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 Kirchh**of**Ts 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