The motion of the clocks as represented in a solution of the clock paradox offered by C. Miller is studied in detail. It is found that in the non-inertial rest frame of the accelerated clock the free clock suffers discontinuities in velocity whenever the "gravitational field" in that frame abruptly changes. Although these discontinuities occur at points of discontinuity of the metric tensor, examination of a case in which the gravitational field is turned on smoothly reveals that the effect is a real one within the framework of the general theory of relativity. By the principle of equivalence it follows that even in a real gravitational field when that field changes in time velocity dependent terms in the acceleration of a particle exist. These become impulsive for abruptly changing fields and can even cause an acceler¬ation in the direction "opposite" to the field.
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