A system of physical chemistry - Index of

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A system of physical chemistry - Index of

32

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

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