In 1871, Josef Stefan published a diffusion model that later became one of the fundamental models of transport phenomena, the Stefan-Maxwell (sometimes called the Maxwell-Stefan) diffusion relation. In his last paper on diffusion, which appeared in 1889, Stefan treated the evaporation-diffusion process in a vertical tube with a moving interface, and gave a complete analytical solution to this problem. This process - known as the Stefan diffusion problem - is frequently referred to in the literature. However, Stefan's own solution to this problem is not mentioned, and its existence seems to be unknown in scientific circles. The present note reproduces the Stefan's treatment of that evaporation-diffusion process. (C) 2012 Elsevier Ltd. All rights reserved.