Longitude and Latidude


The idea of ​​the sphericity of the Earth was not very difficult to accept. The projection of the shadows of the Earth on the Moon during partial eclipses and the shape of the Moon and the Sun, were the signs with which Nature argued against those flat worlds full of precipices for hell.

The Greeks already accepted the sphericity of the Earth and the geographer Eratosthenes, who then directed the famous library of Alexandria, was the first to calculate the perimeter of our planet and with a much smaller error than Christopher Columbus 2,000 years before this. From the shadow of an obelisk in Alexandria he calculated that at midday on the summer solstice day, the sun was at the zenith 1/50 of the circumference. He also knew that in Siena in Upper Egypt (today Aswan), and that day, the sun did not cast any shadow at the bottom of the wells at noon.

As the two cities were approximately on the same meridian, he concluded that the length of the cities would be 50 times the distance between them, a distance that is already known. With the technical means at the time, the accuracy was astounding. An error only every 24,000 miles!

It was perhaps the first notion of latitude, although not angular. Hiparco, a Greek mathematician and a great astronomer, who is credited with creating Trigonometry, started measuring latitude from 0 to 90 degrees from Ecuador and specified places on earth using latitude/longitude coordinates.

Hiparco is also attributed to the creation of the astrolabe, with which heights are measured, an instrument that the Portuguese simplified and adapted for nautical use. Over time, other nautical instruments for taking heights appeared, such as the quadrant, the crossbow, and finally the sextant, whose reading accuracy was improved until the second of the arc.

It is not possible to speak of the problem of latitude in the same way as that of longitude, since the method of determining it was known since antiquity and did not offer major problems.

When the land was not seen, oceanic navigations required knowledge of the position, and since there were no landmarks, it was the stars who served this purpose. The first would have been the Pole star, by which the Portuguese in the 15th century took the height when they left and compared days later, transforming the difference in arc measurement into navigated leagues. In the beginning, one degree was equivalent to 16 leagues and 2/3, reaching 17.5 leagues per degree at the end of the 15th century.

This method required the height to be taken at a certain time. The nocturlábio or polar wheel was the instrument used to know the time and also to make the necessary corrections in the reading since in the 15th century the Polar star was not directly on the pole and made a radius of 3.5º with it. Due to the phenomenon of the precession of the equinoxes, this star was in a movement of approaching the pole and a century later the radius was already well below 3º. The tables had to be corrected successively over time.

This type of navigation was known as the Northern Regiment and was a major advance in astronomical navigation.

As navigation approached the equator, the polar star disappeared and the alternative was to find another star with similar properties. In the southern hemisphere, a star, Crucis or Pé do Cruzeiro, was used to calculate latitude, but the distance from that to the pole will not have allowed very accurate calculations. It was also possible to make a regiment for that star, but the calculation from that star was not much to the liking of most Portuguese pilots.

The use of the meridian, taken from the height of the Sun when it passes through the observer’s meridian, was the most appreciated and easy method, whatever the hemisphere. The rules were simple and there were tables with the declination for all days of the year. This method was known by the Regiment of the Sun.

Nautical charts, hitherto little or nothing precise, are now more rigorous thanks to an observed latitude.

Latitude is the arc of the meridian that passes in place from the equator to the parallel of the place. It counts from 0º to 90º from Ecuador and is North or South depending on the terrestrial hemisphere where the place is located.

In the calculations, the latitude takes a positive value to the North and a negative value to the South. To obtain the latitude of a place we have to take the height of the star (usually the Sun at solar noon, also called meridian) and together with the nautical tables, where we get the declination of the star that day, we do the necessary calculations.

A meridian is a maximum circle that passes through both poles. The parallels, which owe their name to the fact that they are circles parallel to Ecuador, mark the latitudes.


The first to propose the use of two coordinates to define a place on the globe was Hipparchus in antiquity: latitude, a place on a meridian (maximum circle passing through the poles), and longitude, a place on a parallel (circle parallel to Ecuador). The calculation of latitude was relatively easy and known and was obtained with an astrolabe. In turn, longitude offered more problems and was never correctly calculated until the 18th century, even if theoretically it was known how to do it. Science was that it had not yet produced sufficiently precise instruments and mathematics had not yet been able to provide accurate tables.

In terms of land orientation, there were no major problems as the reference points remained fixed. In the sea, where there are no references other than the stars, and these are also mobile, difficulties in orienting themselves were put in place.

When, in the 15th century, the Portuguese launched themselves across the Atlantic, a new era began in sea voyages that forced them to change the type of navigation hitherto carried out. It went from typical coastal navigation to purely oceanic navigation. In the Mediterranean, although some trips were made without the coast in sight, navigation was done in a relatively closed space and with many islands based on directions, where the stars served only as a companion for the pilots, or for them to guide themselves in the directions.

