This article employs a one-dimensional diffusion model to study the phenomenon of electromigration-induced edge drift in a finite, Al-Cu thin-film conductor. Edge drift is caused by the accumulation of vacancies at the negative (upstream) terminal of the conductor as Al diffuses with the electrical current. When the Cu content exceeds its solubility limit, grain boundaries are decorated with Al2Cu precipitates, which must be dissolved before significant Al diffusion occurs. Assuming one-dimensional flow in a homogeneous, polygranular film, we compute the rate of growth of the precipitate-free zone at the upstream terminal, and estimate the incubation time for the onset of edge drift. The results predict an incubation time that increases with the grain size and the initial Cu content, and decreases with the square of the current density. The incubation time is inversely proportional to the ''electromigration diffusivity'', D-E=D-B(Cu) delta Z*(Cu), the product of the grain boundary diffusivity of Cu, the effective grain boundary thickness, and the effective valence of the Cu ion. The results are used to compare a number of prior experimental studies, which are shown (with one exception) to produce consistent values for D-E. An analysis of the experimental results suggests that edge drift begins almost as soon as the precipitate-free zone length exceeds the ''Blech length'' for the line, suggesting that the presence of Al2Cu precipitates in the grain boundaries is essential to retard Al electromigration.