The main aim of the present work is to show, for the case of glycerol, the connection between the macroscopic fragility parameter, defined as m = (d log eta)/(d(Tg/T))|T=Tg+, and the average number of H-bonds per molecule. Furthermore, the relation between the macroscopic and microscopic definitions of fragility, which takes into account the temperature dependence of the atomic mean square displacement, is discussed.