388 



Dr. L. Silberstein on a Time-Scale 



£lt will be lines of constant date and of constant (or fixed) 

 place, respectively*. 



Fiff. 2. 



There is no difficulty whatever in extending this coordinate 

 system to the three-world (o?,y,t) or to our full world (x,y,z,t). 

 But our chief object being not so much space as time itself 

 or in connexion with any one of the space-dimensions, we can 

 continue to confine ourselves to a bidimensional world. 



With this system of projective coordinates the equation of 

 any right world-line, i. e. the equation of uniform motion, will 

 obviously be a linear equation a.v + bt-t-c = Q, which we will 

 conveniently write 



a?=tfo + ^, (1) 



,r , v being constants. If the reader likes to have a name, 

 he may call v the projective velocity of the particle whose 

 motion is represented by (1). More generally, if x=f(t), 

 with/ standing for a o>?<?-valued function, be the equation of 

 motion, d,r/dt=f (t) will be tbe instantaneous projective 

 velocity. Thus, uniform motion will be characterized by 

 a constant projective velocity, as in metrical kinematics 

 (if this be of the kind to be called hereafter parabolic). 

 We can now say that equal ^-intervals are those during 

 which a uniformly moving particle covers equal numbers of 



* The coordinates of Q. x , £l f and of any point of their join 12 will be 

 infinite. We could provide for these world-points by introducing 



homogeneous 

 purpose. 



coordinates. But we shall not need them for our 



