[EVE] PRESIDENTIAL ADDRESS 3 



rate of change of velocity, to escape analogous treatment. Further- 

 more the change of mass with velocity, at least for electrons, had been 

 demonstrated and measured in experiments such as Bucherer's. 



Einstein saw a man fall off a house. It started him on the 

 question of the Theory of Equivalence. It is noteworthy that Newton 

 considered the fall of a traditional apple as a preliminary to the Law 

 of Gravitation, but Einstein required the fall of a man from a roof in 

 order to formulate his theory of gravitation, the only theory so far 

 stated which has led to results which are verifiable, and have to some 

 extent been remarkably confirmed. 



The latest forms of Einstein's theory of Relativity and Equiva- 

 lence are to many physicists and mathematicians obscure, more 

 particularly as they involve a mathematical treatment with which few 

 have made themselves familiar. 



To a man going with the wind and at the same pace there is no 

 wind. To a man falling freely there is no gravity. A system moving 

 upward with acceleration g, when there is no gravity, is indistinguish- 

 able from a system without acceleration, when there is a gravitational 

 field with acceleration g. 



These ideas lead to the First Stage of the Final Form. The 

 results lead to a bending of light round the sun, but of magnitude but 

 one half of that foretold by the Second Stage, and verified by eclipse 

 observation. 



Consider that all phenomena must be independent of the observer 

 and of the system of axes. Use four dimensional space, Xi X2 X3 X4 

 being coordinates, and follow out relentlessly the invariants arising 

 from transformations. Translate your results into x, y, z, ct where t 

 is the time, and c the velocity of light. On translating your four 

 dimensional analysis into analogy with our three dimensional space 

 experience, there is a result indicating that in a gravitational field of 

 varying intensity light travels along a geodesic. The available path 

 is curved. Just so a sailor goes from Liverpool to New York not by 

 the shortest or straightest line, for it is not open to him. He is 

 confined to the surface of the sea and travels along a geodesic. His 

 whole geometry is that of great circle sailing. Of straight lines he 

 knows nothing, for there is no plane open to him. So I take it that 

 to light near the sun, in addition to the bending due to gravitation, 

 expected from the First Stage, there is an extra and equivalent bending 

 of light due to the quasi-bending of space. It was this forecast of this 

 double bending of the Hght of a star passing near the sun which was so 

 marvellous an achievement of Einstein. 



