Methods of preparation and results of measurements of the dielectric constant of solid-solution single crystals of KNbO3 and KTaO3 are presented. Data are given for the composition range 0-80 mole percent KTaO3 in the temperature interval -180°C to 450°C. It is found that all of the crystals studied show Curie-law behavior of the dielectric constant in the paraelectric state. The data indicate that the paraelectric to ferroelectric transition, which is first order for pure KNbO3, becomes second order at a concentration of approximately 55 mole percent KTaO3. Analysis of the results in terms of Slater's model of ferroelectricity in a perovskite lattice leads to the conclusion that the dependence of the Lorentz correction on volume plays a major role in determining the ferroelectric behavior. Ionic polarizabilities and their dependence on volume are also discussed.