An exceptionally sensitive calorimetric technique has been devised for measuring microwave absorption by small samples of ultra-low-loss dielectrics at cryogenic temperatures. The loss factor of sapphire at 2.45 GHz diminished progressively with decreasing temperature from 3.5*10-5 at 300 K down to 2*10-10 at 4.2 K. The rate of decrease showed no tendency to attenuate at temperatures down to 4.2 K.
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