in the dirac membrane model the repulsive electromagnetic forces on the membrane are balanced by the contracting ones coming from the positive tension. in the case of the spherical membrane, classical equations of motion imply that the balance is met for the radius formula_1, where formula_2 is the classical electron radius. using bohr–sommerfeld quantisation condition for the hamiltonian of the spherically symmetric membrane, dirac finds the approximation of the mass corresponding to the first excitation as formula_3, where formula_4 is the mass of the electron, which is about a quarter of the observed muon mass.