Abstract: Extremely low frequency (ELF) propagation formulas for horizontal electric dipole sources radiating in a spherical uniform earth-ionosphere cavity have a range dependence characterized by either the Legendre function of the first kind of complex degree v and order zero or one of its first two derivatives. Using the iterative formulas of Legendre function, A new method is presented in this paper. The resulting waves are expressed as a superposition of T M and T E modes. In the near-filed range, the method of images is expected to be similar to the near fields of a dipole located on a flat finitely conducting, the far field is same as the result of Bannister(dir.+ind.) formulas. This shows that the method is accurate. The result of frequencies under 1 Hz show that the horizontal electric and magnetic components are independent of the azimuth, and the direction of horizontal electric components is parallel to the dipole axis in the isolines chart with distance, whereas, the direction of horizontal magnetic components is orthogonal to dipole axis.