We consider how times of different clocks can be related to each other. The general relation that we obtain can be made more specific for situations that occur in the context of relativity theory. Our considerations concerning the kinematics of time lead to a modification of the Newtonian law. As a result, we obtain equations of movement that can also be deduced from general relativity theory if a Schwarzschild metric is assumed. The present derivation is significantly more simple than the orthodox general relativistic one. For instance, it does not make recourse to a four-dimensional space-time. We point out that different time coordinates must be considered, but spatial coordinates are left unchanged.