Following Ritchie, the anomalous characteristic energy losses of energy lower than the plasmon energy, exhibited by some metals, are attributed to quantized surface waves of the degenerate electron gas. Although Ritchie's theory has been verified for an ideal pure metal surface by Powell and Swan by reflection of high-energy electrons, the transmission experiments show a lower energy loss generally. This is accounted for by taking into account the relaxation produced by the oxide coating on the surface of the metal. In this way, the experimental data is completely accounted for without the assumption of any anomalous bulk dielectric properties of the metal. The present paper studies the dependence on thickness of the oxide coating, and it is found that a surprisingly thin coating, say only 20 angstroms thick, can produce a significant effect. It is established that a measurement of the dispersion of the energy loss versus angle of scattering in the transmission experiment would yield a measurement of the oxide film thickness. A further check on the theory is suggested by a measurement of the angular dependence of the intensity of the lowlying characteristic energy loss. A special effect is predicted for non-normally incident fast electrons. It should be found that the intensity pattern should flare away from the plane of incidence. Besides these special angular effects it is predicted that because of the sensitivity of the surface plasma oscillations to any surface coating the value of the surface characteristic energy loss can be varied between wide limits by choosing the appropriate coating. In particular, making double films of two different metals should produce surface characteristic energy losses in between the bulk characteristic energy losses of the two separate metals.