The heights of nuclear potential barriers are derived from experimental data, corrected for nuclear motion and penetration through the barrier. Barriers differ markedly for different incident particles. It is shown that the heights of barriers to alpha-particles increase with atomic number and that the nuclear radius at the top is proportional to the cube root of the atomic weight. Values for corresponding barrier radii of the neutron and the radioactive elements agree with those given by Dunning and by Gamow. It is suggested that the attraction operative in alpha-particle collisions is only a second order force and that the anomalies in proton barriers are due to a first order force effective much further outside their tops. A method for obtaining information about this force is suggested. The energies of resonance levels are tabulated and an approximate linear increase with atomic number is discussed.