Roever — Geometrical Constructions of Lines of Force. 209 



The asymptote passes through the centre of gravity of the 

 masses m and m' . 



This is proved in a manner similar to that in the last case 

 (Fig. 4). In this case 



or 



The point O in this case is between A and A . (Fig. 3.) 

 The angle a, equation (2), cannot exceed 7r, and when it 

 has this value (a = ir) equation ( 2) becomes 



mco + m'co' = mir 

 or 



m 



CO = — 7 ( 7T CD ) (15). 



This is the equation of the limiting or critical line, which 

 separates the region occupied by the lines of force that start 

 at A (Fig. 3) and go to infinity, from that occupied by the 

 lines of force that start at A and go to infinity. 



The point O', in which A A is cut by the critical line 

 (dashed in Fig. 3), and the centre of gravity O, are symmet- 

 rically situated with respect to the points A and A. 



For any point on the critical line 



r sin co sin co' 



r' sin co sin (ir — co) 



