Equilibrium conditions are determined for plasmas in toroidal vessels of the figure-of-eight type when the plasma containment time exceeds the time for penetration of the magnetic field through the solenoid windings. In this case some of the magnetic lines of force pass through the solenoid windings and return outside it. The cross-sectional radius of the extreme toroidal magnetic surface lying entirely within the vessel is therefore always less than the cross-sectional radius of the solenoid. When the plasma pressure exceeds some critical value there are no toroidal magnetic surfaces and containment of the plasma is in principle impossible.