Striated Electrical Discliar ge. 



259 



therefore y, must be continuous. If we suppose that p also 

 is to be continuous we are reduced to keeping on the same 

 curve, for two curves can never touch each other, since by 

 equation (8) the curvature depends only on y and p. 



The effect of making p discontinuous is to make j~ 



become infinite. If, then, equation (8) is not to be violated, 

 y must be zero at that point. 



An alternative solutiou can therefore be obtained by build- 

 ing up the graph of y out of pieces from the curves in fig. 4, 

 care being taken to only pass from one curve to another on 

 the axis. The solution so obtained is such that the electric 

 force and velocities of the ions are continuous, and it satisfies 

 all the mathematical equations. 



It is, moreover, obvious that there is only one type of 

 solution of this kind possible. This consists of any number 

 of arched curves of the first class placed end to end and 

 terminated by a curve of the second class at the anode, and a 

 curve of the third class at the cathode ; the points ex! and ft' 

 of these curves (fig. 4) being the anode and cathode respec- 

 tively. 



Fio, 5. 



A solution of each of the two types that have been found 

 to be mathematically possible is shown in fig. 5. 



§ 10. When we attempt to interpret this second solution, we 

 are immediately confronted with the fact that it is impossible, 

 for physical reasons, that y should vanish. At a point such 



