This paper examines the debate in the late 19th and early 20th centuries over the acceptability of atomic and molecular physics. It focuses on three prominent figures: Maxwell, who defended atomic physics, Ostwald, who initially rejected it but changed his mind as a result of experiments by Thomson and Perrin, and Duhem, who never accepted it. Each scientist defended the position he did in the light of strongly held methodological views concerning empirical evidence. The paper critically evaluates each of these methodological positions.

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