A magnetic float technique has been developed for the measurement of densities of dilute aqueous solutions to within ±1 part in 10⁶. Apparent molal volumes ϕ_v at 5 and 25° are presented for alkali chlorides and tetra-alkylammonium bromides in the molar concentration range 0.002 < c < 0.1. The results are discussed in terms of deviations from the Debye-Hückel limiting law, and it is shown that for the salts R₄NBr, the concentration dependence of ϕ_v does not conform to the trends normally observed for univalent electrolytes. The ϕ_v(c^½) behaviour is interpreted in terms of cation-cation interactions, induced by co-operative ion-water interactions. Mean apparent molal expansibilities ϕ_E at 15° are presented, and the ϕ_E(c^½) plots for NaCl and KCl show good agreement with predicted limiting law behaviour. For the series R₄NBr (except where R = Me) increasingly large positive excess expansibilities are observed.