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 as i is above 0. 



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 in6nity to plus infinity, equation (1) represents a 

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



Fia. 5. 



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 



1** asymptote co — v 

 2°* " CO = 27r 



lib 



a = n„w 



then for the n*** asymptote equation (2) becomes 



a \ 

 IT a 



(23) 



