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The possibility that the velocity of light, c, is not a fixed constant is reconsidered by statistical analysis of the historical measurements collected from four sources. Our hypothesis testing of the selected data shows the measured value of the velocity of light to have decreased over the past 250 years. Furthermore, the probability of some systematic or experimental problem was found to be low. Brief analysis of constants other than c suggests that those constants which involve atomic phenomena and units of time are also apparently changing. A third set of constants with no obvious dependence on c were analyzed and show no apparent variability with time. A variable velocity of light implies that atomic clocks and dynamical clocks do not run in step -- that atomic time has been decreasing with respect to dynamical time.