32 Journal of the Mitchell Society ISrpfcDihrr 



Einstein, after long investigation, has so chosen his equations that 

 they remain unaltered by any change of co-ordinates, and these ten 

 are the only ones which do satisfy all conditions. What has just been 

 said illustrates Einstein's famous "Principle of Equivalence," which 

 states that for any particle at any instant it is possible to replace the 

 effect of a gravitational field upon it by a mathematical transforma- 

 tion of axes. 



If, therefore, gravitation can be annihilated mathematically by 

 a transformation to an accelerated set of axes, and if its very existence 

 depends upon a choice of axes, which is contrary to the General Rela- 

 tivity Postulate, then gravitation, in the words of deSitter, "becomes 

 almost a property of space." 



Of course a first approximation from Einstein's (■({nations, neg- 

 lecting terms of higher orders, gives the old Newtonian law for com- 

 paratively small velocities. Please notice, however, that Einstein's 

 theory only shows how gravitation acts, not what causes it to act thus. 

 It is in no sense an explanation of gravitation, which remains as 

 much of a mystery as before. Now a new theory, like a tree, is known 

 by its fruits, and when Einstein was asked to make his theory do 

 things to prove its truth he was at first perplexed to find cases in 

 which the actual differences between his theory and that of Newton 

 could be subjected to observation. 



But he was not long at a loss, and presented three eases which 

 would test the correctness of his theory. The first case was the long 

 outstanding discrepancy between theoiy and observation shown in the 

 displacement of the perihelion point of Mercury's orbit. This point 

 shifts around toward the east at the rate of 574 seconds of arc per 

 century. The Newtonian mechanics, allowing for the effect of the other 

 planets on Mercury's orbit, accounts for a shift of only 532 seconds, 

 thus leaving an unexplained shift of 42 seconds of arc per century. 

 Einstein's theory calls for a difference of 43 seconds, — an almost 

 startling agreement. But of course Einstein might have started with 

 this answer, and worked backwards, as it were, to his equations, so 

 a great deal more interest was taken in his second case : a prediction 

 that at the eclipse of the sun on May 29, 1917, the light of certain 

 stars which just grazed the sun on its way to the earth would be found 

 to have a deviation from a straight path because of the sun's gravita- 

 tional field which he estimated would amount to 1.75 seconds of arc. 



