Density as a function of temperature was measured in the nematic and isotropic phases in the immediate vicinity of the nematic-to-isotropic transition temperature (T-NI) of p-n-hexyl-p'-cyanobiphenyl (6CB) and p-n-octyl-p'-cyanobiphenyl (8CB) and in the smectic-A and nematic phases in the immediate vicinity of the smectic-A-to-nematic transition temperature (T-AN') of 8CB. Similar measurements were made on dilute solutions of the quasispherical solutes Et4C (tetraethylmethane) and R4Sn (R = C2H5, n-C3H7, and n-C4H9) in 6CB and 8CB. Addition of these solutes led, as is expected for first-order phase transitions, to a nematic-isotropic two-phase region bounded by temperatures T-N and T-I, which are lower than T-NI, and in the case of the 8CB systems to a smectic-A-nematic two-phase region bounded by temperatures T-A and T-N', which are lower than T-AN'. Volume changes at the transitions of the liquid crystals confirm that they are weakly first-order. beta (N) and beta (I), the moduli of the slopes of the nematic and isotropic boundary lines, respectively, of the nematic-isotropic two-phase regions in the 6CB and 8CB systems were obtained assuming that the respective reduced temperatures T-N* (= T-N/T-NI) and T-I* (= T-I/T-NI) versus solute mole fraction (x(2)) diagrams are linear. PA and beta (N'), similarly defined for the smectic-A-nematic two-phase regions in the 8CB systems, were obtained from the respective linear T-A* (= T-A/T-AN') and T-N'* (= T-N' / T-AN') versus x(2) diagrams. The dependencies of beta (N) and beta (A) on solute and solvent sizes and the nature of the liquid crystalline phase are discussed.