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nydus/The Theory of Heat RadiationPublic
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176.

hence supplied with the dash to denote their mean value. Since for every separate ray the mean electric and magnetic energies are equal, we may always write u = 1 4 π = ( ⋿ x 2 \Strut ― + ⋿ y 2 \Strut ― + ⋿ z 2 \Strut ― ) . \Label [ e q n ] ( 319 ) \upshape (319) If, in particular, all rays are unpolarized and if the intensity of radiation is constant in all directions, 𝖪 ν = 𝖪 ν ′ and, since $\int \sin^{2} \theta\, d\Omega = \iint \sin^{3} \theta\, d\theta\, d\phi = \frac{8\pi}{3} \ \overline{\mathsf{E} {z}^{2}\Strut } = \frac{32\pi^{2}}{3c} \int \mathsf{K} }\, d\nu = \overline{\mathsf{E {x}^{2}\Strut } = \overline{\mathsf{E} }^{2}\Strut

\Label[eqn]{(319a)}\tag*{\upshape (319a)}$ and, by substitution in [eqn:(319)] (319), u=8πc𝖪νdν, which agrees with [eqn:(22)] (22) and [eqn:(24)] (24).

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