In the last episode of this series, we explored the history of the magnetic compass in Europe and marine cartography from the Portolan chart to the Mercator Projection. We will now turn our attention to the other developments in navigation at sea in the Renaissance. As already stated in the last episode, the need to develop new methods of navigation and the instruments to carry them out was driven by what I prefer to call the Contact Period, commonly called the Age of Discovery or Age of Exploration. The period when the Europeans moved out into the rest of the world and exploited it.
This movement in turn was motivated by various factors. Curiosity about lands outside of Europe was driven both by travellers’ tales such as The Travels of Marco Polo c. 1300 and The Travels of Sir John Mandeville, which first appeared around 1360, both of which were highly popular throughout Europe, and also by new cartographical representation of the know world, known to the Europeans that is, in particular Ptolemaeus’ Geographia, which first became available in the early fifteenth century. Another development was technological, the development by the Portuguese, who as we shall see led the drive out of Europe into the rest of the world, of a new type of ship, the caravel, which was more manoeuvrable than existing vessels and because of its lateen sails was capable of sailing windward, making it more suitable for long ocean voyages, as opposed to coastal sailing.
The final and definitely most important factor was trade or perhaps more accurately greed. The early sailors, who set out to investigate the world outside of Europe, were not the romantic explorers or discoverers, we get taught about in school, but hard-headed businessmen out to make a profit by trade or if necessary, theft.
The two commodities most desired by these traders, were precious metals, principally gold but also silver and copper, and spices. The metal ore mines of Middle Europe could not fill the demands for precious metals, so other sources must be found. This is perhaps best illustrated by the search in South America, by the Spanish, for the mythical city of gold, El Dorado, during the sixteenth century. Spices had been coming into Europe from the East over the Indian Ocean and then overland, brought by Arab traders, to the port cities of Northern Italy, principally Venice and Genoa, from where there were distributed overland throughout Europe since the eleventh century. The new generation of traders thought they could maximise profits by cutting out the middlemen and going directly to the source by the sea route. This was the motivation of both Vasco da Gama (c. 1460–1524), sailing eastwards, and Christopher Columbus (1451–1506), sailing westward. Their voyages are, however, one end point of a series of voyages, which began with the Portuguese capture of Ceuta, in North Africa, from the Arabs, in 1415.
Having established a bridgehead in North Africa the Portuguese, who were after all situated on the Atlantic coast of the Iberian Peninsula, argued that they could bypass the middleman, their trading partners the Arabs, and sail down the coast to Sub-Saharan West Africa and fetch for themselves, the gold and the third great trading commodity of the Contact Period, slaves, who they had previously bought from Arab traders. It is fair to ask why other countries, further north, with Atlantic coasts did not lead the expansion into unknown territory? The first decades of the Portuguese Atlantic ventures were still very much coastal sailing progressively further down the African coast; other northern European countries, such as Britain did sail north and south along the Atlantic coast, but their journeys remained within Europe.
Starting in 1520, Portuguese expeditions worked their way down the west coast of Africa until the end of the sixteenth century.
The Nürnberger Martin Behaim (1459–1507), responsible for the creation of the oldest surviving terrestrial globe and member of the Portuguese Board of Navigation (to which we will return), claimed to have sailed with Diogo Cão, who made two journeys in the 1480s, which is almost certainly a lie. At the time of Cão’s first voyage along the African coast Behaim is known to have been in Antwerp. On his second voyage Cão erected pillars at all of his landing places naming all of the important members of the crew, who were on the voyage, Martin Behaim is not amongst them.
The two most significant Portuguese expedition were that of Bartolomeu Dias (c. 1450–1500) in 1488, which was the first to round the Cape of Good Hope, actually Diogo Cão’s aim on his two voyages, which he failed to achieve, and, of course, Vasco da Gama’s voyage of 1497, which took him not only up the east African coast but all the way to India with the help of a local navigator. The two voyages also showed that the Indian Ocean was open to the south, whereas Ptolemaeus had shown it to be a closed sea in his Geographia.
