374 Prof. J. J. Thomson on easily Absorbed 



The other case is when the tangent at R is not horizontal : 

 here the curve crosses the tangent, becoming convex to the 



Kff. 7. 



axis, and X continually increases as we approach the anode. 

 Alter passing R, f(Xe\)— /S is always positive, and hence by 

 equation (1) nu continually increases, in more than geo- 

 metrical progression, as we travel towards the anode. Now, 

 when the discharge is steady, nu + inv = i, hence nu cannot 

 exceed i. Hence in the case when the graph rises through R 

 there must ultimately be instability, or rather unsteadiness; 

 this will occur when the force reaches a value such that nu = i, 

 or by equation (4) when 



Aire ._2dXi 

 k ± 3 dx ' 



that is when the tangent to the graph of X> makes a certain 



angle with the axis of x. For values of X greater than this 



nu would be greater than i, and the current would no longer 

 be steady. Let S, fig. 8, be the point where nu = i, then 

 since negative electricity is streaming out from the region 

 between S and the cathode faster than it enters it, there 

 will soon be an excess of positive electricity behind S : 

 this will lower the electric force between S and the anode, so 

 that the graph for X past S will be somewhat as in fig. 8 



(this represents the 



force, as from the preceding 



