248 Mr. J. H. Jeans on the 



to give place to other phenomena in the region of the 

 electrodes. 



§ 3. The present section consists of an explanation of the 

 notation to be used, and a summary of those parts of Thomson's 

 paper which are essential to the theory. We are considering 

 a discharge in perfectly pure gas, between two parallel and 

 infinite plates. 



Let x be a coordinate measured along the line of discharge, 

 the positive axis of x being drawn from the anode to the 

 cathode. The electrical intensity at any point will be denoted 

 by X. The positive and negative ions are supposed to move 

 in opposite directions with velocities proportional to X 

 (Thomson, /. c. ante, p. 253). These velocities will be denoted 

 by k-[K and # 2 X respectively, the former being parallel to the 

 positive axis of x. The number of positive ions per unit 

 volume is n,, and of negative ions n 2 . Of these a certain 

 number recombine, and this number is supposed to be a«]n 2 , 

 since, other things being equal, it will be proportional to the 

 product n Y n 2 . In the same unit volume, a certain number of 

 molecules become dissociated, and these produce q ions of 

 each sort per unit time. 



No assumption is as yet made as to the way in which q and 

 a depend on other quantities ; but from their definition they 

 must be positive quantities at every point of the line of 

 discharge, 



If e be the charge carried by each ion, the fundamental 

 equations for the case of steady motion are 



-^ =47^(71!-^), (1) 



-^(k l n 1 X)=q-*n l n 2 , (2) 



~dx^ n ^-^~ anin ^ ( 3 ) 



Of these the first is the fundamental equation of electrostatics; 

 the two others contain the fact that the number of ions of 

 either kind in a fixed element of volume remains constant; 

 they are therefore the mathematical expression of the fact that 

 the motion is steady. 



From equations (2) and (3) it appears that (k^ + & 2 n 2 )X 

 is independent of x, and its value is easily seen to be i/e 9 where 

 i is the current across any unit area perpendicular to the axis. 

 Thus 



(k 1 ni + k $ n 2 )Xe=i (4) 



