A stepwise dilution method to determine the dielectric constant at a frequency of 1 MHz has been developed and the dielectric properties of benzene, ethanol, 1-butanol, chlorobenzene, dioctyl succinate, and sodium bis(2-ethylhexyl) sulfosuccinate (AOT) in cyclohexane were determined at 298.15 K. From the precise measurements carried out for very dilute concentrations, it was found that there is a critical concentration for the threshold of solute-solute interactions at a mole fraction lower than 10(-3). Apparent dipole moments for polar liquids were calculated as a function of mole fraction. The limiting dipole moments mu(infinity) for polar molecules were determined from the dielectric constants at mole fractions lower than the critical concentration of the solute-solute interactions by using the Debye and Frohlich equations, The value of mu(infinity) for chlorobenzene calculated by the Frohlich equation agreed very well with literature values determined for the vapor phase.