True astronomical navigation does begin with exploring the oceans and reading the positions of ships on the stars. It was not only the Portuguese who were the forerunners of this type of navigation, which continues today, since at the same time the Chinese explored the sea of ​​Japan and the Chinese coast as far as Mombasa, on the East African coast with the help of Zheng He, using similar methods.

In order to obtain a more rigorous and less complicated latitude at sea, it was necessary to improve and adapt some methods and instruments, already more or less known. The search for longitude, however, was an adventure that lasted for about three hundred years with numerous attempts at a solution, revealing a very fertile and varied imagination in the solutions presented.

At the time, the only method used to obtain longitude was esteem, which sometimes led to errors that were too gross. Thanks to their experience, some pilots obtained satisfactory results but always subject to doubts. The estimate was the result of the ship’s course, of the speed, which was done literally “by eye” and of the time traveled with the use of hourglasses. Therefore, it counted a lot, the experience of the pilots.

As can be seen, credible results could never be obtained and the first concrete case took place as early as 1494 when the two Iberian kings signed the Treaty of Tordesillas that divided the globe into two zones of influence. One Castilian and the other Portuguese, delimited by a meridian that passed 370 leagues west of Cape Verde. This meridian “moved” according to interests and later resulted in some problems regarding the possession of the Moluccas and part of Brazil.

Cartography, in turn, had improved, it was only about latitude, as longitude was roughly obtained.

This problem has become a matter of state for several countries involved in the exploration of the seas and several European monarchs have offered rewards for discovering a simple and effective method for obtaining longitude at sea.

In 1598 Filipe III of Spain offered 10,000 duchies as a prize. Among those who competed was Galileo who proposed in 1610 the measurement of time-based on observations of Jupiter’s moons. A few years’ correspondences with the Spanish court did not convince the king. The Dutch also institute a prize in 1636 and take Galileo more seriously, only that in the meantime he is prevented from being contacted by the Inquisition and after a few years he ends up dying.

The solution was in fact to conserve the time of the reference meridian during the trip, but everyone recognized that with the types of watches that existed at the time, the necessary precision was not possible. In 1514 Johann Werner introduced the method of lunar distances and, although theoretically correct, the technique of that time was still insufficient. At the same time, João de Lisboa imagines a process of determining longitude by varying the magnetic declination, assuming that there was a linear proportionality between them. D. João de Castro proved in 1538 the impossibility of this theory.

Varied and elaborated methods for determining longitude have been presented over the years. They were based on the observation of solar and lunar eclipses, Jupiter’s satellites, the concealment of stars by the Moon, clocks, and even bomb explosions! This last solution, by M. Whiston and Ditton, proposed the installation of mortars along the coast and islands that would fire at certain and regular times. So the navigators would know the hours on land that compared to the ship’s would give the difference in longitudes between two places !!

In France, the Academie Royale des Sciences was created in 1666 with the aim of bringing together the best scientists of the time and, of course, committed to the practical resolution of the problem of longitude. A Louis XIV prize of 100,000 florins was the incentive for this discovery. The French believed in a clock to measure the time difference between the local meridian and a reference, and for that purpose, they created in 1667 the Paris Meridian, which passed the Faubourg Observatory in St. Jacques. However, the use of the pendulum in onboard clocks did not provide the precision for a calculation at sea.

Previously the hourglass was also the obstacle in the calculation, as its precision did not give any confidence. Just to get a sense of error, remember that a 4-second error results in a difference of 1 nautical mile!

In 1707, as a result of a catastrophe in which an English squadron and its renowned admiral were lost in the rocks of the Isles of Scilly, the English parliament created in 1714 the Board of Longitude with the specific purpose of solving the problem. Losing a fleet at the height of English navigation by accident and not by enemy action was humiliating. In turn, a prize of £ 20,000 was the reward offered.

There was no shortage of candidates, including Newton who proposed the lunar method, and in 1735 John Harrison presented the first prototype of a marine chronometer and later won the prize.

Despite everything and due to the lack of confidence in the instrument and its price, it was only when the hourly signal began to be emitted by radio that the use of the stopwatch became widespread. Until then, the lunar method was used to obtain time and each country used its reference meridian to obtain the place. Portugal the meridian of Lisbon, which passed through the Royal Observatory of the Navy, Spain the one of Cadiz, France the one of Paris and the English the one of Greenwich since 1767, date when Nevil Maskelyne began to edit nautical tables. This obliged each country to make different tables according to the chosen meridian.