206 



Trans. Acad. Sci. of St. Louis. 



Fig. 4. 



force. The angle d is measured 

 from the same line, A AX, and 

 in the same direction as a. 



The asymptote passes through 

 the centre of gravity of the masses 

 m and — m'. 



In order to show this draw a 

 tangent PT to a line of force 

 ^PatP. (Fig. 4.) 



Also draw the two radii vectores 

 AP = r and A'P = r', and the 

 two polar subtangents AT and 

 AT'. 



Then, from the figure, 



AT= AP tan TPA = rtan4>=zr 



r dcu 

 dr 



and 



A'T = A'P tan TPA' = r' tan 4^' = ? 



, r' dco' 

 dr' 



Whence 



AT r^ dr' dco 



A'T'~ r'^drdco' 



But from equation ( 1 ) 



da) 

 dio' 



in 

 m 



As r approaches r' 



AT r'^dr'm' 



AT' r"^ dr m 



AT , m' 



— — approaches — 

 AT' ^^ m 



