Abstract
We present a translation of Poincaré's hitherto untranslated 1912 essay together with a brief introduction describing the essay's contemporary interest, both for Poincaré scholarship and for the history and philosophy of atomism. In the introduction we distinguish two easily conflated strands in Poincaré's thinking about atomism, one focused on the possibility of deciding the atomic hypothesis, the other focused on the question whether it can ever be determined that the analysis of matter has a finite bound. We show that Poincaré admitted the decisiveness of Perrin's investigations for the existence of atoms; he did not, however, anticipate the kind of resolution of which the second question is susceptible in light of recent developments