526 Mr. J. H. Jeans on the 



tube. Consider for the moment an ideal discharge in which 

 the velocity of every individual positive ion is &iX. and the 

 velocity of every negative ion is & 2 X. Let us further 

 suppose that tbe equations of § 3 are absolutely true at every 

 point, and tbat the distribution of electric force is that given 

 by the ideal mathematical graph of fig. 5, these suppositions 

 not being inconsistent with one another. 



The volume-densities of ions are now given at every point 

 of the tube by the equations of § 3 — 



_ 1 f 9 -, hi if\ 



(ki + ^eX \ \.Trdx)' 



n 2 



We shall accordingly meet the following distribution of 

 densities as we pass along the tube, starting from the cathode 

 E (fig. 7). The volume-density of positive ions n x will be 

 finite at E, that of negative ions n 2 will be zero. Passing 

 along ED both % and n 2 increase, until finally n i becomes 

 infinite at D, the first discontinuity, while n 2 has a finite 

 value. In passing D an abrupt change of densities occurs,, 

 and on the further side of D and close to D, n x is finite 

 while n 2 is infinite. As w T e pass along DC, n x increases and 

 n 2 decreases, so that as we approach C the same state is 

 reached as occurred at D, n x becomes infinite and n 2 finite ; 

 while the same abrupt change occurs in passing through C 

 as occurred at D, and so on. 



The velocity of ions of both sorts becomes zero at D, C . . ., 

 so that at these points we get a wall of positive ions in 

 contact with a wall of negative ions, both faces being at rest. 

 In the ideal case there is a succession of such " slabs " of 

 ions. The slabs are at rest, and ions pass from slab to slab 

 with finite velocities. The discharge may therefore be re- 

 garded as a series of small discharges between consecutive 

 slabs. 



In nature the conditions are different. The velocities ^X, 

 # 2 X are not velocities of individual ions, but measure the 

 mean forward velocity of a swarm of ions, the velocities of 

 individual ions varying both in amount and direction. 

 Hence it is impossible that a " slab " of ions such as we have 

 been considering should exist in nature, and even if this were 

 not so, such a slab would be immediately broken up by the 

 bombardment of undissociated molecules. 



Hence it becomes clear that the accumulation of ions 

 which occurs in the neighbourhood of a point of minimum 



