Richard Chace Tolman

“ Hence in order to accelerate a body in a given direction, we may apply any force in the desired direction, but must at the same time apply at right angles another force whose magnitude is given by equation (5) .
From a qualitative consideration, it is also possible to see the necessity of a component of force, perpendicular to the desired acceleration. Referring again to fig. 1, since the body is being accelerated in the Y direction, its total velocity and hence its mass are increasing. ”

“ If force is defined as the rate of increase of momentum, the equation
allows for a change in mass as well as a change in velocity. This is the fundamental equation of non-Newtonian mechanics [2] .
It has been shown from the principle of relativity [3] that the mass of a moving body is given by the equation
where is the mass of the body at rest and is the velocity of light. ”

“ Substituting in equation (1) we obtain
From an inspection of equations (1) and (2) it is evident that the force acting on a body is equal to the sum of two vectors, one of which is in the direction of the acceleration and the other in the direction of the existing velocity u, so that in general the force and the acceleration it produces are not in the same direction. ”