Longitude by chronometer

It is an astronomical method of calculating the longitude at which a position line, drawn from a sight by sextant of any celestial body, crosses the observer's assumed latitude.

The angle between the sea horizon and the celestial body is measured with a sextant and the time noted.

The actual declination and hour angle of the celestial body are found from astronomical tables for the time of the measurement and together with the 'True Altitude' are put into a formula with the assumed latitude.

The desperate need for an accurate chronometer was finally met in the mid 18th century when an Englishman, John Harrison, produced a series of chronometers that culminated in his celebrated model H-4 that satisfied the requirements for a shipboard standard time-keeper.

It is impossible to determine longitude with an accuracy better than 10 nautical miles (19 km) by means of a noon sight without averaging techniques.

By taking a sextant reading within 15 to 30 minutes prior to local noon (culmination) and noting the time, then leaving the sextant set to the same angle and subsequently observing the moment in time at which the sun passes through the sight tube on its descent from its highest altitude between a half-hour and hour later, the two times can be averaged to obtain a longitude sufficiently accurate for navigation (within 2 nautical miles [3.7 km]).

Consequently, noon at the Prime Meridian is rarely if ever exactly at 12:00 UTC, but rather it occurs some minutes and seconds before or after that time each day.

This slight daily variation has been calculated and is listed for each day of the year in the Nautical almanac[4] under the title of Equation of time.

This variation must be added to or subtracted from the UTC of local apparent noon to improve the accuracy of the calculation.

Without time averaging, the difficulties in determining the exact moment of local noon due to the flattening of the Sun’s arc across the sky reduce the accuracy of calculation.