Striated Electrical Discharge. 257 



The curves of the second class are single slant lines, which 



leave the axis of x, making with it an angle tan -1 ( -r—J 



in the negative direction. After passing through at least 

 one point, of inflexion the tangent again makes an angle 



tan -1 ( -r— I with the negative axis of x, and at this point, in 



so far as they are of interest in connexion with the present 

 problem, they terminate abruptly. There is a superior limit y l 

 (see § 5) to the value of y at this point of termination. 



The limiting curves of this class are : — 



(i.) An indefinitely short straight line close to the axis of 



x, and making with it an angle tan -1 /-^-). 



(ii.) A curve which approaches the line y=y asymptotically, 

 has a point of inflexion on this line, and again recedes from 

 it asymptotically. The length on both sides of the point of 

 inflexion is therefore infinite. 



There is no difference between curves of the third class 

 and those of the second, except that the slant is in the 



opposite direction, and that -7— must now be substituted for 



4l7TI 



~i — . There is again a superior limit y 2 to the value of y. 



Curves of the fourth class are inverted arches, which 

 terminate abruptly in two points a, ft. At a the tangent 



(4:7Tl\ 

 -t— ) with the negative axis of a?, and 



after the value of y has passed through some minimum % the 

 curve terminates in ft, at which point its tangent makes an 



angle tan -1 1 -7— I with the positive axis of x. The value of 



y at a has an inferior limit y 1 (see p. 252), and the value at 

 ft an inferior limit y 2 . Also % has an inferior limit, y 

 (equation 12). 



The limiting curves are : — 



(i.) A curve which approaches y=y asymptotically in both 

 directions. 



(ii.) A finite arc of a parabola, at every point of which 

 y is infinite, the latus rectum of the parabola beino- finite 

 (see p. 252). 



A curve of each of the four classes is shown in fig. 4. 

 The dotted lines show the three critical values for y, which 

 have been denoted by y , y ly y^ 



