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In this thesis an experiment to detect anisotropies in the one-way velocity of guided electromagnetic waves and a theoretical model to interpret these anisotropies is presented. The experiment utilized the rotation of the earth to rotate the propagation path of a pulse train generated by a Cesium atomic clock via an environmentally controlled coaxial cable to a second Cesium clock. The second Cesium clock generates an identical pulse train and both are then compared at a time interval counter located near the second clock. Ideally, the difference in arrival times of the two corresponding pulses, one from each clock, represents the arbitrary initial synchronization of the two clocks and the one-way time of flight of the pulse generated by the first clock. Any variation in the time of flight is detected as a modulation superimposed on a constant offset in the differences of arrival times as measured by the time interval counter. In practice, along with the aforementioned offset and modulation, phase noise due to clock instabilities require that coherent summing techniques be used to increase the single day signal to phase noise (S/N) of 1/10 to an acceptable level. A sidereal based coherent sum of 147 days of one -way data results in the possible detection of a 80 ps peak amplitude sinusoidal modulation with a S/N of 1.2:1. The sidereal coherent sum for 75 days of roundtrip data, taken simultaneously with the one-way, yields no coherent signal with a period equal to the fundamental summing period having an amplitude greater than 5 ps. The solar based coherent sum of the identical one-way and roundtrip data results in no detectable sinusoidal modulation in the one-way data similar to that seen in the sidereal sum. The roundtrip sum detected a solar modulation consistent with the temperature related electrical length variations of the cable with a peak amplitude of 20 ps. An interpretation of these results through the theoretical model presented indicates the possible presence of an absolute velocity component in the equatorial plane parallel to 85(DEGREES) from the autumnal equinox greater than our orbital velocity of (TURNEQ) 30 km/sec.