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XXIX. On the Conduction of Electricity through Gases 

 between Parallel Plates. By Alfred A. Robb *. 



HE differential equation 



occurs in the theory of the conduction o£ electricity through 

 gases between parallel plates. 



In this equation X represents the electric intensity at a 

 point defined by the coordinate x, measured in a direction 

 perpendicular to the plates. i represents the current per 

 unit area ; Ri and R 2 are the velocities of the positive and 

 negative ions under unit electric intensity ; q is the rate of 

 ionization per unit volume and a. is the coefficient of 

 recombination. 



The equation has been solved by Professor J. J. Thomson 

 for the case when R^R?,; but in general it does not lend 

 itself to solution. It is proposed here to show (i.) that this 

 equation may readily be transformed so that it becomes a 

 characteristic one for any gas under definite conditions of 

 temperature and pressure : and (ii.) that for any gas for 

 which R x and R 2 are unequal there exist two pressures at 

 which the equation becomes soluble. 



In order to effect the first of these objects, we have only 

 to write : 



(2) 



dv 2 



and the equation becomes 



dy /l_ i\ r • _ _^ 



^™ \ Ri + R J V ehf (Ra + R 2 )* 



The form of this equation does not depend either on the 

 strength of the current or the intensity of the ionization, and 

 therefore is characteristic for the gas. 



In order to show that for certain pressures this equation 



* Communicated by the Author. 



