We make a numerical study of the solutions of the equations of motion for the electromagnetic field in a one-dimensional model of a radiant cavity. Our main results are as follows: (1) There exist stochasticity thresholds such that below them one has ordered motions without energy exchanges, while chaotic motions with intense energy exchanges occur above them; (2) above thresholds there is a trend toward equipartition of energy (in time average) among the normal modes of the field, but this occurs in the sense of Boltzmann and Jeans, namely, with the higher frequencies requiring longer and longer times in order to be involved in the energy sharing.