A fluid of rigid spheres in equilibrium is considered from a viewpoint which allows the deduced equation of state to reflect very sensitively the accuracy of two approximations to the triplet distribution function. Specifically, these approximations are: (1) the usual Kirkwood superposition scheme, and (2) assumption that the correlation of excess particles near a fixed particle pair is additively composed of the excesses induced individually by each member of the pair (linear correlation field hypothesis). Granted only these hypotheses, each in turn, the rigorous statistical mechanical relations between rigid‐sphere distribution functions and the thermodynamic pressure and compressibility lead unambiguously to nonlinear first‐order differential equations for the pressure as a function of density. The simply obtained numerical solutions clearly demonstrate that assumption (1) is considerably superior to (2).