A system of physical chemistry - Index of

APPLICATION OF MECHANICS TO RADIATION 31

however, in this connection to show that while the principle **of** partitionequi-

is partially true, in the form given by Boltzmann it is not

sufficiently comprehensive. It might be thought that a sufficient ex-

planation **of** the observed increase in atomic heat with rise in temperature

lies in the

supposition

**of** new degrees **of** freedom coming into

existence. We cannot, however, imagine a " fractional "

degree **of**

freedom. It must either exist definitely, or not at all. One would

expect, therefore,

temperature

that the atomic heat should rise by steps as the

rises. All observations, however, have shown that the increase

in atomic heat is a perfectly conti?iuous function **of** the temperature.

Leaving the problem **of** specific or atomic heats, let us turn to

another important problem, namely, that **of** thermal radiation ; for it

was through investigation carried out in this field that the modifications

**of** the principle **of** equipartition were eventually introduced, which in

the hands **of** Planck and Einstein have permitted a satisfactory explanation

to be given **of** the discrepancies hitherto existing between theory

and experiment, not only in the domain **of** radiation itself, but likewise

in that **of** the heat content **of** solids. Whether these modified views

form the ultimate solution **of** the problem, it is at present impossible to

say. They represent, at any rate, a fundamental stage in the development

**of** the subject.

Application **of** [Classical] Statistical Mechanics to Radiation.

We are here concerned with temperature radiation only. A definition

**of** this term has already been given toj;ether with a short account

**of** the radiation laws in Chap. XIV. **of** Vol. II.

In studving the question **of** radiation, that is **of** the exchange **of**

radiant eneigy between matter and ether, it is necessary, **of** course, to

limit our consideration to the equilibrium state. If an enclosed material

**system** is maintained at a temperature T, the interior **of** the **system**

contains energy constantly radiated to and from the boundary. When

these energy exchanges arrive at equilibrium each cubic centimetre **of**

the **system** contains energy in what we may call the undulatory form.

The problem is how to calculate the most probable distribution **of** the

energy between the various wave-lengths not only for the single temperature

T but for any temperature ; for the equilibrium state may be

defined as that for which the distribution **of** energy (at the given temperature)

between the various is wave-lengths the most probable. To

work out this statistical problem we must know something about the

number **of** degrees **of** freedom possessed by the matter and by the ether

(present throughout the matter) respectively. It will now be shown

that absolutely different results are arrived at, according as to whether

we regard the ether as continuous [i.e. structureless) or it regard as

having a structure. Let us first consider the ether as continuous. In

this case the ether is a medium capable **of** vibrating in an infinite number

**of** ways the wave-lengths propagated throughout it having all possible

values between o and 00 . This is the same thing as saying that the