G. Wald has suggested a compartment theory for the functioning of the rods which corresponds mathematically to that of the Geiger–Muller counter. In this paper a discussion is given as to how the compartment theory fits various models for Geiger–Muller counters. Numerical examples are given to illustrate how the mathematical models can be compared with observed threshold curves.A method is also presented for mathematically extending Wald’s compartment theory to having the compartments correspond to structures positioned in a manner similar to the Sjostrand membranes. Suggestions for further research are presented.