A system of physical chemistry - Index of


A system of physical chemistry - Index of



If such ideas are to be generalised and extended to the ether of an

enclosure, a definite notion as to the structure of the ether is imperative

before any headway can be made in its calculating degrees of freedom.

At the outset it is fairly evident that the usual conception of the ether

as a perfectly continuous medium indivisible into an enumerable number

of discrete parts, should lead to an infinite number of degrees of freedom,

with the resulting conclusion that in a state of equilibrium the ether in

the enclosure should contain all the energy and the walls none. The

well-known illustration of the gradual loss of vibratory energy from the

particles of a sounding body to the surrounding air may serve to make

this point clearer. This conclusion is in fact reached by the Rayleigh-

Jeans analysis, and is very much at variance with the facts as we know

them. The formula arrived at, however, is a close approximation to

the truth for long wave-lengths, and the calculation of the number of

degrees of freedom has proved of signal service in itself. It is impossible

to reproduce the analysis here, but an analogy from sound waves

may serve to show the principles on which it is based. It is well known

that an organ-pipe will resound only to notes of definite frequencies, the

fundamental and its overtones. This is due to the fact that any state

of " stationary " wave-motion which will persist in the air of the pipe has

to satisfy certain end conditions—

e.g. at a closed end there can be no

vibratory motion of the air particles, at an open end no change of pressure.

Any text-book on sound shows that from these conditions there

can exist in a very narrow pipe, closed at both ends or open at both

ends, only waves whose wave-lengths are 2/, — , —

... — , etc., where

2/ 2/ 2/

2 3 «





V iox we see that the number of

n—j, possible modes of vibration whose

O if

I IS the lengthh ot of the pipe, pipe. The ihe trequencies frequencies are, ot of course, —„ 2—,

V V . . — ...

. . .

j> n-, etc., where v is the velocity of sound. Now if we write

frequencies are not greater .


than v is « = — v. Remembenng that

this is the result for a narrow pipe in which the wave-motion is parallel

to one direction, let us extend the method to a fiat shallow box, enclosed

between two square ends so that the wave-motion takes place in any

direction lying in one of the ends. The number of modes of vibration

having v as the upper limit of their frequencies would now be propor-

(2I V

tional to ( .

vj ,

a. result not difficult to apprehend, since we can in a

rough sort of way suppose that with any one type of wave-motion

parallel to one edge of the flat ends, we can compound any of the types

which can exist parallel to the rectangular edges so as to obtain a possible

wave- train travelling obliquely round and round the box, reflected

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