Weight and Fate of Light. 553 



could exert an optical effect by its very neighbourhood — 

 as it undoubtedly exerts a gravitational effect. 



Hence it appears erroneous to speak of light as having 

 weight, or to treat it as a substance to which Newtonian 

 considerations can be applied. It must be deflected optically, 

 not mechanically. The ether is affected by the gravitational 

 potential- -the tension set up in it by a mass — so that its 

 refractive index \Z(/u.k) is increased. The property corre- 

 sponding to rigidity, 2tt/k, is probably reduced by the 

 gravitational tension or reduction of ether pressure, GrM/r, 

 caused by the neighbourhood of a mass of matter (cf. my 

 paper in Phil. Mag. for February 1920, page 172). 



Trapping of Light by Relativity Method. 



It seems worth while to consider further the optical 

 behaviour of a very extensive and concentrated stellar 

 system, using the Einstein method of calculation and avoiding 

 the conceptions of ordinary weight as applicable to light. 



It is well known that a gravitational influence on a beam of 

 light originated in the theory of relativity, which blossomed 

 into equations summarising in striking fashion this and much 

 other information ; and it may be interesting to physicists 

 who have not specially attended to relativity to show, in 

 elementary fashion, how that theory would treat the subject. 



A vital Relativity equation — first given I understand by 

 Schwarzschild (see Eddington's Report, pp. 43-47) — is the 

 expression for the square of a small interval between two 

 point-events, which in ordinary geometry is merely the 

 distance between two neighbouring points, or in polar 

 coordinates 



ds 2 =: dr 2 + v 2 d6 2 + r 2 sin 2 6 # 2 . 



Minkowski introduced time, and Einstein introduced 

 gravitation, so that it became 



ds 2 = l/ry .dr 2 + r 2 d& 2 + r 2 sin 2 6d<j> 2 -yc 2 dt 2 . . (1) 



where time, as imaginary space, contributes to the interval, 

 and where y represents a numerical factor involving a 

 potential due to neighbouring gravitational matter — say a 

 mass m at distance r — a factor which is nearly equal to unity 

 in ordinary cases, and is such that 



^ 2Gcm 



more generally, it' V is the gravitation potential — say inside 

 a body or system of bodies — 



7 =1-2V/V 2 . 



