( 592 ) 



§ 2. We shall always consider a gaseous body. Let, in any point 

 of it, 'S. be the electric force, Sp the magnetic force, ''P the electric 

 polarization and 



S = € + ^13 (1) 



the dielectric displacement. Then we have the general relations 

 ö.Dr ö.fp,; _ 1 dSx öJp., d.^- _ 1 d^,, 

 dy dc c dt ' ds da; c dt 



dS?, d^, 1 Ö2). 

 d.v oy c ot 



0®, _ ö£,, _ _ J_ 0^ ^- _ ^ _ _ J_ ^/ 

 dy dz c dt dz d,v c dt 



d.v dy c dt ^ 



ill which c is the velocity of light in the aether. 



To these we must add the formulae e.'ïpressing the connexion 

 between £■ and '^, which we can find by starting from the equations 

 of motion for the vibrating electrons. For the sake of simplicity we 

 shall suppose each molecule to contain only one movable electron. 

 We shall write e for its charge, in for its mass and (x, y, z) for 

 its displacement fi'oni the position of equilibrium. Then, if N is the 

 number of molecules per unit volume, 



%\. =r .V e X, %\, = N e y, p. = A' e z (4) 



§ 3. The mo\able electron is acted on by several forces. First, 

 in virtue of the state of all other molecules, except the one to which 

 it belongs, there is a force whose components per unit charge are 

 given by ') 



« being a constant that may be shown to ha\'e the value Vi i" 

 certain simple cases and which in general will not be widely different 

 from this. The components of the first force acting on the electron 

 are therefore 



e(e, + «iV), e(^,, + a%\,), e((v. + «p,-) ... (5) 

 In the second place we shall assume the existence of an elastic 

 force directed towards tiie position of equilibrium and proportional 

 to the displacement. We may write for its couiponents 



— /x. — ,/'y, -./'z (6) 



/ being a constant whose value de|)euds on the nature of liie molecule. 



') LoRENïz, Math. Encycl. Rd. 5, Art. 14, §g 85 and ;^G. 



