Einstein's declared reason for postulating the special relativity time lag is the maintenance of the constancy of c. When the hypothesis of the Lorentz contraction is followed to its mathematical consequences, it leads to a dilatation of the path of light and therefore an apparent decrease of its speed. The special relativity time lag seems to have been conceived as a correction for this, just as the gravitational time lag seems to have been conceived to counteract the consequences for c of a gravitational frequency shift. This gravitational effect as originally postulated would have implied a change in the speed of light. This hypothesis was later modified by Einstein by the introduction of another time lag intended to shelter such a variation of c at the surface of a gravitational body from detection. Thus a detectable gravitational frequency shift at the surface of the Earth militates against a gravitational time lag: the two hypotheses are mutually exclusive. In addition, the presence of two separate and distinct time lags at the same site is paradoxical. To reduce the two to one by algebraic addition undermines the constancy of c and obviates the effect for which these lags were created. A time lag presupposes an alteration in rhythm of all surrounding physical phenomena, not just in the rate of the clock. All research on the subject should be assessed with the above principles in mind.