Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/442

 position and motion of the charges, satisfy the Maxwellian equations

The theory of Lorentz is based on these four aethereal equations of Maxwell, together with the equation which determines the ponderomotive force on a charged particle; this, which we shall now derive, is the contribution furnished by Clausius' theory. The Lagrangian equations of motion of the electron are

and two similar equations, where denotes the total kinetic potential due to all causes, electric and mechanical. The ponderomotive force exerted on the electron by the electromagnetic field has for its -component

or

which, since

reduces to

or so that the force in question is

This was Lorentz' expression for the ponderomotive force on an