The nineteenth-century history of the mole concept, of the determination of the Loschmidt number and of the Avogadro constant, is interesting in several respects. While Avogadro's hypothesis (1811) played a key role in the development of the mole concept, it was only one of the epistemic tools that chemists used in their long search for a consistent system of molecular and atomic weights. This line of research and thought was fully mature in the 1880s. Following a Laplacian programme until the 1880s, physicists tried to guess the range of the so-called molecular forces, but the development of the kinetic theory of gases introduced a new interest in the determination of the number of "particles" present in gaseous systems. In this respect Loschmidt's papers (1865) represented the transition between the two types of interest in the molecular reality. However, it was only in the first decade of the twentieth century that the theoretical and experimental determination of physical quantities directly related to the Avogadro constant received full attention by scientists such as Planck, Einstein, Rutherford and Perrin.