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The ultimate bandwidth and stability of Pound-stabilized microwave oscillators are investigated. It is shown that, if high Q-factor cavity resonators are used and steps are taken to eliminate modulation at the mains frequency, a bandwidth of 1 part in 1010 and a stability of 1 part in 108 per hour can be obtained. The residual drift seems to be largely associated with changes in the crystal diode used as the modulator in the control circuit. Some applications of stable microwave oscillators are discussed and the results of measurements of the spatial variations of the refractive index of the atmosphere are given. Neighbouring air pockets of about 1 litre in volume can, under disturbed conditions, have refractive indices differing by as much as 1 part in 105, and variations of 1 part in 106 are fairly general, even inside the laboratory.