The Medal was inaugurated in 1827 as a result of a gift from Alexander Keith of Dunnottar, the first Treasurer of the Society. It was awarded quadrennially, alternately for a paper published in: Proceedings A (Mathematics) or Transactions (Earth and Environmental Sciences). The medal bears the head of John Napier of Merchiston.
1849–51: Philip Kelland,[4]on General Differentiation, including his more recent Communication on a process of the Differential Calculus, and its application to the solution of certain Differential Equations
1859–61: John Allan Broun, on the Horizontal Force of the Earth’s Magnetism, on the Correction of the Bifilar Magnetometer, and on Terrestrial Magnetism generally
1881–83: Sir Thomas Muir,[4]Researches into the Theory of Determinants and Continued Fractions
1883–85: John Aitken,[6]on the Formation of Small Clear Spaces in Dusty Air
1885–87: John Young Buchanan,[2]for a series of communications, extending over several years, on subjects connected with Ocean Circulation, Compressibility of Glass, etc.
1899–1901: Hugh Marshall,[4]for his discovery of the Persulphates, and for his Communications on the Properties and Reactions of these Salts
1901–03: Sir William Turner,[4]for A Contribution to the Craniology of the People of Scotland and Contributions to the Craniology of the People of the Empire of India
1903–05: Thomas Hastie Bryce,[2]for his two papers on The Histology of the Blood of the Larva of Lepidosiren paradoxa
1905–07: Alexander Bruce,[4]on the Distribution of the Cells in the Intermedio-Lateral Tract of the Spinal Cord
1907–09: Wheelton Hind, On the Lamellibranch and Gasteropod Fauna found in the Millstone Grit of Scotland
1909–11: Alexander Smith,[4]for his researches upon Sulphur and upon Vapour Pressure
1911–13: James Russell,[4]for his series of investigations relating to magnetic phenomena in metals and the molecular theory of magnetism