284 



Trans. Acad. Sci. of St. Louis. 



Therefore normals to lines of force at points in which they 

 are cut by the axis OX pass through a point in the axis OY 

 which is as far below O as 1 is above O. 



If we assume that the rotating line OP (Fig. 1.) extends 

 in both directions from its axis and that co can have any value 

 from minus infinity to plus infinity, equation (1) represents a 

 curve which has an infinite number of branches, of which only 



'(Tv 



Fia. 6. 



one passes through the point O. Fig. 5, which explains itself, 

 shows a portion of the complete curve represented by equa- 

 tion (1). 



In order to investigate this curve for asymptotes put for 

 the 



l 8t asymptote <y = tt 

 2 nd " u> = 2tt 



th a 



n 



<a = n„7r 



then for the n^ asymptote equation (2) becomes 



(23) 



