the Perihelion of a Planet. 343 



to the equations for the motion of a planet 



/rfrf , o /<70\ 2 2 . 2 m 2m/. 2 



M7 =/ '' (11 ^ 



reaches equations from which he argues that no motion of 



perihelion is to be expected, but only non-constancy in the 



rate of description of areas, although he does not appear to 



show where the supposed fallacy in Einstein's argument lies. 



2m/t 2 

 Now the small additional term ■ ., ■ in (ii.) which is intro- 



V 2 



duced by Einstein's theory is of order ( — J (for h will be 



of the same order as in Newtonian mechanics, where 

 h = \/ma(l — e 2 )) ; and therefore, as Prof. Anderson is ad- 

 mittedly neglecting squares of m — i.e. terms of order 



(5)' 



-it is to be expected that (i.) will transform (ii.) into 

 the ordinary Newtonian equation 



where c 2 — 1 is identified with . In fact, we are not 



a 



making use of Einstein's theory at all, and the equation 



ri X 1 + TjdI= h > ^ 



which Prof. Anderson obtains by applying transformation 

 (i.) to (iii.) has no more significance than it would have 

 if we were treating the problem on purely Newtonian 

 lines. 



It is perhaps of interest to note that if we substitute for r 

 from (i.) in (ii.) and (iii.) and do not neglect terms in 



( — J we obtain, as is to be expected, an equation of motion 



giving the advance of perihelion. Equations (ii.) and (iii.) 



