RECENT ADVANCES IN SCIENCE 561 



magnetic origin, there would be no difficulty, as mentioned 

 above ; but it is a commonplace that gravitation has hitherto 

 obstinately withstood any attempt to bring it within the 

 electromagnetic scheme. 



It was in 191 1 that Einstein published his first work attempt- 

 ing to bring gravitation into conformity with Relativity, by 

 extending the principle so as to cover systems of reference 

 in variable motion to one another for which the postulate 

 enunciated above is still supposed to hold. The equations 

 connecting the measurements made in one system of reference 

 with those made in another are naturally more complicated 

 than the linear ones written above. In fact, from the purely 

 mathematical point of view, for any four equations connecting 

 x' y' z' t' with x y z t however complex, we could conceive two 

 systems of reference whose metrical relations would be formu- 

 lated in the equations. As physicists, however, we are con- 

 cerned solely with such equations of transformation as would 

 transform the mathematical equations for some complex 

 physical phenomenon when expressed in terms of measure- 

 ments made in one frame of reference to a simpler mathematical 

 form when expressed in terms of measurements made in another 

 frame. What Einstein ultimately succeeded in doing (Annalen 

 der Physik, 191 6) was to give a criterion for such transformations 

 as are of service to us in the investigation of natural phenomena 

 constituting only one portion (but to physicists the vital por- 

 tion) of all conceivable transformations. The criterion is 

 embodied in a group of differential equations which are usually 

 referred to as Einstein's " law " of gravitation. One simple 

 illustration will give some idea of the application of his method 

 to the problem of phenomena in the neighbourhood of a single 

 gravitating centre. A group of observers moving in any 

 path under the action of the centre would observe that the paths 

 of all bodies in their immediate neighbourhood would for the 

 time being be straight, because observers and bodies would be 

 experiencing the same acceleration towards the centre with 

 reference to axes whose origin is at the centre. Of course, 

 distant bodies would not be moving in straight paths relative 

 to the observers (because in different parts of the field the 

 accelerations are different), and the bodies at the moment 

 adjacent would in time separate from the observers and 

 lose the property of rectilinear motion relative to them. Still, 

 for proximate bodies the frame of reference natural to these 

 observers is one in which motion is the simplest possible — 

 uniform ; and so this frame is equivalent to one in which force 

 is absent ; i.e. we " transform away " the gravitation of this 

 centre in our immediate neighbourhood by choosing such axes, 

 and obtain a very simple equation for an element of an orbit. 



