president's address — SECTION A. 11 



It is found from the above result that, the value of eSa for the planet 

 Mercury is + 8" • 82 per century. It appears probable that the absence 

 of the term 2nih-/r^ from the Newtonian equations B accounts for the 

 discrepancy 8" •24 per century between the observed motion of the 

 planet and the motion predicted by Newtonian Theory. The intro- 

 duction of this term by the Einstein Theory does not appreciably 

 disturb the results for the other planets, and the reason is not far to seek. 

 The term leads to an additional term 3mu^ in the differential equation 

 of the path, and this term decreases in importance as the dimensions 

 of the orbits increase. In the case of Venus and the Earth, the next 

 two planets in which the effect might be expected, the orbits are nearly 

 circular, and thus the predicted effect is too small for verification by 

 observation. 



The small value of m/r makes possible a useful transformation of 

 the expression for c/s''. If r is replaced by r + m and second and higher 

 powers of m/r are neglected, we have 



rfs'' = - y-i \dr' + rdd^ + r' sin^ 0(14'] + ydt\ 

 = — y-' [dx^ + dy- + dz^] + ydf. 



It should be noticed that it is impossible to say that one /• co-ordinate 

 rather than the other represents the polar co-ordinate of our ordinary 

 measure. The transformation represents a radial shrinking of the 

 deformed Minkowski fourfold, which is concealed in the same way . 

 as the Fitzgerald-Lorentz contraction in the earlier work. 



A second verification of the Einstein Theory is found in the action 

 of gravitation upon light. 



In the absence of a gravitational field, ds^ = along the world line 



of a light pulse. By the Principle of Equivalence this equation remains 



true in a gravitational field. Hence, in terms of the co-ordinates just 



introduced, the velocity of the radiation is given by v^ = y^. The 



path of the radiation in the three-dimensional Euclidian space specified 



by the Cartesian co-ordinates x, y, z is therefore the same as that of a 



2w 

 ray through a refracting medium in which ^ = y "^ = 1 H This 



path is a hyperbola with eccentricity approximately equal to 

 R/2m where R is the distance of perihelion. The deflection of the ray, 

 measured by the angle between the asymptotes of the hyperbola, is 

 ^m/R. 



This deflection which amounts to l"-74 for a ray grazing the limb 

 of the sun is double that which would be obtained by applying the 

 Newtonian theory to a particle moving through the field with the 

 velocity of light. 



The observations of the Solar Eclipse Expeditions of 1919 appear 

 to be generally accepted by astronomers as verifying the Einstein 

 prediction. The values of the deflections were estimated as 1"-61 

 with a probable error of 0"-3 at Principe, and l"-98 at Sobral. The 



