594 



Leigh Page, 



Hence, to an observer in S, the velocity of a point in S' is 



given by / 



v= — icn tan - 



a 



ct 



ct 



= C 



and its acceleration by 



(i8) 



J = c sec /I >, - tan — 



\a a dx a 



= C 





(19) 



In a similar manner it may be shown that the acceleration of 

 a point in S, relative to system S', is given by 



/' 



('-?y^ 



(20) 



where 7 is a positive constant. 



The expression (19) gives the acceleration which bodies at 

 rest in S' , or in a system reciprocal to S', appear to have relative 

 to an observer in S. This apparent acceleration is due to the 

 fact that system 5" is itself accelerated relative to S' , and conse- 

 quently an observer fixed in 6" finds that bodies at rest in S' are 

 accelerated in the opposite direction when referred to his refer- 

 ence frame. The observer, not realizing that this apparent ac- 

 celeration is due to his own motion, may attribute it to a field 

 of force. Such a field of force is known as a geometric field. 



Now, the world line of a particle at rest in S', or in a system 

 reciprocal to S', is a straight line in the X Y Z L four dimensional 

 space. As a straight line is the shortest distance between two 

 points, it is defined by 



^j\h = o. (21) 



