520 



Prof. W. B. Morton on the Forms of 



as "hyperbolic/'' Their equation is that of (v.) with nega- 

 tive f$ y but for purposes of calculation it is better to use the 

 form of case (iii.) and write 



u=j3 + (l-j3)sn 2 i P e, p' = 2?n(a-/3), F=(l -£)/(«-£). 



p0 then runs from the value which makes u = up to K, 



Fir. 9. 



when w — 1. The angular range from the apse to infinity (or 

 the half-swerve of the orbit increased by 90°) is given by 



2 {K-sn- 1 (~/3) i (l-/3)- 1 }/^. 



