The Pressure of Radiation

Abstract

IN his letter of January 1 Prof. Callendar gives his reasons for doubting the formula for the pressure of radiation as it is usually accepted. He makes use of Boltzmann's proof of the fourth power law for the complete radiation, extends it to each separate frequency, and deduces that the energy in every frequency aught to be proportional to the fourth power of the absolute temperature. Since this is known to be untrue he concludes: “ither Carnot's principle does not apply, or E/v is not equal to 3p for each separate frequency” and chooses the latter alternative. But it would appear that Prof. Callendar's use of Carnot's principle is somewhat questionable. For, in order to investigate the pressure in an enclosure it is essential to alter its volume, and any change of size will bring the Doppler effect into play and cause a small change in the frequency of the radiation. If this be taken into account, the result leads straight to the displacement law of Wien—Eλ = f(λT)/λ5—and beyond this gives no information. Moreover, a recapitulation of Wien's work with a different law of pressure fails to give the displacement law, so that this law must be abandoned, if the pressure formula is to be altered.