Developments in navigational science can be traced from beginnings 23 centuries ago when the Greeks tried to calculate latitude to the present when satellite systems can easily pinpoint positions to within millimetres. The history of navigational science offers vivid insights into the areas of human endeavour which have driven it: the need for discoverers such as Columbus to locate and claim distant lands for their sovereigns and paymasters; the need of merchants in a world of expanding horizons and trade for efficient and reliable shipping; the new an durgent needs of rapidly developing air travel where safety demands accurate and quick navigation in very difficult conditions; the deadly needs of the military in targetting missiles and sailing submarines in radio silence. In servicing these needs navigational science has made use of very diverse scientific discoveries: simple geometry and calculations in dead-reckoning and the use of magnetic compasses; more complicated mathematics and more accurate mechanisms in astronomical navigation; the properties of radio waves in homing and direction-finding systems; the self-contained world of gyros and inertial guidance systems; and most recently the combination of computing power, micro-electronics, and satellites to give the startling millimetre-accuracy of current systems.