Darwin–Fowler method

In statistical mechanics, the Darwin–Fowler method is used for deriving the distribution functions with mean probability. It was developed by Charles Galton Darwin and Ralph H. Fowler in 1922–1923.

Distribution functions are used in statistical physics to estimate the mean number of particles occupying an energy level (hence also called occupation numbers). These distributions are mostly derived as those numbers for which the system under consideration is in its state of maximum probability. But one really requires average numbers. These average numbers can be obtained by the Darwin–Fowler method. Of course, for systems in the thermodynamic limit (large number of particles), as in statistical mechanics, the results are the same as with maximization.