Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/200

 Χwhere

here i denotes the angle of incidence, ρ the inertia of the aether, and n its rigidity.

Let the reflected light be a function of the argument

where, in order to secure continuity at the boundary, b and c must have the same values as before. Since Green's formulae are to be still applicable, we must have

where $$\sin i = \mu \sin r$$, but μ has now a complex value. This equation may be written in the form

Let the complex value of μ2 be written

the real part being written ρ1/ρ in order to exhibit the analogy with Green's theory of transparent media: then we have

But an equation of this kind must (as in Green's theory) represent the condition to be satisfied in order that the quantity

may satisfy the differential equation of motion of the aether; from which we see that the equation of motion of the aether in the metallic medium is probably of the form

This equation of motion differs from that of a Greenian