284 



Trails. Acad. Sci. of St. Louis. 



Therefore normals to lines of force at points in which they 

 are cut by the axis O^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 to 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 



Fig. 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 o) = tt 

 2°"^ «' CO = 2'Tr 



n 



O) = n^TT 



then for the n^" asymptote equation (2) becomes 



(23) 



