The young student found some literary occupation and a little teaching in Edinburgh, and sometimes he was asked to make investigations in subjects connected with applied chemistry. Thus he struggled on for four or five years, during which time he began to publish papers on chemico-physical subjects. In the year 1829 he was appointed Lecturer on Chemistry at the Mechanics' Institution in Glasgow, and next year he was removed to the more important position of lecturer on the same science at the Andersonian Institution in that city. This position he occupied for seven years, when he was elected Professor of Chemistry in the University of London (now University College): he had been elected to the Fellowship of the Royal Society in the preceding year. During his stay at the Andersonian Institution Graham had established his fame as a physical chemist; he had begun his work on acids and salts, and had established the fundamental facts concerning gaseous diffusion. These researches he continued in London, and from 1837 to 1854 he enriched chemical science with a series of papers concerned for the most part with attempts to trace the movements of the atoms of matter. In 1854 Graham succeeded Sir John Herschel in the important and honourable position of Master of the Mint. For some years after his appointment he was much engaged with the duties of his office, but about 1860 he again returned to his atomic studies, and in his papers on "Transpiration of Liquids" and on "Dialysis" he did much in the application of physical methods to solve chemical problems, and opened up new paths, by travelling on which his successors greatly advanced the limits of the science of chemistry. Graham was almost always at work; his holidays were "few and far between." By the year 1868 or so his general health began to grow feeble; in the autumn of 1869, during a visit to Malvern where he sought repose and invigorating air, he caught cold, which developed into inflammation of the lungs. On his return to London the disease was overcome by medical remedies, but he continued very weak, and gradually sank, till the end came on the 16th of September 1869.