in the Uniform Positive Column in Air. 185 



J. J. Thomson* has shown that this radiation produces 

 ionization in gases such as air by which it is rapidly 

 absorbed. 



It seems probable that this radiation is emitted by the ions 

 during the process of recombination. On this supposition the 

 amount of radiation emitted per c.c. may be taken as pro- 

 portional to the amount of recombination fin^, and to the 

 kinetic energy of the ions, which latter is proportional to X^. 



If, then, Ro is the amount of energy emitted per c.c. as 

 '^ Entladungstrahlen," we hav^e Rq = A^/3>i^X^, where A' is a 

 function of the pressure. 



The radiation emitted by a small element of volume dv 

 will be Rq^^i", and at a distance r from the element its intensity 



will be — -, — ^— , where \ is the coefficient of absorption of 



the radiation by the gas. 



At any point in the discharge-tube the intensity of radiation 

 will be the integral throughout the positive column of 



—J — ^ — . It is easy to show that this gives for the intensity 



R at the axis of a discharge-tube of radius a 



Re 



X 



R= -^(l-e-^«). 



If a is not very small we may, therefore, take -^ as the 



intensity of radiation anywhere in the positive column except 

 very near the walls of the discharge-tube. The ionization 

 due to radiation, say qr, will therefore be given by the 

 equation 



A/3n^X^ 



where A is a function of the pressure only. 



Denoting the ionization due to negative ions by g^ we 

 have 



Now q^ is evidently equal to ?2a^'2, so that 



no(.V2 H ^-r = pn\ 



X 



Eliminating n by means of the equation 

 i, = ne{vi +V2), 

 * Proc. Camb. Phil. Soc. vol. x. pt. ii. p. 74. 



