A system of physical chemistry - Index of

176

A SYSTEM OF PHYSICAL CHEMISTRY

to waves **of** frequencies in the range v, v + 8i'. This number is in fact the

number **of** independent co-ordinates or degrees **of** freedom for such quali-

ties **of** radiation. Ascribing the usual kY units **of** kinetic and potential

energy to each degree, we obtain for the energy **of** radiation in the range

Q

V, r -H 8i', the amount -^kHv"- . 8v ergs, or for the energy-density,

Stt

-j-/^Ti'- . 8v ergs per c.c. In terms **of** wave-lengths we obtain by put-

ting V = r- and 8v = - -,8A, that the energy-density **of** radiation

A A'

whose wave-lengths he in the range A, A -f- 6A is — rpoA ergs per

A^

c.c.^

It is an obvious drawback to the Rayleigh-Jeans expression

that it

does not approach a finite limit, as A decreases to zero. In fact, the

ether would appear to contain an infinite amount **of** energy per c.c.

since—

is certamly infinite.

We might evade this objection by observing that exchange **of** energy

from one type to another must be effected by the material **of** the enclosure

(as was pointed out above), and that we might reasonably suppose

the radiating mechanisms in the atoms to be **of** such a nature that

they could not emit radiation **of** a quality higher than a certain limiting

frequency, and so the upper limit **of** the integral would be a finite

quantity and not zero. But this would not meet the difficulty that for

the same amount **of** range in wave-lengths 8A, there is a greater contribution

to the energy density from high-grade qualities than from low-

grade, according to the Rayleigh-Jeans formula ; whereas experiment

shows that the factor **of** 8A exhibits a maximum value for a certain wavelength

A,„ (dependent on temperature), and approaches zero as a limit

as A approaches zero or infinity.

It has been suggested that the tendency, expressed in the Rayleigh-

Jeans Law, **of** the radiation energy to pass more and more into the higher

qualities, is in reality a true phenomenon **of** nature, and that we fail to

appreciate it in our experimental tests because all temperature enclosures

fail to confine the energy **of** the highest frequencies ; such energy leaks

out, as it were, through the walls and through the small opening facing

the radiometer, almost as fast as it is supplied from low-frequency radiation

by the agency **of** the walls and so the condition we ; actually observe

is a compromise— a stage on the way to the final consummation

expressed in the ideal formula, but unattainable except after an enormous II

'

Phil. Mair., 49, 539, igoo ; lo, gi, 1905; 17, 229, igog. Nature, ^2, p. 94 and

p. 243, 1905.