Much earlier in the century the Portuguese had ventured out into the Atlantic and when blown off course by a storm João Gonçalves Zarco (c. 1390 –1471) and Tristão Vaz Teixeira (c. 1395–1480) discovered the archipelago of Madeira in 1420 and one expedition discovered the Azores, 1,200 km from the Portuguese coast in 1427. The Canaries had already been discovered in the early fourteenth century and were colonised by the Spanish in 1402. The Cap Verde archipelago was discovered around 1456. The discovery of the Atlantic islands off the coasts of the Iberian Peninsula and Africa was important in two senses. Firstly, there developed myths about other islands further westward in the Atlantic, which encouraged people to go and look for them. Secondly, by venturing further out into the Atlantic sailors began to discover the major Atlantic winds and currents,, known as gyres essential knowledge for successful expeditions.
Dias could only successfully round the Cape because he followed the prevailing current in a big loop almost all the way to South America and then back past the southern tip of Africa. Sailors crossing the Indian Ocean between Africa and India had long known about the prevailing winds and currents, which change with the seasons, which they had to follow to make successful crossings. The Spanish and the Portuguese would later discover the currents they needed to follow to successfully sail to the American continent and back.
The idea of island hopping to travel westwards in the Atlantic that the discoveries of the Azores and the other Southern Atlantic islands suggested was something already been followed in the North Atlantic by fishing fleets sailing out of Bristol in Southwest England in the fifteenth century. They would sail up the coast of Ireland going North to the Faroe Islands, settled by the Vikings around 800 CE and then onto Iceland, another Viking settlement, preceding to Greenland and onto the fishing grounds off the coast of Newfoundland. This is the route that Sebastian Cabot (c. 1474–c. 1557) would follow on his expedition to North America in the service of Henry VIII. It is also probable that Columbus got his first experience of navigating across the Atlantic on this northern route.
Columbus famously made his first expedition to what would be erroneously named America in 1492, in an attempt to reach the Spice Islands of Southeast Asia by sailing westward around the globe. This expedition was undertaken on the basis of a series of errors concerning the size of the globe, the extent of the oikumene, the European-Asian landmass known to the Greek cartographers, and the distance of Japan from the Asian mainland. Columbus thought he was undertaking a journey of about 3,700 km from the Canary Islands to Japan instead of the actual 19,600 km! If he hadn’t bumped into America, he and his entire crew would have starved to death on the open sea. Be that as it may, he did bump into America and succeeded in returning safely, if only by the skin of his teeth. With Columbus’ expedition to America and da Gama’s to India, the Europeans were no longer merely coastal sailors but established deep sea and new approaches to navigation had to be found.
The easiest way to locate something on a large open area is to use a geometrical coordinate system with one set of equally spaced lines running from top to bottom and a second set from side to side or in the case of a map from north to south and east to west. We now call such a grid on a map or sea chart, lines of longitude also called meridians, north to south, and lines of latitude also called parallels, east to west. The earliest know presentation of this idea is attributed to the Greek polymath Eratosthenes (c. 276–c. 195 BCE).
The concept was reintroduced into Early Modern Europe by the discovery of Ptolemaeus’ Geographia. It’s all very well to have a location grid on your maps and charts but it’s a very different problem to determine where exactly you are on that grid when stuck in the middle of an ocean. However, before we consider this problem and its solutions I want to return to the Portuguese Board of Navigation, which I briefly mentioned above.
Both the Portuguese and the Spanish realised fairly early on as they began to journey out onto the oceans that they needed some way of collecting and collating new geographical and navigation relevant information that their various expeditions brought back with them and also a way of imparting the relevant information and techniques to navigators due to set out on new expeditions. Both countries established official institutions to fulfil these tasks and also appointed official cosmographers to lead these endeavours. Pedro Nunes (1502–1578), who we met in the first episode on navigation, as the discoverer of the loxodrome, was appointed Portugal’s Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547, a post he held until his death.
The practice of establishing official organisations to teach cartography and navigation, as well as the mathematics they needed to carry them out to seamen was followed in time by France, Holland, and Britain as they too began to send out deep sea marine expeditions.
