Densities of Li2O-B2O3, Na2O-B2O3 and K2O-B2O3 glasses have been measured. The density-composition curves are analysed to obtain the volume of both the BO3 and BO4 structural units. It is found that the volume changes with the alkali oxide content for the two types of structural unit. A new explanation of the boron oxide anomaly is presented. It is proposed that the volume contraction of the BO3 units should be responsible for the change of properties of alkali borate glasses with alkali oxide content <16 mol%. For higher alkali oxide concentrations, the interconnection of the spaces associated with the BO4 tetrahedra should cause the properties to change in the opposite direction.