The physical and electrical properties of typical VLF transmitters are described, and new formulas are given for the electromagnetic field they generate on the surface of and at any depth in the sea. These apply to the spherical earth at frequencies in the range 14≤f≤30 kHz. They are useful for distances up to 10,000 km. Special application is made to communication with submerged submarines equipped with horizontal antennas.¿ 1997 American Geophysical Union