A system of physical chemistry - Index of

APPLICATION OF MECHANICS TO RADIATION .^3

in the spectrum. It has been shown experimentally that the intensity

**of** energy radiating from a black body and in equilibrium with the body

shows a maximum for waves in the infra-red region at ordinary temperatures,

and vanishes almost completely for very long or very short waves.

Representing it graphically we obtain a curve containing a maximum,

as already shown in Fig. 53, Vol. II. On the other hand, the theoretical

expression for the distribution **of** radiation energy, referred to above

(which expression is identical with Rayleigh's radiation law, already

stated in Chap. XIV., Vol. II., viz. 47r/^TX-'* . ^A), yields a curve

which contains no maximum but rises rapidly as the wave-length

diminishes.

We are considering the case in which wave-lengths **of** all magnitudes

exist between the infinitely long denoted by the symbol X^ and the

limiting value A^, but none shorter than this. If we integrate the Rayleigh-Jeans

expression between the limits A,, and A^, we obviously obtain

an expression for the total radiant energy in the enclosure. The integration

leads to the expression—

4 /vT

3 ^'o'

It follows from this expression that only one-eighth **of** the total energy

will be **of** wave-length greater than 2A0, whilst seven-eighths reside in

wave-lengths between 2A0 and Ao itself. In the case **of** the ether— if we

give it a structure at all— the size **of** its grains must be considerably less

than 10"" cm. (the order **of** magnitude **of** a gas molecule). Taking this

value, however, as applying to the ether grains, it follows that no wavelength

shorter than io~'^ cm. can be transmitted. (As a matter **of** fact

we know that X-rays are only about one-tenth **of** this.) Even with this

limit to the w?ve-length it can be shown on the basis **of** the Rayleigh-

Jeans formula that only one-millionth **of** the total energy would reside

in wave-lengths **of** the order 10"^ cm. and longer. This is quite con-

trary to what is observed, for the greater part **of** the energy is known to

lie in the region io~* cm. We conclude, therefore, that the assumption

that the number **of** degrees **of** freedom **of** the ether is not infinite, is

in itself insufficient to yield an expression (involving the equipartition

principle) which will agree with experiment. We are forced to the conclusion,

therefore, that the principle **of** equipartition itself is not applicable

to the problem **of** distribution **of** radiant energy between matter

and the ether. The result obtained on the equipartition basis always

gives a partition **of** energy **of** such a kind that the energy is almost

entirely confined to the short wave-lengths, and in the limit, i.e. if the

ether be structureless, the energy goes completely into the ether and no

distribution is possible at all. Experiment shows, on the other hand,

that distribution certainly does exist, and furthermore, the distribution

does not require that all the energy shall be located in the shortest

the contrary, the distribution is such that very little

wave-lengths ; on

energy is distributed among the very short or the very long waves, the

greater part **of** it belonging to waves **of** intermediate magnitude. This

VOL. III. 3