An investigation is made into the structure of the umbra of a single circular spot which is in quasi-static equilibrium. The coolness of the spot surface is supposed due to the magnetic field, which both cuts down the efficiency of convective transport of energy and at the same time reduces the surface flux by channelling the convection parallel to the field. The centre of the spot surface is found to lie about 500 km below the normal surface. A consistent umbral model can be produced in which, as the ratio of the magnetic to the thermal energy density decreases with depth, the temperature and the density in the spot approach the corresponding physical values in the undisturbed layers at the same depth ; the flux increases to the normal solar value ; and the reduction in the efficiency of convection vanishes.