524 SCIENCE PROGRESS 



In studying natural phenomena we have hitherto started 

 off with a definite notion of the properties of space, namely, 

 the Euclidean. The various phenomena have been explained 

 on a mechanical basis in the sense that motion and changes 

 of motion considered vectorially have been referred to forces : 

 a considerable fraction of scientific work has in fact consisted 

 in the devising of systems of forces to explain the observed 

 motions, and in using these systems in order to predict motions 

 yet to iDe observed, leading to verification or modification of 

 the original hypotheses. 



The new theory reverses the procedure. We have no right 

 to postulate d priori the properties of space in which phenomena 

 take place. If we accept the fundamental notion of generalised 

 relativity, namely, the Principle of Equivalence, then our investi- 

 gations of natural phenomena, in so far as they relate to motion, 

 must not be directed towards the devising of systems of forces 

 which explain the observed motions in an already postulated 

 space, but must be directed rather towards the devising of a 

 space in which the motions observed are just as natural as 

 uniform motion in a straight line seems to be natural in a 

 Galilean frame of reference. We are accustomed to this kind 

 of investigation in ordinary mechanics, where many phenomena 

 are attributed to so-called centrifugal forces : in other words, 

 we explain the phenomena by showing that they are what we 

 would expect to obtain with reference to a frame which is not 

 at rest but moving in some assigned manner, as, for example, 

 rotating about a fixed axis. The theory of moving axes in 

 particle dynamics, and the complicated expressions obtained 

 for the linear and angular momenta of a rigid body when 

 referred to axes fixed in the body, are also familiar instances 

 of the same idea. Einstein's principle of equivalence is this 

 idea pushed to its logical extreme as far as gravitation is 

 concerned ; the motions that we are accustomed to refer to 

 gravitational forces are now to be explained by assuming 

 properties of space defined by these very motions. Henceforth 

 the motion of a body in space does not define the forces acting 

 on the body, but the properties of the space in which the 

 body moves. 



It follows at once that the classical laws of motion need 

 revision if we accept the principle of equivalence : we refer to 

 the first and second laws. The second law disappears as a 

 separate law. The principle of equivalence eliminates the 

 objective existence of all forces, gravitational as well as centri- 

 fugal, and the first law of motion must be restated in a modified 

 form so as to include the second law. The two laws are con- 

 densed into the single statement that the path of a particle is 

 along a geodesic in the space in which it moves. 



