than it is in the unstriated discharge. 

 Tims we may conclude that the formula agrees quite as well 

 with the observations as is to be expected. 



Equation (7) will also give some idea of the order of 

 magnitude of k, and will confirm Townsend\s statement that 

 the collisions between electrons and molecules do not always 

 result in combination of the two. Assuming this equation 

 to be correct, we have 



dx c v, /i + /,-\ n + k\ v, 



x8 rfS 



Since p = ch where c' is a constant, this equals ^-. 



■* aJL 



* dp 

 We have some knowledge of all the quantities on the right- 

 liand side of the last equation, but unfortunately it is not an 

 accurate knowledge, and a slight change in any of these will 

 produce a very large change in k. We can, however, get 

 ?orae idea of the value of these quantities. If we take 

 13'25 volts per cm. per mm. of pressure for d~K/dp, which 

 is found from the data of Herz on the discharge in hydrogen, 

 10*55 volts for Y\, and '0839 cm. for \ when p is 1 mm., as 

 given by Davis t? Ihe value of 1/k is 13,230. That is, only 

 one collision in 13,230 results in combination of an electron 

 with a molecule. It is possible that this number is too large, 

 but it does not appear altogether unreasonable, since 

 Townsend J concludes from measurements on the diffusion 

 of ions, that after 8000 collisions a large majority of the 

 negative ions are still in the electronic state. 



It would seem as if the combination of electrons and 

 molecules might be entirely neglected, since they occur so 

 seldom, but if this were done equation (2) would reduce 



to X=cS -r log— r^-, in which X becomes zero when 8 



becomes zero. This is contrary to the measurements which 

 have been made on the unstriated discharge. 



* Ann. d. P/n/s. xxxii. p. 76 (1910). 

 f Phys. Kev.'xxiv. p. 101 (1907). 

 t Phil. Mao-. [()! xxiii. p. 807 (1912). 



