The conductivities of body-centred (b.c.c.) and face-centred (f.c.c.) cubic lattices of spheres of a conducting material in a conducting matrix are calculated by using a method originally devised by Lord Rayleigh. Measurements of the conductivity of the b.c.c. lattice of perfectly conducting spheres are presented. Good agreement between theory and experiment is obtained. Our results are shown to be in agreement with asymptotic equations derived by other authors. A formula is given for the case of a disordered array.