A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX II 175

continuously from the narrow long faces which also bound the box. If

we still further extend these considerations to a cubical box, the number

of possible modes come out to be proportional to (


V , I.e. to 8-, . V"*,

tfi

T is the volume of the box. A differentiation shows that the number of

possible modes which lie between narrow limits of frequency v and

7*

V + hv, is 24-|j . v"8v. As a matter of fact a complete analysis shows

that the numerical factor should be 477 and not 24. Now the point of

this analogy lies in the fact that whatever be the nature of a beam of

radia'nt energy, a certain definite condition has to be obeyed at a per-

fectly reflecting surface— on the electro-magnetic theory the tangential

component of the electric intensity in the wave must be zero there—and

this condition limits the number of types of radiation wave-trains which

can persist unchanged as stationary waves in an enclosure with reflecting

walls. Consequently, if we introduce a small portion of perfectly ab-

sorbing matter into a cube with perfectly reflecting walls, we can assert

that, despite the fact that the matter can radiate and absorb any type of

radiation, only those types will exist in the final state of equilibrium

which satisfy the boundary conditions referred to above, just as our box

•organ-pipe would not resound to every small whistle introduced into it,

but only to a whistle having one of a definite series of pitches. These

types of radiation will constitute complete radiation at the temperature,

since experiment has certainly justified KirchhofTs conclusion that the

frequencies and energies of the constituents of radiation in a temperature

enclosure are independent of the size or nature or shape of the walls, so

long as there is present a portion of non-perfectly reflecting matter.

The number of types of radiation, therefore, which exist in full radiation,

having frequencies between the narrow limits v -and v + Sk, would ap-

ipear to be 47r -^ . v^hv, where c is the velocity of light ; but,

of fact, this number has to be doubled,

as a matter

since radiation waves are transverse

to the direction of propagation (not longitudinal to it, as in the

case of sound waves), and therefore any particular wave has to be re-

garded as due to the composition of two waves of the same period and

phase, each polarised in one of two definite rectangular planes. So the

final result for the number is -^rv'^v- This means that in order to

specify the electro-magnetic condition (electric and magnetic intensities)

at any assigned point in the ether of the box, at any assigned instant,

expressions involving a number — j-v'-^Sv of terms each varying harmoni-

cally with the time would be required to designate that part of the effect due

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