Traditional navigation systems were based on observation of the relative position of the Sun, Moon and stars. Navigators could determine their latitude by measuring the sun's angle at noon. However to find their longitude, they needed a portable time standard that would work on a ship. Conceptually, at local high noon they could compare the chronometer's time to the time at a reference point to determine their longitude. The need for accurate navigation led to the development of progressively more accurate clocks.
The scheme of celestial navigation is that at any given instant, a celestial object will appear to be over some particular place on the Earth. So, when a navigator measures the angle to a celestial object, the navigator then knows that he is on a circle of positions which all have the same measured angle to the celestial object. By measuring a second object, the intersection of the two circles gives a measurement accurate-enough for most purposes. Theoretically, there are two positions defined by the intersction of the two circles, however the other position is usually so far away that it's not possible for the navigator to have moved to that location. If it's a problem, a third sight fixes the position exactly.
In modern celestial navigation, a navigational almanac and trigonometric sight reduction tables permit navigators to measure the Sun, Moon, visible planets or any of 57 navigational stars at any time of day or night. The mathematics required for navigation is simple addition and subtraction of logarithmic, trignometric quantities from a sight reduction table in a book. Most people can master the procedure after a day or two of instruction.
Celestial navigation can be very effective using just the sun and moon. In this case, the two sights are separated in time. However, use of the visible planets and navigational stars marks a master navigator. The numerous celestial objects permit navigators to shoot through holes in clouds, or during moonless nights. Radio navigational aids were developed to cope with cloudy conditions.
A nautical mile is about an arc-minute of error in most latitudes. Sextants can be read reliably within 0.2 arc-minutes. From two sights, a time within a second and an estimated position, a position can be determined within (theoretically) 0.2 miles, about 400 yards. Most navigators can achieve a practical accuracy of 1.5 miles, more than close enough to see a harbor or city.
The angle is measured with a special optical instrument called a "sextant". Sextants use two mirrors to cancel the relative motion of the sextant. During a sight, the user's view of the star and horizon remains steady as the boat rocks. An arm moves a split image of the sun relative to the split image of the horizon, When the lower edge of the sun's image touches the horizon, the angle can be read from the sextant's scale. Some sextants create an artificial horizon by reflecting a bubble. Inexpensive, less-accurate plastic sextants are available.
Time is measured with a chronometer, a quartz watch. or a short wave radio broadcast from an atomic clock. A quartz wristwatch normally keeps time within a half-second per day. If it is worn constantly, keeping it near body heat, its rate of drift can be measured with the radio, and by compensating for this drift, a navigator can keep time to better than a second per month. Traditionally, a navigator set his chronometer from his sextant, at a geographic marker surveyed by a professional astronomer. This is now a rare skill, and most harbor masters cannot locate their harbor's marker.
Traditionally, three chronometers are kept in gimbals in a dry room near the center of the ship. They were used to set a watch for the actual sight, so that no chronometers were ever risked to wind and water. Winding the chronometers was a crucial duty of the navigator, logged as "chron. wound." for checking by line officers.
Navigators also set the ship's clocks and calendar.