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A generalized Appleton-Hartree equation is derived, applicable to any variation of electron collision frequency with electron speed and any degree of ionization. Regions of the parameters where simplification occurs are given. Results are shown for the ionosphere (60 to 320 km) and compared with experimental data. Good agreement is obtained for the D layer. Experimental data for the E layer can also be explained by assuming an electron temperature several times the gas temperature. This is consistent with rocket data and a measurement by Sputnik III. It is shown that the classic Appleton-Hartree equation should be applicable with no corrections necessary for the F2 layer, provided the collision frequency is averaged appropriately.