Unstriated Discharge and in the Are. 285 



When X and 8 are taken as the variables, this becomes 

 the equation of a discontinuous curve, one part of which is 

 similar in shape to that shown in fig. 1. This may be shown 



as follows. When the density is laro-e y|^- approaches zero 



and -^ approaches c-= log/— ^ — J. Since k is a constant, 



this quantity is a constant and the curve approaches an 

 asymptote through the origin, whicli is indicated by the 

 dotted line. 



Again, when the number of combinations with positive 

 ions equals the total number of collisions between electrons 

 and molecules bnfi = a^m or b8 = a^n and 



los {r+/,( 1+ jm) } =log 1=0 and x = f) = infinit y> 



since 8 is not zero for this value. 



This corresponds to the conclusions already reached, 

 namely, that when the density is large, the electric force 

 increases as the density increases, and that when the number 

 of combinations of electrons and positive ions equals the 

 number of collisions between the electrons and molecules, 

 the electric force must be infinite. 



Comparison of the Theory with the Data on Unstriated 

 Discharge. 



Since c is equal to a constant times V], the value of the 

 electric force as given in equation (6) is proportional to 

 the potential through which an electron must go in order 

 to ionize. It is, however, not possible to test the formula 

 by this means ; first, because we have little data about the 

 value of V 1 in different gases ; and secondly, because it is 

 not possible to change Y 1 without changing some of the 

 other quantities in this formula. 



When the relation between the electric force and the 

 density of the gas is considered, we are better able to test 

 the results of the preceding explanation. 



The observations which have been made on the unstriated 

 discharge have been made with small currents and with 

 pressures of several millimetres. Lower pressures than 

 these cannot in general be used without having the discharge 

 change to the striated form. As a result, the only part of 

 the curve shown in fig. 1 which applies to the measurements 

 made on this form of discharge is the part at the right where 

 8 is large. In such cases the number of molecules is many 

 times greater than that of the positive ions, and the number 



