206 



Trans. Acad. Set. 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 i^adii vectores 

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

 two polar subtangents AT and 

 AT'. 



Then, from the figure, 



AT=AP tan TPA = r ianip =r 



rd 



w 



dr 



and 



AT = AP tan TPA = r' tan i' = i 



, r' dco' 

 dr' 



Whence 



AT _ ?-2 dr' d(o 

 AT'~ r'^dFd^'' 



But from equation ( I ) 



dco 

 dco' 



in 

 m 



AT r'^dr'm' 



AT' ~ r"' dr m 



As r approaches r' 



AT . m' 

 approaches — . 



AT ^' m 



