152 Prof. R. 0. Tolman on 



equations that, if a point has a uniform acceleration (£, y, z) 

 with respect to an observer in system S, it will not in general 

 have a uniform acceleration (%', y' ', '%') in another system 

 S', since the acceleration in system S' depends not only on 

 the constant acceleration but also on the velocity in system 

 S which is necessarily varying. 



We may next obtain transformation equations for a useful 



function of the velocity, namely, ~~j~ ~~, where we have 



placed q 2 = x 2 + y 2 -f i 2 . By substitution of equations (6), 

 (7), and (8) and simplification we obtain 



Vl-?'7e 2 "" Vl-^/c 2 



• • • (12) 



It has been shown in an earlier article* that the prin- 

 ciples of non-Newtonian mechanics lead to the equation 



m = , 2/ 2 for the mass of a moving body, where m is 



the mass of the body at rest and q is its velocity. By sub- 

 stitution of equation (12) we may obtain the following 

 equation for transforming measurements of mass from one 

 system of coordinates to the other: 



m'=^l-^f W, (13) 



where m is the mass of the body and x the X component of 

 its velocity as measured in system S and m! its mass as 

 measured in system S'. 



By differentiation of equation (13) and simplification we 

 may obtain the following transformation equation for the 

 rate at which the mass of a body is changing owing to change 

 in velocity : 



. , . mv .. / \ vi\ -1 /1IX 



m'=m— -jf*ll— jj-J (14) 



x and j? are the X components of the velocity and acceleration 

 of the body in question as measured in system S. 



We are now in a position to obtain transformation 

 equations for the force acting on a particle. The force 



* Phil. Mag. xxiii. p. 375 (1912). 



