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Pieces of single crystals of rutile show high Q resonances in the microwave range. A piece about (1/7Â¿)3 has a Q as high as that of a metal-walled cavity at room temperature. Lowering the temperature increases both the Q and the resonant wavelength. Q's of 105 were seen at 4Â°K. A frequency equation of first- and second-order approximations was derived in terms of the dimensions and the anisotropic dielectric constant, Â¿Â¿, for rectangular parallelepiped resonators. Accurate values of anisotropic Â¿Â¿ were obtained. In the anisotropic medium there are two types of resonant modes, one of which has an outside E field similar to an electric multipole, and the other an outside magnetic field similar to a magnetic multipole. These two types of modes degenerate into one type if the dielectric is isotropic. Resonators were also made of ceramic rutile and strontium titanate, both of which had Q values of thousands. An extremely high unloaded Q, of the order of a million, was seen at 1.4Â°K on a KRS-5 (ThBr-Thl) single crystal at X band.