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The frequency of a crystal oscillator can be varied by means of a variable capacitor, but the range obtainable is extremely small. Methods of increasing the range by associating inductance with the crystal are described. It is estimated that the range of a 3-Mc/s oscillator, using an AT-cut plate, could be increased from 0.8kc/s (267 parts in 106) with variable capacitance alone, to 4kc/s (1 330 parts in 106) or more with added inductance, while preserving far better frequency stability than that of a tuned-circuit oscillator. Experiments have confirmed these results, a range of 7.7 kc/s (2560 parts in 106) being obtained with one 3-Mc/s plate. Spurious responses limit the range with some plates, but changes of rather more than 1000 parts in 106, with good frequency stability, are not difficult to achieve. Many arrangements of inductance and capacitance, capable of giving the same range, are possible. Circuits are described whereby the frequency can be made a linear function of a controlling reactance or capacitance, and the possibility of linear variation by means of a reactance valve is briefly considered. Various fields of application for an oscillator of the kind described are indicated.