The successful uses of atomic theory described in Chapter 1 did not settle the existence of atoms in all scientists’ minds. This was in part because of the appearance in the first half of the nineteenth century of an attractive competitor, the physical theory of thermodynamics. With thermodynamics one may derive powerful results of great generality, without ever committing oneself to the existence of atoms or molecules. But thermodynamics could not do everything. This chapter describes the advent of kinetic theory, which is based on the assumption that matter consists of very large numbers of particles, and its generalization to statistical mechanics. From these, thermodynamics could be derived and, together with the atomic hypothesis, it yielded results far more powerful than could be obtained from thermodynamics alone. Even so, it was not until the appearance of direct evidence for the graininess of matter that the existence of atoms became almost universally accepted.