The surface diffusion coefficients (D_s) for Au^(198) on (100) and (111) surfaces of copper have been determined between 1050˚and 780℃ using a new analysis and experimental procedure. The results are ; (111) : D_s (Au)=2.1×10^5 exp (-51,100/RT) sq cm per sec. (100) : D_s (Au)=3.6×10^5 exp (-52,000/RT) sq cm per sec. D_s has also been determined for Cu^(64) at 870℃ and the values found are 4.5 times larger than these by the grain boundary grooving technique for the same surface orientations. This difference is felt to result from the approximate nature of the mathematical solution used in the present work. Attempts to measure D_s for silver on copper and silver surface indicated a means of matter transport different from surface diffusion was dominant in missing tracer from the source out over the surface. Calculations and experiment both indicate that this is the flow of silver through the vapor phase which completely masks the much smaller flow due to surface diffusion. The previous self-diffusion studies of D_s for silver and copper are discussed in terms of our own analysis and found to yield values of D_s factors of 10^5 or more greater than found by the grain boundary grooving technique.