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Using a double parabola approximation to the Chapman distribution of electron density as a function of height, and the assumption of a curved-ionosphere, curved-earth geometry, analytic expressions are obtained for the true height of reflection, ray path, reflection coefficient, ground range, and group path. Graphical results are given for the maximum usable frequency factor. Where possible, the above results are compared with results obtained by assuming a plane ionosphere. All of these calculations are made under the usual restrictions of neglecting the earth's magnetic field and most of the effects of collisions of electrons with heavy particles.