The physical constitution of matter appeared uncertain in the nineteenth century. Although an ontology of particles of matter in motion was fundamental to the programme of mechanical explanation and to the conceptual coherence of the science of thermodynamics, physicists were careful to distinguish between the general supposition of a particulate theory of matter and the adoption of more specific models of molecular structure. Though the mechanical view of heat as the motion of the particles of matter underlay the principle of the equivalence of heat and work, physicists found compelling evidence for a molecular theory of matter only with the development of the kinetic theory of gases in the 1850s. But the problem of explaining the phenomena of spectroscopy indicated the need to suppose complex internal molecular vibrations, and raised difficult questions about the formal coherence of the kinetic theory of gases. The problems of molecular physics raised crucial issues about the conflicting empirical constraints (from spectroscopy and the kinetic theory of gases) on the formulation of a coherent theory of the molecular structure of bodies. The problems of molecular physics shaped the development of thermodynamics: The statistical theory of molecular motions, which was formulated as a seminal feature of the kinetic theory of gases, led to the interpretation of the second law of thermodynamics as an irreducibly statistical law. For chemists, the problems of matter theory seemed equally complex, and the status of the atomic theory remained the subject of debate.