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values I, 2, 3, 4 independently ; but they actually reduce to 

 2o conditions, Einstein recognised that space-time is not 

 " flat," i.e. the transformation to quasi-Cartesian co-ordinates 

 is not in general possible, so he proposed as a guide to the 

 determination of the ^-coefficients that outside matter they 

 should satisfy the differential equations 



XBx'a-o (2) 



where Bx% is a symbol employed to denote the left-hand side of 

 the equation (i). Equations (2) are clearly less stringent than 

 ( I ). The values of the ^-coefficients corresponding to ' ' fictitious ' * 

 fields, satisfying (i) as they do, would, of course, also satisfy (2) ; 

 but (2) would also include possibilities wider than those admitted 

 by (i) ; and Einstein's assumption is that these correspond to 

 " real " fields which cannot be resumed under (i). Equations 

 (2) are generally written in the form 



Oxy. = o. {2a), 



On account of the equality of G^^ and G^^x there are ten of them. 

 For points within matter, Einstein has proposed the equations 



Gx^ = Ux;. (3), 



where Ux^ are another set of ten quantities calculated from the 

 density of the matter, its momentum and energy. Owing to 

 the form of the ten expressions Gx^ it can be proved that they 

 satisfy four conditions, and, when they are replaced by Ux^ in 

 these conditions, four equations are obtained which are simply 

 the laws of conservation of energy and momentum. Thus 

 Einstein's complete Law of Gravitation, (3) (viz. the equality of 

 the " gravitational tensor " and the " matter-tensor ") are really 

 a set of dynamical equations in which gravitational effects are 

 inherent and not imposed by external " forces." Another 

 important feature is that if we replace x^, x^, x^, x^ by any four 

 functions of these in 



ds* " i" gap dxa dxp, 



I 



so that we obtain a new set of ^-coefficients ; and if at the 

 same time we make the necessary changes in the energies and 

 momenta in Ux^ corresponding to a new frame of reference, 

 the new ^-coefficients still satisfy equation (3) ; so the principle 

 of General Relativity is quite satisfied. 



This brief r^sum^ may serve to show what is meant by the 

 statement that Relativity has led to the " geometrisation " 

 of physics. But there is one point lacking in the complete 

 geometrisation. We can illustrate it by the example of the 



