422 The Theory of Aether and Electrons in the 



position and motion of the charges, satisfy the Maxwellian 

 equations 



div d = 47rc 2 / o, 



div h * 0, 



curl d = - K, 



curl h = d/c 2 + 47r/ov. 



The theory of Lorentz is based on these four aethereal 

 equations of Maxwell, together with the equation which deter- 

 mines 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 e are 



^-0 



fa- 



and two similar equations, where L denotes the total kinetic 

 otential due to all causes, electric and mechanical. The 

 ponderomotive force exerted on the electron by the electro- 

 magnetic field has for its ^-component 



dx ~ dt\ dx 

 or 



fda x . da v . da z . d<t>\ da x 



e{ x + - it H z c*} e '- 



\dx dx* dx dxj dt 



which, since 



reduces to 



- e I & -^ 



or ed x + e (yh z - z 



so that the force in question is 



ed + e [v . h]. 

 This was Lorentz' expression for the ponderomotive force on an 



