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The $\epsilon$ ring is the widest and most eccentric of the Uranian rings, with two attendant shepherd satellites which serve to keep the ring sharp-edged and confined. Using nearly 50 high SNR occultation profiles of the $\epsilon$ ring obtained between 1977--1993, we have searched for waves in the outer and inner edges of the ring with the expected pattern speeds, amplitudes, and phases predicted by shepherding theory. Important consistency checks are that the longitude of the maximum or minimum of the disturbance be aligned with the corresponding shepherd satellite in its orbit, that the pattern speed be within the uncertainties in the satellite's mean motion, and that the amplitude of the edge wave be comparable to theoretical predictions. All of these tests are passed for both edge waves. In the fit for the 14:13 inner eccentric resonance of Ophelia with the outer edge of the $\epsilon$ ring, the observed edge wave amplitude is $0.5\pm0.2$ km, compared to the predicted value of $A_L^{1/2}$=0.58 km, the longitude of the wave is $297.58\pm1.20^\circ$ compared to the satellite longitude at epoch of $298.369\pm0.072^\circ$, and the fitted pattern speed of the wave is $956.41707\pm0.00095^\circ$ d$^{-1}$, compared to the satellite mean motion of $956.4068\pm0.0374^\circ$ d$^{-1}$. For the inner edge, the 24:25 outer eccentric resonance with Cordelia gives a predicted edge wave amplitude of $A_L^{1/2}$=0.48 km, compared to the best fit of $0.6\pm0.15$ km. Thus, there is good reason to believe that edge waves are present in the $\epsilon$ ring, but post-fit residuals remain larger than measurement uncertainties, and other physical effects may be at work. Longaretti and Rappaport (Icarus 1994) developed a theory for the viscous excitation of coupled libration modes in planetary rings, and they pointed out that the eccentricity and pericenter of the $\epsilon$ ring undergo librations with periods on the order of several years and amplitudes $\sim0.3$ km. Because edge waves and librations have comparable amplitudes in orbital radius, both must be included when searching for the librations. We will present the results of these searches, along with Monte Carlo experiments to measure the robustness of our findings. This work was supported in part by NASA grants NAGW-1368 and NAGW-544.