To determine latitude and longitude are two very different problems and I will start with the easier of the two, the determination of latitude. For the determination of longitude or latitude you first need a null point, for latitude this is the equator. In the northern hemisphere your latitude is how many degrees you are north of the equator. You can determine your latitude using either the Sun during the day or the North Star at night. At night you need to observe the North Star with some sort of angle measuring device then measure the angle that makes to the horizon and that angle is your latitude in degrees. During the day you need to observe the Sun at exactly noon with an angle measuring device then the angle to makes with a vertical plumb line is your latitude. This is only strictly true for the date of the two equinoxes. For other days of the year, you have to calculate an adjustment using tables. For these observations mariners initially used either a quadrant,
which had been in use since antiquity or a Jacob’s Staff or Cross Staff, the invention of which is attributed to the French astronomer Levi Ben Gershon (1268–1344).
Contrary to many claims, astrolabes were never used on ships for this purpose. However, around the end of the fifteenth century a much-simplified version of the astrolabe, the mariner’s astrolabe began to be used for this purpose.
Because looking directly into the Sun is not good for the eyes, the backstaff was developed over time. With a backstaff the mariner stands with his back to the Sun and a shadow is cast onto the angle measuring scale. Thomas Harriot (c. 1560–1621) is credited with being the originator of the concept. The mariner John Davis (c. 1550–1605) introduced the double quadrant or Davis quadrant in his book on practical navigation, The Seaman’s Secrets in 1594, a device that evolved over time.
In 1730, John Hadley invented the reflecting octant, which incorporated a mirror to reflect the image of the Sun, whilst the user observed the horizon.
This evolved into the sextant the device still used today to “shoot the Sun” as it is called. Here we see an evolution of instruments used to fulfil a specific function.
The determination of longitude at sea is a much more difficult problem. First, there is no natural null point, and any meridian can be and indeed was used until the Greenwich Meridian was chosen as the international null point for the determination of longitude at the International Meridian Conference in Washington in 1884. Because the Earth revolves once in twenty-four hours the determination of the difference in longitude between two locations is equivalent to the difference in local time between them, one degree of longitude equals four minutes of time difference, so the determination of longitude is basically the determination of time differences, which is easy to state but much more difficult to carry out.
The various European sea going nations–Spain, Portugal, France, Holland, Britain–all offered financial awards to anybody who could come up with a practical solution for determining longitude at sea.
In antiquity, the difference in longitude between two locations was determined by calculating the difference in the observation times of major astronomical events such as lunar or solar eclipses. Then, if one had determined the difference in longitude between two given locations and their respective distances from a third location, it was possible to calculate the difference in longitude for the third location geometrically. Using these methods, astronomers, and cartographers gradually built-up tables of longitude for large numbers of towns and cities such as the one found in Ptolemaeus’ Geographia. This method is, of course, not practical for mariners at sea.
Starting in the early sixteenth century, various methods were suggested for determining time differences in order to determine longitude. The Nürnberger mathematicus Johannes Werner (1468 – 1522) in his In hoc opere haec continentur Nova translatio primi libri geographiae Cl’ Ptolomaei … (Nürnberg 1514) proposed the so-called lunar distance method. In this method an accurate table of the position of the Moon relative to a given set of reference stars for a given location for the entire year needs to be created.
The mariner then has to observe the position of the Moon relative to the reference stars for his local time and then calculate the time difference to the given location from the tables. Unfortunately, because the Moon is pulled all over the place by the gravitational influence of both the Sun and the Earth, its orbit is highly irregular and the preparation of such tables proved beyond the capabilities of sixteenth century astronomers and indeed of seventeenth century astronomers, when the method was proposed again by Jean-Baptiste Morin (1583–1656). There was also the problem of an instrument accurate enough to measure the position of the Moon on a moving ship. It was Tobias Mayer (1723–1762), who first managed to produce accurate tables and Hadley’s octant or rather the sextant that evolved out of it solved the instrument problem. The calculations necessary to determine longitude having measured the lunar distance proved to be too complex and too time consuming for seamen and so Neville Maskelyne produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766.
The next solution to the problem of determining longitude suggested during the Renaissance by Gemma Frisius (1508–1555) was the clock, published in his De principiis astronomiae et cosmographiae. (Antwerp, 1530).
