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A new method to construct a high stability sapphire oscillator is presented. The method relies on the anisotropic fractional temperature coefficients of frequency (TCF) of orthogonally polarized modes. We show that it is possible to design a resonator with transverse electric and magnetic modes at different frequencies, but with the same TCF in units hertz per kelvin, resulting in temperature compensation of the difference frequency. Compensation was demonstrated between 50 to 77 K by measuring the difference frequency of two microwave oscillators frequency locked to orthogonally polarized whispering gallery modes. Curvature of the compensation points was measured to be 1 to 3 /spl times/ 10/sup -8/ K/sup -2/ between 50 and 77 K. This technique enables the construction of temperature compensated oscillators at any temperature and does not require dielectric, paramagnetic, or mechanical compensation techniques. Considering the above parameters, we show that it is possible to construct oscillators with fractional frequency instability at /spl tau/ = 1 s, of order 7.6 /spl times/ 10/sup -15/ at solid nitrogen temperature (/spl sim/50 K).