PRESIDENT 8 ADDRESS — SECTION A. 15 



The directions of the asymptotes are given bv m = 0, or 

 mA cos^ (f) — cos (f) — 2m, A = 0. 



, 1 -ri +8m-.4-l- 



cos = : — 



^ 2mA 



= -— 2mA. 



It follows that the angle between the asymptotes is approximately 

 imA . 



From (3), A = R'^ approximately, where R is the distance of 

 perihelion. 



Hence the deflection is 4 !n/R. 



The above line of argument makes no a])peal to the principle of 

 Least Time nor to any other principle of pre-Relativity Physics. 

 Consequently in adopting it we avoid any assumptions which may 

 conflict with the general Relativity ideas. There is no a priori reason 

 for assuming that a definite period in t is transmitted by the radiation. 

 For my own part I incline to the view, suggested by the fact that s is 

 constant along the w^orld line of each pulse, that the interval 8s rather 

 than the time interval 8t is transmitted unchanged ; and, consequentlv, 

 that the Einstein effect is not to be expected. 



If the above contention is sound the transference of the observer 

 to a region in which the gravitational field was different from that 

 existing in his original position should lead to the observation of the 

 Einstein displacement, but it is hard to see how the necessary variation 

 of the gravitational field could be realized in practice. 



A full discussion of the applications of the Theory of Relativity to 

 General Dynamics would take too much time and involve more detailed 

 mathematical work than is suitable for a Presidential Address. I will 

 confine myself, therefore, to the merest outlines of results. 



It is found that gravitational effects are propagated with the velocity 

 of light, and that the constant m, introduced first as a constant of 

 integration and afterwards identified with the gravitational mass 

 satisfies, in the absence of a gravitational field, conservation laws 

 justifying its identification with the inertial mass. 



The distinction between mass and energy disappears and flux of 

 negative momentum, flux of energy, negative momentum and energy 

 appear as the sixteen components of a tensor. This tensor does not 

 obey a Conservation Law in a gravitational field, but the disappearing 

 portion reappears as a quantity belonging to the field. Thus the Laws 

 of Conservation of Energy and Momentum break down when applied 

 to a material system in a gravitational field, but they remain valid when 

 applied to the system and the field together. Thus we have an inter- 

 change of energy and momentum between the system and the field 

 similar to that with which we are familiar in the Maxwell Electro- 

 magnetic Theory. 



