A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX II 183

similar to Einstein's, by considerations based on his hypothesis of

Faraday tubes in the ether emanating from cliarged particles.^

It

should be noted that Thomson's view of a " filamental " structure in the

ether might well be expected to lead to a different result for energydensity

than that reached by Rayleigh and Jeans ; for their calculation

of the degrees of freedom in the ether, it will be recalled, depends on

taking the ether as a perfectly continuous medium. Such a view would

indeed be more like the adoption of the first of the alternatives referred

to previously as methods of escape from the Rayleigh- Jeans discrepancy.

In reference to such views, it must be admitted that, however useful

they may be for the immediate purpose of overcoming such difficulties

as those connected with the photo-electric effect, and X-rays, and how-

ever well they suit the needs of radiation formulae, they involve a return

to the corpuscular theory of light, a raising of all the old difficulties of

accounting for diffraction and interference on such a theory, and at

present they lack a system of fundamental postulates, such as those on

which stands the present edifice of dynamics and electro-dynamics. Of

course, there is no gainsaying that the construction of such a system

may be attempted and may be successfully carried out, and Newtonian

dynamics placed in the position of a good approximation to truth, but

without absolute validity.

As has been already suggested, Planck meets these difficulties in a

he abandons the hypothesis of discontinuous

less revolutionary fashion ;

absorption, retaining discontinuous emission. By so doing he meets fairly

successfully (though not entirely, as I hope to show presently) the objection

lodged against his method of obtaining equation (i). His new

hypothesis concerning his oscillators is that they can emit only at definite

instants, viz. when they contain an integral number of quanta, hv. If

they contain any fraction of a quantum over an integral number they

cannot radiate. When radiation does take place it is " catastrophic,"

i.e. it cannot cease until the whole energy of the oscillator has been

lost. The particular number of quanta possessed by an oscillator when it

radiates are determined by the laws of chance, the chance of its reaching

a given number being less the greater the number and the smaller the

radiation-density. In fact, Planck's new line is based on three

postulates :—

(a) In any finite time the total emission equals the total absorption.

ib) For small frequencies {i.e. long wave-lengths), the quanta of

energy are so small that emission is practically continuous, and the

ordinary dynamical and electro-dynamical laws are a good approximation

to the facts even for individual oscillators and their immediate neighbourhood.

{c) The chance of a particular oscillator emitting when arriving at a

"critical" state (i.e. containing an integral number of is quanta) less

the stronger the field. In particular,

the chance of no emission taking

place to the chance of an emission is a ratio proportional

to the radia-

tion-density.

1

Electricity and Matter (Constable, 1904).

Phil. Mag., 19, 301. iQio.

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