On the Application of Bethe's Method to the Grand Canonical Ensemble for a Fluid

The grand partition function for a large fluid system is expressed in a form equivalent to a grand partition function for a small volume v including factors representing the effect of the surroundings on the distribution inside v. An explicit expression for these factors is found by making a general assumption concerning the interaction of molecules inside v with the rest of the fluid. The molecular distribution inside v is then completely determined by one function which is a solution of an integral equation containing in its terms up to n‐time integrals, where n is the maximum number of molecules which can occupy v simultaneously. The nature and efficiency of the approximation are discussed.