Page:TolmanNon1.djvu/2

 velocity. This is the fundamental equation of non-Newtonian mechanics.

It has been shown from the principle of relativity that the mass of a moving body is given by the equation

$m=\frac{m_{0}}{\sqrt{1-\frac{u^{2}}{c^{2}}}},$|undefined

where $$m_0$$ is the mass of the body at rest and $$c$$ 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 $$d\mathsf{u}/dt$$ 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. If the force which does produce acceleration in a given direction he resolved perpendicular and parallel to the acceleration, it may be shown that the two components are connected by a definite relation.