Striated Electrical Discharge. 



523 



has been made to supply a formal proof of the principle upon 

 which the argument rests. 



The curved line in fig. 7 is the graph which was found to 

 represent the distribution of intensity along the line of dis- 

 charge which is predicted by theory. The anode is repre- 

 sented by A, the cathode by E, and the ordinate at any 



intermediate point is equal to y, the semi-square of the electric 

 intensity at that point. The line Imn . . . is the line (y=7j) 

 below which- the differential equation with which we have 



been working ceases to hold. The value of p ip= ~- J at a 



point m at which the graph meets this line will be slightly 

 different from the value of p at the adjacent point B in which 

 the ideal mathematical graph meets the axis y = 0. Let this 

 small difference be denoted by w m , the difference being taken 

 so that v m is positive. Thus we shall have 



VT = 



m 



4-777 



+Prn> 



TV — 

 n 





—pn, 



™p= 



4777 



+Pv, 



and so on, the suffixes m, n, p . . . referring to the points 

 m n lo • • in n^f. 7. 



Fig. 8 represents the plane of p, y (cf. fig. 2), and STU is 

 the line y=v. In this plane the graph for y will be repre- 

 sented bv a single curve, and each striation will correspond 



2 M 2 



