Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/424

 

the concentrated rays of the electric lamp. Such rays falling on a thin metallic disk, delicately suspended in a vacuum, might perhaps produce an observable mechanical effect. When a disturbance of any kind consists of terms involving sines or cosines of angles which vary with the time, the maximum energy is double of the mean energy. Hence, if $P$ is the maximum electromotive force, and $\beta$ the maximum magnetic force which are called into play during the propagation of light,

${\frac {K}{8\pi }}P^{2}={\frac {\mu }{8\pi }}\beta ^{2}={}$ mean energy in unit of volume.

(24)

With Pouillet's data for the energy of sunlight, as quoted by Thomson, Trans. R.S.E., 1854, this gives in electromagnetic measure

$P={}$ 60000000, or about 600 Dainell's cells per metre;

$\beta ={}$ 0.193, or rather more than a tenth of the horizontal magnetic force in Britain.

 

Propagation of a Plane Wave in a Crystallized Medium.

794.] In calculating, from data furnished by ordinary electromagnetic experiments, the electrical phenomena which would result from periodic disturbances, millions of millions of which occur in a second, we have already put our theory to a very severe test, even when the medium is supposed to be air or vacuum. But if we attempt to extend our theory to the case of dense media, we become involved not only in all the ordinary difficulties of molecular theories, but in the deeper mystery of the relation of the molecules to the electromagnetic medium.

To evade these difficulties, we shall assume that in certain media the specific capacity for electrostatic induction is different in different directions, or in other words, the electric displacement, instead of being in the same direction as the electromotive force, and proportional to it, is related to it by a system of linear equations similar to those given in Art. 297. It may be shewn, as in Art. 436, that the system of coefficients must be symmetrical, so that, by a proper choice of axes, the equations become

$f={\frac {1}{4\pi }}K_{1}P$,$g={\frac {1}{4\pi }}K_{2}Q$,$h={\frac {1}{4\pi }}K_{3}R$,

(1)

where $K_{1}$, $K_{2}$, and $K_{3}$ are the principal inductive capacities of the medium. The equations of propagation of disturbances are therefore