An account is given of a method of employing differential gas thermometers to measure the thermal conductivity of metals at low temperatures, with temperature differences of only 0$\cdot $02 degrees K in the specimen. Experimental curves are presented showing the variation of thermal conductivity with temperature between 1$\cdot $7 and 4$\cdot $3 degrees K for pure tin, alloys of tin with mercury, pure mercury, alloys of mercury with cadmium and indium, pure indium and pure tantalum, in both superconducting and normal states. The normal conductivity of strain-free specimens containing less than about 0$\cdot $1% of impurity appears to be mainly electronic, and to behave roughly in accordance with the theory of Wilson, although notable discrepancies arise in the detailed application of this theory. The ratio of superconducting to normal thermal conductivity varies with temperature roughly in the manner suggested by Heisenberg when the electrons are mainly scattered by impurities, but follows a radically different curve, for which no theoretical explanation is yet available, when lattice vibrations are the dominant scattering mechanism. For impurity contents greater than 0$\cdot $1%, or severe internal strains, the normal thermal conductivity contains an appreciable lattice component. The behaviour of the superconducting curve suggests that where crystal boundaries scatter the lattice waves, the lattice conductivity is unaltered as the metal passes from the superconducting to the normal state, but where electrons scatter the lattice waves, the lattice conductivity is reduced in this transition, possibly because of the increase in the number of scattering centres.