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A sensitive and accurate method for the measurement of the refractive indices of gases at 3 360 Mc/s is described and critically examined to assess the systematic errors. The method is based on the measurement of the change of the resonant frequency of a cavity resonator when evacuated and when filled with a gas. A frequency modulation technique is used in conjunction with an oscillograph display. The standard deviation in the measurement of changes of the resonant frequency of the high-Q-factor cavity employed, was 77 c/s; this made possible the determination of (n Â¿ 1), where n is the refractive index, to four significant figures. This accuracy was achieved with the aid of a crystal-controlled frequency standard. The results obtained for (n Â¿ 1) Ã 106 at 0Â° C, 760 mm Hg are as follows: Dry carbon-dioxide-free air 288.26 Â± 0.2 Nitrogen 294.47 Â± 0.2 Oxygen 266.17 Â± 0.2 Carbon dioxide 494.59 Â± 0.35 Water vapour (at 20Â° C and 10 mm Hg) 61.31 Â± 0.1 The permanent electric moment of the water molecule was calculated to be (1.845 Â± 0.001) Ã 10Â¿18 e.s.u. The method of measurement is equally suitable for other microwave frequencies.