Striated Electrical Discharge. 



251 



If the carve of which this is the equation be drawn in the 

 plane of p, y, it will meet the curves of the graph in the 

 points at which the tangents to the latter are parallel to the 

 axis of y. This curve will in future be spoken of as the 

 curve (a), and the two singular points in which the axis of p 



meets the lines p — ~r~ and p= -j— will be denoted by A 



and B. It is clear that the curve (a) passes through the two 

 points A and B. 



§ 5. In the simplest case, in which q and a are constants, 

 this curve is a parabola whose axis is parallel to the axis of y, 

 and whose concavity is turned downwards (fig. 1). Consi- 

 dering only those parts of the plane for which p is positive, 

 equation (9) shows that for curves of the original system 



-^ is positive at all points outside the parabola, and negative 



at all points inside ; the reverse is true when p is negative. 



Fig. 1. 



ft 



Hence in fig. 1 the value of -j? at any point must have the 

 same sign as the value of y- for a point moving in the direc- 

 tion indicated by the lines of the shading at that point. 

 Every curve of the system cuts the line p = at right angles, 



for at points on this line -/ = 0, and therefore y passes through 

 a maximum or minimum value. 





