The astronomical methods of position finding at sea used at the present time are the culmination of an evolutionary process which began even before the first Phoenician sea traders navigated their vessels in the waters of the western Mediterranean and the Atlantic coast of northwest Europe 3,000 years ago, using the heavenly bodies to guide them. It could be that the true origin of nautical astronomy was the realization that the star known today as Polaris, or the Pole Star, always lay to the north. The Phoenicians knew this and it is probable that this fact had not escaped the notice of earlier navigators. That an observation of Polaris or of the midday sun, also gave the latitude of the observer, and this was the principle that has been used since the earliest navigations. But the problem of finding longitude has not been so simple.

There were two methods of discovering the longitude of an observer at sea, one by time and one by lunar observation. First was a reliable chronometer which would keep accurate and constant time on board ship in all conditions of weather, heat and cold, the second by the high degree of math skill required to work out the astronomical measurement of lunar distances. The method of calculating longitude by time measurement was first suggested by Gemma Frisius as far back as 1530, but it was to be another 250 years before John Harrison produced a chronometer accurate and reliable enough to solve this problem at sea. The nautical astronomer, or navigator, relies on astronomical tables to solve problems in spherical trigonometry before he can translate his observations of heavenly bodies into a position on a chart.

During the 19th century the finding of longitude at sea by the time method was simplified by the discoveries of Captain Thomas Sumner and Admiral Marcq St. Hilaire, and their methods of obtaining a ship's position by observation of one or more heavenly bodies became the navigator's standard practice. The sextant, the chronometer, the Nautical Almanac, and mathematical tables are the instruments of nautical astronomy, and with them a navigator can find his position on a chart anywhere in the world. The triangle is solved by calculations on the lines of the Cosine Theory and involve extensive use of mathematical tables. But the new air navigation tables, now in wide use by many navigators at sea, have made the solution much simpler, and with these and a Nautical Almanac, a navigator can obtain his true position without the long calculations.

From his observed altitude of the celestial body a navigator obtains from the tables the true zenith distance of the body and from the Nautical Almanac the zenith distance from his dead reckoning or assumed position. The difference between these two distances is known as the "intercept" and shows the navigator how far his real position is from his assumed position in one direction. He finds this direction from the exact time at which he took his sight which, from the tables, gives him the Greenwich Hour Angle.

His assumed longitude then gives him the Local Hour Angle and, using thc body's declination from the Nautical Almanac, the azimuth, or bearing, is obtained. By drawing this bearing on the chart from his assumed position and measuring off the intercept, a line drawn through that point at right angles to the azimuth provides a position line. A similar sight taken at the same time of a second celestial body on a different bearing will provide a second position line and the observer's true position is at the point of intersection of these two position lines. An alternative method for use during daylight hours when the sun is normally the only celestial body in sight is to take a second observation of the sun some 3 or 4 hours. The solution of this second observation produces a position line in exactly the same way as the first. The first position line is transferred on the chart with a parallel ruler to take the distance run and the course steered during the time which has elapsed between the two observations, the point of intersection of the two position lines is the true position of the vessel. This is known as the Marcq St. Hilaire method.

The new tables, though much quicker and simpler to use, do not give quite the accuracy of the older method of calculation. Where the new tables will produce an observed position within about a nautical mile of the true position, navigators using the older method normally worked to a tenth of a nautical mile, or 200 yards, and would expect their sights, providing they were taken from a reasonably steady platform, to produce an observed position within this distance of the true position.