Striated Electrical Discharge. 



253 



system is therefore identical with the first system which we 

 considered, namely, the series of arches which join the points 

 A, B. 



The remainder of the part of the p, y plane with which we 

 are dealing is filled up by a system of curves which meet OG 

 above G, each carve having its lowest point on OG. For 

 curves of this type there is an inferior limit to the value of y, 

 and this is the value y already found in equation (11). 



The curves in the p, y plane are thus seen to fall into four 

 classes. These are represented in their essential features by 



the curves in fig. 2, and the four classes will in future be 

 referred to by the numbers in this diagram. 



The limiting curves are the two curves AGB', A'GB, which 

 are drawn in thick lines in the diagram. These curves intersect 

 in G and divide the plane into four regions, in each of which 

 lie all the curves in one of the four classes. 



§ 6. Let us now examine to what extent the arrangement 

 of curves found in the last section will be altered if we replace 

 the assumption that q and a are constant by the more general 

 assumption that they are positive quantities which vary 

 with y. 



From the equations of § 4, it follows at once that : 



(i.) The curve (a) is no longer a parabola, but is still a 

 curve which passes through the points A and B, and is sym- 

 metrical about the same axis as before. 



