For the free aether the velocity has the value c. Now it had been found that the ratio c between the two units of electricity agrees within the limits of experimental errors with the numerical value of the velocity of light in aether. (The mean result of the most exact determinations[17] of c is 3,001·1010 cm./sec., the largest deviations being about 0,008·1010; and Cornu[18] gives 3,001·1010 ± 0,003·1010 as the most probable value of the velocity of light.) By this Maxwell was led to suppose that light consists of transverse electromagnetic disturbances. On this assumption, the equations (16) represent a beam of plane polarized light. They show that, in such a beam, there are at the same time electric and magnetic vibrations, both transverse, and at right angles to each other.
It must be added that the electromagnetic field is the seat of two kinds of energy distinguished by the names of electric and magnetic energy, and that, according to a beautiful theorem due to J. H. Poynting,[19] the energy may be conceived to flow in a direction perpendicular both to the electric and to the magnetic force. The amounts per unit of volume of the electric and the magnetic energy are given by the expressions
½ (ExDx + EyDy + EzDz),
(17)
and
½ (HxBx + HyBy + HzBz) = ½ H2,
(18)
whose mean values for a full period are equal in every beam of light.
The formula (15) shows that the index of refraction of a body is given by √ε, a result that has been verified by Ludwig Boltzmann’s measurements[20] of the dielectric constants of gases. Thus Maxwell’s theory can assign the true cause of the different optical properties of various transparent bodies. It also leads to the reflection formulae (9) and (10), provided the electric vibrations of polarized light be supposed to be perpendicular to the plane of polarization, which implies that the magnetic vibrations are parallel to that plane.
Following the same assumption Maxwell deduced the laws of double refraction, which he ascribes to the unequality of ε1, ε2, ε3. His results agree with those of Fresnel and the theory has been confirmed by Boltzmann,[21] who measured the three coefficients in the case of crystallized sulphur, and compared them with the principal indices of refraction. Subsequently the problem of crystalline reflection has been completely solved and it has been shown that, in a crystal, Poynting’s flow of energy has the direction of the rays as determined by Huygens’s construction.