The results strongly suggest that the Fermi surfaces for copper, silver and gold make contact with the eight [ 111] faces of the Brillouin zone (B.Z. ). Thus the de Haas-van Alphen effect demonstrates that the general shape of Fermi surface proposed by Pippard (1957) for copper applies also to silver and gold. Except when-the small departures from sphericity are of importance a convenient simplified model of this surface is a sphere (the 'belly') with eight short cylinders ('necks') protruding from it along the [111] directions to meet the hexagon faces of the B.Z. normally. The B.Z. can of course be thought of as the unit cell of an infinite lattice in which each cell contains a Fermi surface of the kind just described. \Ve thus have a complicated multiply-connected surface and corresponding to any closed circuit of extremal area (which encloses either holes or electrons) produced by pla~es cutting the surface normally to the magnetic field direction, there should be de Haas-van Alphen oscillations of a period

106D.Shoenbergonthe

inverselyproportionaltotheextremalarea.Itturnsoutthatthereis quiteavarietyofpossibleextremalcircuitsandthecorresponding deHaas-YanAlphenoscillationsforsomeofthesehavebeenobserved.