The theory of relativity shows that the times measured by two observers will in general be different if they are in relative motion, so that their respective times between any two coincidences will differ. Bergmann [1] has investigated the problem of a particle moving in a small simple harmonic motion in a static gravitational field, and has found that the time difference for this particle and an observer at rest becomes zero whenever the particle passes through the centre and limits of its swing. This problem will now be dealt with in a different manner, using Schwarzschild's interior solution of the gravitational equations. The exterior solution for a point mass is not suitable in the present case, due to the singularity of the field at a point in the path of the particle.