Quantum Radiation

Abstract

THE fraction x/(e^x – 1), by which the quantum theory of radiation differs from the classical theory, is so important that it seemed of interest to study it for its own sake. I accordingly wrote to my brother Alfred Lodge, as a pure mathematician, asking him what he had to say about it. He directed my attention to some points which may be of interest to other students of Planck's theory as expounded in Great Britain by Dr. Jeans. First, that the function was studied by John Bernoulli and expanded in a series involving his particular numbers; and next, that it is the ratio of simple interest to continuous compound interest for the same period. Or in other words, the compound interest hv on E, the actual basic energy, is equal to the simple interest on RT; so that E has to be reduced below the average value in order to allow compound interest to be taken on it, while the rate of interest, x, is apparently dependent on the ratio v/T.