628 Advance of the Perihelion of a Planet, 



In obtaining the path of a ray of light, we have changed r 

 in the original particular integral to (2r + m) 2 /4zr, and it 

 must be legitimate to go back to the case of the planet and 

 make the same change. We thus get 



where c is a constant, and 



v ^ .. o . -T- — ">, a constant. 

 16H as 



Neglecting squares of m, these equations become 



m 

 It is clear that c 2 — 1— , and dividing the first equation 



by the square of the second, we get, neglecting squares of ?n, 



(duX 2 ( 9 _ ??i 2m , w 



<:Fu m , 1 



or — ^ +i6= -.' where U— -, 



the ordinary Newtonian equation for elliptic motion. So 

 that Mercury, uu fortunately, is left with the advance of his 

 perihelion unexplained. But his rate of description of areas 

 is not constant ; it is least at perihelion and greatest at 

 aphelion. 



The astronomical unit of mass used in the above is 9 X 10 25 

 times the ordinary astronomical unit of mass ; the unit of 

 length is the kilometre, and the unit of time the time 

 required for light to travel one kilometre in a forceless 

 field. 



University College, Galwav, 

 13th February, 1920. * 



