In 1915 Parson proposed the so-called ring model for the electron. This flat geometry for the electron can also be interpreted as a superposition of two orthogonal harmonic oscillators in the same plane. For these two harmonic oscillators a new relativistic Lagrangian is conjectured from which Hooke’s law follows. Explicit expressions for the spring constant and electron energy are deduced from this simple ring model.

Spring constants and energies for all leptons can also be deduced from the recently postulated more complex toroidal model for leptons. The ring torus model appears to apply to charged leptons and the electron neutrino, whereas the spindle torus model may apply to the muon and tauon neutrino.

It appears that the magnetic dipole moments of the charged leptons predicted by the toroidal model agree with the observed ones, first order anomalous corrections included. Furthermore, explicit expressions for the magnetic dipole moments of all neutrinos are also obtained.

Moreover, a comparison is made between the magnitude of the electromagnetic and elastic contribution to the energy of the electron. It is found that the elastic energy may be dominant.