The mariner should take a clock, capable of maintaining accurate time over a long period under the conditions that prevail on a ship on the high seas, set to the time of the point of departure. By comparing local time with the clock time, the longitude difference could then be calculated. The problem was that although mechanical clocks had been around for a couple of centuries when Gemma Frisius made his suggestion, they were incapable of maintaining the required accuracy on land, let alone on a ship at sea. Jean-Baptiste Morin thought it would never be possible, “I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try.” A view apparently shared by Isaac Newton, when he sat on the English Board of Longitude.
Only when Christiaan Huygens (1629–1695) had the first pendulum clock constructed by Salomon Coster (c. 1620–1659) accord his design in 1657 that Frisius’ idea began to seem realistic.
One of Huygens’ clocks was actually sent on sea trials but failed the test. In what is, thanks to Dava Sobel[1], probably the most well-known story in the history of technology John Harrison (1693–1776)
finally succeeded in producing a clock capable of fulfilling the demands with his H4 in 1761, slightly later than the successful fulfilment of the lunar distance method. In one sense the problem was still not really solved because the H4 was too complex and too expensive for it to be mass produced at a reasonable cost for use in sea transport. It was only really in the nineteenth century, after further developments in clock technology, that the marine chronometer became a real solution to the longitude problem.
Back tacking, at the beginning of the seventeenth century with the discovery of the four largest moons of Jupiter another method suggested itself. These moons, Io, Europa, Ganymede, and Callisto, have orbital periods of respectively, 1.77, 3.55, 7.15, and 16.6 days.
This means that one or other of them is being fairly often eclipsed by Jupiter. Galileo argued that is one could calculate the orbits accurately enough they could be used as a clock to determine longitude. He tried to sell the idea to the governments of both Spain and the Netherlands without success. The principal problem was the difficulty of observing them with a telescope on a moving ship. Galileo worked on an idea of an observing chair with the telescope mounted on a helmet, but the idea never made it off the paper. Later in the seventeenth century Jean-Dominique Cassini (1625–1712) produced tables of the orbits accurate enough for them to be used to determine longitude and he and Jean Picard (1620–1682) used the method on land to accurately determine the borders of France, leading Louis XVI to famously quip that he had lost more territory to the cartographers than he ever lost to his enemies.
In the first part of this account of navigation I described the phenomenon of magnetic variations or declination, which is the fact that that a compass does not point to true north but to magnetic north, which is somewhat removed from true north. I also mentioned that magnetic declination is not constant but varies from location to location. This led to the thought that if one were to map the magnetic inclination for the entire Atlantic one could use the data to determine longitude, whilst at sea. Edmond Halley (1556–1742) did in fact create such a map on a voyage from1699 to 1700. However, this method of determining longitude was never really utilised.
Although the methods eventually developed to determine longitude on the high seas all came to fruition long after the Renaissance, they all have their roots firmly planted in the practical science of the Renaissance. This brief sketch also displays an important aspect of the history of science and technology. A lot of time can pass, and very often does, between the recognition of a problem, the suggestion of one or more solutions to that problem, and the realisation or fulfilment of those solutions.
Having gone to great lengths to describe the principal methods suggested and eventually realised for determining longitude, there were others ranging from the sublime to the ridiculous that I haven’t described, there remains the question, how did mariners navigate when far away from the coast during the Early Modern Period? There are two answers firstly latitude sailing and secondly dead reckoning. In latitude sailing, instead of, for example, trying to cross the Atlantic by the most direct course from A to B, the navigator first sails due north or south along the coast until he reaches the latitude of his planned destination. They then turn their ship through ninety degrees and maintain a course along that latitude. This, of course, nearly always means a much longer voyage but one with less risk of getting lost.
In dead reckoning, the navigator, starting from a fixed point, measures the speed and direction of his ship over a given period of time transferring this information mathematically to a sea chat to determine their new position. The direction is determined with the compass, but the determination of the ship’s speed is at best an approximation, which was carried out in the following manner. A log would be thrown overboard at the front of the ship and the mariners would measure how long it took for the ship to pass the log, and the result recorded in a book, which became known as the logbook. The term logbook expanded to include all the information recorded on a voyage on a sip and then later on planes and even lorries. Of note, the word blog is an abbreviation of the term weblog, a record of web or internet activity, but I’m deviating from the topic.
