518 Prof. W. B. Morton on the Forms of 



(iv.) When h = h 2 the root /3 = 1, and the orbit is a circle 

 of unit radius (for the sake of continuity in the diagrams 

 this is included as fig. 7). The "velocity in a circle ^ of 

 unit radius is m*j(l — 3 <ri)- instead of m? as on the ordinary 

 theory. 



Fur. 7. 



The "value of the root « is now /- 2). The apsidal 



angle of the last case approaches 7r/(l — 6»i)% which replaces 

 7T as the " apsidal angle of a nearly circular orbit." 



(v.) For Ji 2 <h<h 3 the root {3 is less than unity and the 

 arrangement is a, 1, /3 ; w runs from 1 to /3, and we have an 

 *' elliptic orbit from perihelion" (fig. 8). This is the case 

 considered by Prof. Forsyth; his u p" is the reciprocal of p. 



n /i o\ 1 + cn/^ f cn 2 -J;?<9 



