A general review of temperatures and enthalpies of (solid + solid) and (solid + liquid) transitions of pure normal alkanes is presented. Mean values are determined from literature data on pure normal alkanes for methane up to the alkane of carbon atom number n equal to 390. Melting temperatures and (solid + liquid) and (solid + solid) transition enthalpies are expressed as a function of the carbon atom number n. Broadhurst's models are fitted again using 67 melting temperatures from methane up to the normal alkane of carbon atom number n = 390 and it is shown that the enthalpy difference between the ordered phase and the liquid phase varies linearly as a function of the carbon atom number n whatever its parity; the same behaviour is observed for the melting enthalpy difference when fusion corresponds to a state change (disordered phase --> liquid).