Forms of Planetary Orbits on Theory of Relativity . 511 

 We have also 



\ dfjb _ \ 2 1 b 



^' dX~~~f?V + 2 -/3 2 ) 



2 )2 J- 



Using these formulae, I have constructed the following- 

 table similar to that on p. 44 of ' Relativity and the Electron 

 Theory/ 



Wave-length XlO 3 



ATF- 



•4615 



•4615 



K Z . 



•465 



4500 



•4424 



4580 



•4420 



•4579 



•4634 



•463 



5461 



•4383 



■4501 



•4541 



•451 



6870 



i 



•43 IS 



•4438 



•4464 



•447 



In this table /e F is the convection coefficient a cording to 

 Fresnel's formula. at a according to my formula, kq according 

 to Mr. Cunningham's formula, and Kz the value found in 

 Zeeman's experiments. It will be seen that for only one of 

 the four wave-lengths does my formula give a closer approxi- 

 mation to the experimental result than Mr. Cunningham's. 



LXI. The Forms of Planetary Orbits on the Theory of 

 Relativity. By W. B. Morton, M.A., Queen's University, 

 Belfast *. 



AN exact integral of the differential equation for a 

 planetary orbit on Einstein's theory can be expressed, 

 ;;s Prof. Forsyth has pointed out "f, by use of elliptic 

 functions. The chief interest, of course, attaches to the 

 <-ase actually occurring in astronomy, where the departure 

 from the elliptic orbit of the classical theory is very small. 

 But it is interesting also, if only from the purely mathe- 

 matical point of view, to examine the forms which these 

 orbits assume in the most oeneral case. To a certain extent 

 it is easy to foresee how the elliptic form will be further 

 modified as the magnitudes involved are progressively 

 altered. Increasing the strength of the centre will bring 

 about an increase of the apsidal angle. As the velocity in 



* Communicated by the Author. 



f Proc. Roy. Soe. xcvii. p. 1-15 (1920). 



