39 (> Leigh Page, 



Consider for a moment a body moving in the geometric field 

 defined by (24). If the body's velocity is small compared to 

 that of light, the second term of this expression will be negligible 

 compared to the first. Moreover, h and k will never dififer much 

 from unity except in the case of extremely strong fields. There- 

 fore the quantity k plays much the part of the potential in ordi- 

 nary gravitational theory. As the derivative of h makes itself 

 felt in the case of greater relative velocities, it is natural to con- 

 sider both h and k as generalized potentials determining the 

 nature of the sfeometric field. 



(b) THE EQUIVALEXCE HYPOTHESIS. 



The equivalence hypothesis states that a permanent gravitational 

 field is identical zvith a geometric field produced by the acceler- 

 ation of the observer's reference frame relative to the bodies 

 observed. 



For example, consider an observer stationed out in space far 

 away from any gravitational field. Let there be present in his 

 neighborhood a number of bodies, wdiich, according to Newton's 

 first law of motion, are either at rest or moving in straight lines 

 with constant velocities. Now let the observer be given a constant 

 acceleration of 32 ft/sec". Not realizing that he is accelerated, 

 he will refer observations to a reference system carried along 

 with him, and conclude that all bodies observed have an acceler- 

 ation of 32 ft/sec- in the direction opposite to his true ( ?) 

 acceleration. So far as the motion of material particles is con- 

 cerned, this geometric field is exactly equivalent to the gravi- 

 tational field near the earth's surface. Now Einstein extends 

 this equivalence to all phenomena, and postulates that a gravi- 

 tational field is identical in all respects with a geometric field. 

 For instance, a ray of light would follow a curved path in a 

 geometric field of the type described. Hence it must be deflected 

 by a gravitational field. 



The above crude example is only very approximate, as no 

 account has been taken of dififerences in the geometry, standards 

 of length and time, etc. of the two mutually accelerated systems 

 mider comparison. A more exact investigation brings to light 

 manv difficulties. 



