Planetary Orbits on tjie Theory of Relativity. 517 

 (iii.) Ji 1 <h<h 2 . 



The quadratic has now two real roots, separated in oppo- 

 site directions from ( - — — - ), which is >1. Call these a, ft 

 \4m 2; 



in descending order, then the arrangement of roots of the 

 cubic is a, ft, 1. The range of values of u is now from 1 to 

 ft, i. £.,from aphelion to perihelion. The orbit corresponds 

 to a planetary ellipse Avith the Einstein advance of the apse. 

 This case may be described as an " elliptic orbit from 

 aphelion " (fig. 6). 



Fig-. 6. 



The equ-.ition is 



«=iHi3-i);J-^J=i +( /3-iw^ 



with p 2 = 2m(oc-l) 1 P=(/3-l)/(«-l). 



(In all cases of three real roots the difference of greatest and 

 least roots occurs in p'\ and the difference of middle and 

 least roots divided by this gives P.) The apsidal angle is 

 2K/p, decreasing from the infinite value which it has in 

 case (ii.). 



