The French physicist Jean Baptiste Perrin is widely credited with providing the conclusive argument for atomism. The most well-known part of Perrin’s argument is his description of thirteen different procedures for determining Avogadro’s number (N)–the number of atoms, ions, and molecules contained in a gram-atom, gram-ion, and gram-mole of a substance, respectively. Because of its success in ending the atomism debates Perrin’s argument has been the focus of much philosophical interest. The various philosophers, however, have reached different conclusions, not only (...) about the argument’s general rationale but also the role that the multiple determination of N played in it. This paper emphasizes the historical development of Perrin’s experimental work in order to understand the role that the multiple determination of molecular magnitudes played in his argument for molecular reality. It claims that Perrin used the multiple determination strategy to put forward an exceptionally strong no-coincidence argument to argue for both the correctness of the values for the molecular magnitudes determined and the validity of the auxiliary assumptions upon which the different determinations were based. The historicist approach also allows the identification of the elements responsible for the epistemic strength of Perrin’s no-coincidence argument. (shrink)