TWO UNEQUAL MASSES OF OPPOSITE SIGNS. 157 



X _^__^__ 



The asymptote which corresponds to w = c/, is defined by the 

 equation 



(i / 2 ) cos a = i 2 cos 6] 



it passes through the centre of gravity O of the two masses. This 

 point is given by the ratio 



OA w'i 



For the asymptote to be real, cos a must be > - i, or 

 i - & cos e 



The condition 



i - 2 cos 



gives the value of corresponding to the limiting line of force. 

 The equation of this line of force is then 



cos a/ 2 cos to = / 2 i ; 



it evidently bounds the flow /^(m - m') from the point A, and corre- 

 sponds to the value of Q given by the equation 



. N 2(m-m') 

 i - cos = = 



m 

 or 



44) 



cos = i. 



This line of force 2 passes moreover through the point of equi- 

 librium I, as can be easily shown. 



