This paper describes a system of navigation by measurement of the Doppler shift in the radio transmissions from a near-Earth satellite, and simple equipment for making the measurements. It also shows that the current information which is needed by the navigator can be reduced to a number containing six decimal digits. Finally, it shows that the computations needed for the navigator to obtain a fix can be performed witlh the aid of tables that can be prepared at least 18 months in advance. Using these tables and a simple slide rule, but no other computational aids, a fix accurate to about 500 meters can be obtained in about 10 minutes. More accuracy can be obtained at the expense of time, or time can be saved at the expense of accuracy.