Ray of Light in the Solar Gravitational Field* 585 

 on eliminating the parameter t by means of r 2 sin 2 6 . (// = A, 



we find without difficulty, since -,— = 9 . ., „ -77, 

 17 rtT ? >2 sin- (9 a<£ 



d 2 . , a /d0\ 2 . - . 

 which simplifies on writing ~ = cot# to 



Hence, if initially z=0, tt = 0, z=0. Choosing accordingly 



onr co-ordinates so that initially 6 = 77/2, -j-=0, we have 

 = 7rj2, and our integrals simplify to 



r 2 4>' = li; (l-2m/r)t' = C, 



to which we add F = 0, or 



(l-2mlr)(t') 2 ~{l-2m/ry 1 (r') 2 -r 2 ((j>y = 0. 



On writing u-- and again eliminating r, we find 

 or 



(S)' -«--'♦?• 



Here ??i is the gravitational mass of the sun, which has the 

 dimensions of any one of the co-ordinates * (the velocity of 

 light tends to unity as r->co , so that a time-unit of 1 cm. 

 = -^.10" 10 second). Taking, with Eddington, the kilo- 

 metre as the unit of length, ?n = l*47; the smallest value 

 that r can have for the light-pulse is equal to the radius of 

 the sun, or 697,000. Hence we obtain a first approximation 

 to the light-ray on neglecting the term in u 3 in comparison 

 with that in w 2 , and find immediately 





 u = ^sin((/>-<£o), 



where <£ is a constant of integration. (This would be the 

 equation of a straight line if the space were Euclidean, 



* If the gravitational constant of Newtonian mechanics is regarded as 

 a mere number, mass has the dimensions L 3 T' 2 = L if L and T have the 

 same dimensions. 



