372 Prof. J. J. Thomson on easily Absorbed 



positive, i. e. when X is greater than X , the value it has in 



d 2 X% 

 the uniform positive column a is positive, i. e. the graph 



Ct<x 



of X 2 is convex to the axis of x } while when X is less than 

 X it is concave to that axis. 



Though the differential equation which gives X is a some- 

 what complicated one, yet we can without much difficulty 

 see what must be the general nature o£ the distribution of 

 electric force along the tube. We can do this from the 

 principle that the graph for X^ must be convex or concave 

 to the axis of X according as X is greater or less than X ; 

 and that the electric force is increasing or diminishing as we 

 move towards the anode, according as there is an excess of 

 negative or positive electrification at the place of observation. 

 Suppose, then, that we start with a few negatively electrified 

 corpuscles near the cathode ; under the strong field near the 

 cathode these will acquire sufficient energy to ionize the gas, 

 fresh ions will be produced ; and since the negative ones are 

 driven away by the electric field, there will be an excess 

 of positive ions next the cathode, and thus the electric force 

 will diminish as we leave the cathode. The graph for XI 

 (fig. 5) will be convex to w until we come to P, the place 



Fig-. 5. 



where X satisfies the equation f(Xe\) — /3 = 0, i.e. until 

 X = X ; at P the curvature changes, and there are two cases 

 to be considered. In the first case the tangent to the graph 

 is horizontal, in this case the rest of the graph will be the 

 horizontal line through P: this straight part of the curve 

 corresponds to the uniform positive column, and the case is 



