CodalSearch this book — or all of Codal…⌘K
nydus/The Theory of Heat RadiationPublic

This text examines the physical distinction between heat conduction and heat radiation, noting that radiation is independent of the medium through which it passes. It establishes that heat rays are physically identical to light rays and applies the principles of experimental optics to the study of thermal radiation.

Page 198 of 236
Table of Contents

169.

  • h_{3}^{2} = a^{2} = e_{1}^{2} + e_{2}^{2} + e_{3}^{2}.

\Label[eqn]{(306)}\tag*{\upshape (306)}$ Moreover the sum of the products of corresponding terms in any two parallel rows is equal to zero, for example, ${3} \mathsf{a} e_{1} &+ \mathsf{b} e_{2} &&+ \mathsf{c} e_{3} &&= 0 \ \mathsf{a} h_{1} &+ \mathsf{b} h_{2} &&+ \mathsf{c} h_{3} &&= 0.

\Label[eqn]{(307)}\tag*{\upshape (307)}$

Moreover there are relations of the following form: h 1 a = e 2 a · 𝖼 c 2 l ν − e 3 a 𝖻 c 2 l ν , and hence h 1 = c 2 l ν ( 𝖼 e 2 − 𝖻 e 3 ) ,  etc. \Label [ e q n ] ( 308 ) \upshape (308) If the integral numbers 𝖺 , 𝖻 , 𝖼 are given, then the frequency ν is immediately determined by means of [eqn:(306)] (306). Then among the six quantities e 1 , e 2 , e 3 , h 1 , h 2 , h 3 , only two may be chosen arbitrarily, the others then being uniquely determined by them by linear homogeneous relations. If, for example, we assume e 1 and e 2 arbitrarily, e 3 follows from [eqn:(307)] (307) and the values of h 1 , h 2 , h 3 are then found by relations of the form [eqn:(308)] (308). Between the quantities with accent e 1 ′ , e 2 ′ , e 3 ′ , h 1 ′ , h 2 ′ , h 3 ′ there exist exactly the same relations as between those without accent, of which they are entirely independent. Hence two also of them, say h 1 ′ and h 2 ′ , may be chosen arbitrarily so that in the equations given above for given values of 𝖺 , 𝖻 , 𝖼 four constants remain undetermined. If we now form, for all values of 𝖺 𝖻 𝖼 whatever, expressions of the type [eqn:(305)] (305) and add the corresponding field components, we again obtain a solution for Maxwell's equations of the field and the boundary conditions, which, however, is now so general that it is capable of representing any electromagnetic process possible in the hollow cube considered. For it is always possible to dispose of the constants e 1 , e 2 , h 1 ′ , h 2 ′ which have remained

198