The explanation of the phenomenon of Brownian motion, given by Einstein in 1905 and based on the kinetic–molecular conception of matter, is considered one of the fundamental pillars supporting atomism in its victorious struggle against phenomenological physics in the early years of this century. Despite the importance of the subject, there exists no specific study on it of sufficient depth. Generally speaking, most histories of physics repeat the following scheme: the discovery made by Robert Brown in 1827 , of the (...) continuous movement of small particles suspended in a fluid did not arouse interest for a long time. Finally, at the close of the century, Gouy's research brought it to the attention of the physicists. Gouy was convinced that Brownian motion constituted a clear demonstration of the existence of molecules in continuous movement. Nevertheless, he did not work out any mathematized theory that could be subjected to quantitative confirmation. All nineteenth-century research remained at the qualitative level and yet it was able to clarify some general characteristics of the phenomenon: the completely irregular, unceasing, motion of the particles is not produced by external causes. It does not depend on the nature of the particles but only on their size. The first significant measurements, carried out by Felix Exner in 1900, appeared to deny the possibility of reconciling the kinetic theory with Brownian motion. The discovery of the ultra-microscope then allowed Zsigmondy to perceive the presence of movements, which were completely analogous to Brown's, in the particles of the colloids; these movements were rather smaller in size than those invesigated up to then. Thus Zsigmondy aroused interest in the phenomenon. Finally, in 1905, Einstein succeeded in stating the mathematical laws governing the movements of particles on the basis of the principles of the kinetic–molecular theory. The following year Smoluchowski arrived at conclusions which corresponded to Einstein's. These laws received a first, rough confirmation in the years immediately following by the work of The Svedberg, Seddig and, for some historians, Henri. Then in 1908 Jean Perrin gave it a definitive confirmation. (shrink)