The analysis of Erwin Schrödinger's first major theoretical work demonstrates his early commitment to Boltzmann's statistical-mechanical tradition, which also influenced his later contributions to quantum theory. It further reveals two central elements of his research style: The extension and modification of works by others, and the extensive use of analogies. Schrödinger extended Debye's theory of liquid dielectrics using Langevin's and Weiss's theories of magnetism, taking a formal analogy between mathematical laws of two separate phenomena as an indication for a physical analogy between them. His approach followed his commitment to "scientific realism". Schrödinger attributed "reality" to the basic assumptions of a theory and therefore explored their consequences in various domains. For him, accordance with experimental findings proved the correctness of his assumptions. Following this methodology, Schrödinger advanced a kinetic (i.e., statistical) theory of solid dielectrics. His 1912 theory explained the behavior of solid dielectrics in an external electric field, piezoelectricity, pyroelectricity, and the change of melting temperature with pressure. It even provided a microphysical explanation for solidification itself. These explanations, however, required several rather speculative and doubtful assumptions, stemming from Schrödinger's reliance on analogy. This illustrates one of the pitfalls of the use of analogies.