and corresponding Gravitational Fields. 



707 



where e is a constant, Substituting this value of J$ m 

 the first equation, we obtain 



and taking a, to be an angular velocity we have the equations 

 of motion in a centrifugal field. < _ , 



In the manifold (4) the non-vanishing Ohnstottel ex- 

 pressions are 



T 3 13 = - and r' 33 = —j. 

 The equations of motion (8) become 



d?r r /#V =0 

 1 ds 2 A \ds J 

 d 2 6 , 2 dr dtf> _ n 



ds 



cZs ds 



as 3 



d 2 t 



— = 0. 



(^ 2 



(9) 



If, instead of <£ we use <//, where 

 </> = \/A(//, 

 the equations (9) become 



ds* u ' 



« = 0. 



ds 2 



AVe may therefore regard equations ( ( .)) as the equations 

 of motion of a particle moving with uniform velocity in a 

 straight line with respect to 'an inertia system (r, z 9 <j>'), 



