A system of physical chemistry - Index of

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A SYSTEM OF PHYSICAL CHEMISTRY

ether possesses an infinite number **of** degrees **of** freedom. Matter

imbedded in the ether has on the other hand z. finite number **of** degrees

**of** freedom in virtue **of** its discontinuity, i.e. in virtue **of** its discrete or

heterogeneous structure. If now we apply the principle **of** equipartition

**of** energy to such a **system** composed **of** both matter and ether, it is clear

that the ether will take all the energy (since its number **of** freedoms is

infinite) leaving none at all for the matter.

The following mechanical analogy is suggested by Jeans. Let us

suppose that we have a number **of** corks held together by elastic and

floated upon the surface **of** still water. Cause the corks to move

violently to and fro. Waves will be formed, i.e. energy will be given

out from the cork **system** to the water by this kind **of** "radiation," as

well as by friction, until finally the corks come to rest. All the energy

originally given to the corks has now passed to the water. Permanent

movement **of** the corks is unthinkable. It will be observed that the

cause **of** this lies in the fact that the corks are large units compared

with water molecules ; in fact, the water is a sensibly continuous medium

compared with the coarse-grained structure consisting **of** corks. It is

impossible therefore to conceive **of** an equilibrium being set up as

regards energy interchange between matter and ether except at the

absolute zero **of** temperature. In other words, we cannot deduce any

radiation law. It is clear, therefore, we must follow out some other line

ot reasoning. Let us take the second case, namely, the assumption that

the ether does possess a structure. On this basis the number **of** degrees

**of** freedom **of** the ether is no longer infinite, and it is possible to conceive

**of** equilibrium states being reached at different temperatures as a

result **of** energy transfer between matter and ether. If we think **of** the

ether as possessing a fine-grained structure, it follows that the waves

which can be propagated by such a medium must not become shorter

than a certain limiting size Aq. It is easy to see this by analogy.

Waves which can be transmitted by a material **system** (sound waves, for

example) must be great compared with the distance **of** the molecules

which compose the **system**, as otherwise the waves would not be transmitted

at all. Similarly, we must suppose that even the shortest light

waves which we know **of** must be large compared with the grain structure

**of** the ether itself. If this structure exists it ceases to be legitimate to

speak **of** infinitely short waves in the mathematical sense. The shortest

conceivable waves must be **of** the order **of** magnitude **of** the distance

apart **of** the "molecules **of** the ether ".

Starting out with the idea that the number **of** degrees **of** freedom

possessed by the ether is finite, Jeans has shown that by applying the

principle **of** equipartition **of** energy, the energy distributes itself in the

normal spectrum in such a way that the intensity—

corresponding to a

region lying between A and X -f- d\.— is proportional to the temperature

and inversely proportional to the fourth power **of** the wave-length.

That is, the energy in the spectrum will so distribute itself that it will

be almost entirely confined to the region **of** extremely short wave-lengths.

As a matter **of** fact, however, this is not the real distribution **of** energy