The thermal and electrical magnetoresistance tensors are expected to depend in identical ways on the electronic structure of a metal provided that scattering is predominantly elastic. It is shown that the lattice contribution to the thermal conductivity tensor can be neglected in copper at 2°K up to a field of 10
6
G, and that there are experimental reasons which suggest the thermal effect to be more amenable to accurate experimental investigation than the electrical one. The expected details of the electrical Hall effect in and around high symmetry directions are discussed in terms of the extended zone Fermi surface, and it is shown that the high field limits of the Hall coefficient with magnetic field exactly along the high symmetry directions are very simply related to a caliper dimension of the Fermi surface necks. Experimental techniques using carbon resistance thermometers and of making accurately placed thermal contacts to a copper crystal are described, and are followed by the results obtained in two samples, of resistance ratio 1600 an d 7000, in fields up to 40 kG. The open orbit dominated behaviour expected for the electrical effect near the high symmetry directions is satisfactorily confirmed in the thermal experiment, but the high field limits of the coefficients exactly along the symmetry directions do not agree at all well with the calculations, particularly in <111>. It is clearly necessary to measure the electrical and thermal effects in the same sample to check the validity of the Wiedemann-Franz law.