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An analytical solution of the Hartley oscillator circuit is made to determine the amplitude of the alternating voltage of the output wave in terms of the tube and circuit parameters. The approach to the solution makes use of a rotating vector, which alternately gains and decays in amplitude, applied to idealized tube characteristics. The growth and decay of the vector points up the regions of amplification and nonamplification of the oscillation. The paper is divided into sections: I. The differential equation of the circuit is set up with the aid of certain simplifying assumptions and put in a form for convenient use. II. The equation is applied to a class C condition using an idealized tube characteristic without saturation. The points of demarcation between amplification and nonamplification are determined and the amplitude of the alternating output voltage is calculated. III. The equation is applied to a class C condition using an idealized tube characteristic with saturation but otherwise following the procedure of Section II.