The process of measuring the ships speed evolved over time. The log was thrown overboard attached to a long line and using an hourglass, the time how long the line needed to pay out was recorded. Later the line was knotted at regular intervals and the number of knots were recorded for a given time period. This is, of course, the origin of the term knots for the speed of ships and aircraft. Overtime the simple log of wood was replaced with a so-called chip-log, which became standardised:
The shape is a quarter circle, or quadrant with a radius of 5 inches (130 mm) or 6 inches (150 mm), and 0.5 inches (13 mm) thick. The logline attaches to the board with a bridle of three lines that connect to the vertex and to the two ends of the quadrant’s arc. To ensure the log submerges and orients correctly in the water, the bottom of the log is weighted with lead. This provides more resistance in the water, and a more accurate and repeatable reading. The bridle attaches in such a way that a strong tug on the logline makes one or two of the bridle’s lines release, enabling a sailor to retrieve the log. (Wikipedia)
The invention of the log method of determining a ship’s speed is attributed to the Portuguese mariner Bartolomeu Crescêncio at the end of the fifteenth century. The earliest known published account of using a log to determine a ship’s speed was by William Bourne (c. 1535–1582) in his A regiment of the Sea in 1574, which went through 11 English editions up to 1631 and at least 3 Dutch edition from 1594.
Dead reckoning is a process that is prone to error, as it doesn’t take into account directional drift caused by wind and currents. Another problem was that not all mariners processed the necessary mathematical knowledge to transfer the data to a sea chart. Those mariners, who disliked and rejected the mathematical approach used a traverse board, which uses threads and pegs to record direction and speed of a ship. William Bourne writing in 1571 said:
I have known within these 20 years that them that were ancient masters of shippes hathe derided and mocked them that have occupied their cards and plattes and also the observation of the Altitude of the Pole saying; that they care not for their sheepskinne for he could keepe a better account upon a board.
This blog post is already far too long, so I’ll skip a detailed description of the traverse board, but you can read one here.
We have one last Renaissance contribution to the art of navigation from the English mathematical practitioner, Edmund Gunter (1581–1626), who we have already met as the inventor of the standard English surveyor’s chain in the episode on surveying. Gunter invented the Gunter scale or rule, simply known as the “gunter” by mariners, which he published in his Description and Use of the Sector, the Crosse-staffe and other Instrumentsin 1623. Developed shortly after the invention of logarithms, the scale is usually somewhat more than a half metre long and about 40 mm broad. It is engraved on both sides with various scales or lines. Usually, on the one side are natural line, chords, sines, tangents, rhumbs etc., and on the other scales of the logarithms of those functions. Navigational mathematical problems were then worked through using a pair of compasses.
Despite its drawbacks, uncertainties, and errors dead reckoning was used for centuries by European mariners to crisscross the oceans and circumnavigate the globe. It continued to be used well into the nineteenth century, long after the perfection of the marine chronometer and the lunar distance method.
This over long blog post is but a sketch of the contributions made by the Renaissance mathematical practitioners to the development of methods of deep-sea navigation required by the European mariners during the Contact Period, when they swarmed out to investigate the world beyond Europe and exploit it. Those contributions were in the form of theories, publications, instruments, charts, and practical instruction (which I haven’t really expanded upon here). For a more detailed version of the story, I heartily recommend Margaret Scotte’s excellent Sailing School: Navigation Science and Skill, 1550–1800 (Johns Hopkins University Press, 2019).
[1] Sobel’s account of the story is somewhat less than historically accurate and as always, I recommend instead Dunne and Higgitt, Finding Longitude: How ships, clocks and stars helped solve the longitude problem (Collins, 2014)
The Renaissance Mathematicus 
Sorry for my bad English concerning sailing.
@picture 2: There ist a longer distance when you changes often the course relativ to two long parts and only one change – the sailing vessel, especially a greater vessel, will always be thrown back a little distance during the manoeuver. On modern racing yachts you can ignore this, but with schooner and similar boats and strong wind it can be impossible to gain distance forward because you loose to much while changing the course.