1484 – The Rule of the Sun

While Diogo Cão pushed the boundaries for how far a man could sail south along the coast of Africa, cartographers and scientists in Europe busily analyzed the survey and astrological data Portuguese and other explorers had brought home with them. In 1484, probably before Diogo Cão returned from his first expedition, King João established a council of astronomers and mathematicians to perfect navigation instruments and devise a method to measure latitude using solar observations – the Rule of the Sun. The explorers who had sailed below the equator returned with complaints that their astrolabes were no longer useful when they lost site of Polaris. The scientific council became known as the Junta Matemático.

Astronomers in Nuremberg, where the majority of astrolabes and other precision instruments were manufactured, and Abraham Zacuto (1452-1515/20), an astronomer at the University of Salamanca in Castile, had already been working on this problem. They had concluded that navigators needed a method for determining the angular distance north or south of the celestial equator at midday [noon].

The mathematicians in King João’s Junta Matemático were given the task of creating mathematical functions that involved the physical relationships of the sun to the horizon and the equator. The astronomers were given the task of measuring those physical relationships – measurements that changed from place to place every day. The tools available to the astronomers were the cross-staff, quadrant, magnetic compass, and astrolabe.

During the first part of the century, astronomers could compare the positions of the celestial bodies [planets, stars, moon, and sun] at different times of the day, night, and season from various places in Europe. But not until Fernão do Po returned from crossing the equator in 1469, and Diogo Cão displayed how easy it was to dash between the equator and Lisbon in his caravel in 1484, could astronomers take measurements of the relationship of celestial bodies from the equator itself, or south of it.

This data was recorded on tables known as ephemerides [a single table is an ephemeris] and compiled into books and calendars that were useful guides known as almanacs. Abraham Zacuto had, between 1470 and 1478, created a book called Ha-ḥibbur ha-gadol [in Hebrew] or The Great Book [in English] with sixty-five detailed astrological charts predicting and describing hundreds of celestial activities. The book is more commonly known by its Latin title Almanach Perpetuum [Perpetual Almanac].

Abraham Zacuto’s Almanach Perpetuum, Salamanca, Castile, bet. 1470 and 1478 written in Hebrew.(1)

The inventions and research by Abraham Zacuto – who was thirty-five years old in 1486 and close in age to Christopher Columbus, John Cabot, and Martin Behaim – would become key ingredients to the exploration of the southern Atlantic. [As you shall see, he becomes the personal tutor of Vasco da Gama.] Zacuto was a Sephardic Jew whose talents included astronomer, mathematician, rabbi, astrologer, and historian. He was also versed in Jewish law. [Later he will write the first comprehensive history of the Jewish People.] He was referred to as being from Salamanca, where he became the chief astronomer at the university there. Some of his research was based on the fourteenth century work of a group of astronomers known as the Majorcan School. [We met Abraham Cresque of that school.]

In 1484, the Junta Matemático updated and simplified Zacuto’s almanac. They also developed methods to help competent mariners use the revised guidebook. A former student and protégé of Zacuto’s named José Vizinho, whom King João had drafted for his Junta Matemático, translated the almanac from Hebrew to Latin.

In 1485, after Diogo Cao returned from his first expedition, José Vizinho sailed south to the equator to test the new methods and double check Abraham Zacuto’s measurements. It is probable that Vizinho sailed with Diogo Cão as part of his second expedition. Along with Cão was João Afonso de Aveiro, who, it appears, later submitted the report on the expedition. According to the Nuremberg Chronicle published in 1493, Martin Behaim, the German scholar, astrologer, mapmaker, and prospective explorer from Nuremberg, was also part of the expedition(2).

Martin Behaim of Nuremberg had been a student of the German mathematician and astronomer Regiomontanus (1436-1476), also from Bavaria. Regiomontanus, who had passed away in 1476, was a generation older than Abraham Zacuto and Martin Behaim. Behaim was also interested in the Rule of the Sun and may have been part of King João’s Junta Matemático.

Once Diogo Cao’s ship neared the equator, the scientists followed a complicated, time consuming, and difficult procedure, made more difficult by a moving ship. Their goal was to note the highest altitude of the sun at the very moment it occurred at mid-day. With an hour-glass and Zacuto’s tables at hand, the scientists began taking their measurements a bit earlier than they thought mid-day would occur and kept taking the same measurement until the altitude started to diminish, indicating that they had passed the exact moment of meridian transit [the exact moment of mid-day].

The scientists probably jotted their measurements down on some sort of slate board [like a black board], then translated the data to pen and ink manuscripts at a later time. The results of their experiments were then published in Portugal in a new almanac titled Regimento do astrolabio e do quadrante [Official astrolabe and quadrant recordings].

Abraham Zacuto’s translated Almanach Perpetuum, Portugal, c1486.(3)

The almanac included a number of things. It listed the latitudes from Lisbon to the equator. [By today’s standards, those measurements were off by only ten minutes to a half degree.] The book predicted lunar eclipses and even contained sun-sightings for leap year. It would remain a basic reference for Portuguese and Spanish navigators for the next hundred years.

However, it took a skilled and well educated navigator to use the almanac. Learning to navigate by mathematical reasoning was a new process for seamen in the 1480s. As we discussed in our article about navigation, mariners had previously relied on their experience and understanding of the sea, pole star, and other natural landmarks. Nonetheless, the new methods would rely on a navigator’s ability to measure how far he had sailed using landmarks, his ability to tell time with the hourglass, and the ability to measure speed with a chip-reel – all rudimentary tools.

The new technology helped navigators measure a ship’s position north and south, in other words, his latitude. However, it would be a long time before navigators learned how to precisely measure a ship’s location east and west – i.e. longitude. Longitude measurement is bound to time measurement. The clock, or time-piece, had yet to be invented. And whereas the distance between one latitude and another latitude is consistent, the distance between one longitude and another longitude varies depending on the latitude. For example, the distance between 45 degrees west longitude and 60 degree west longitude is greater at the equator than it is at 45 degrees north latitude.

Martin Behaim used the information he acquired from his trip to the equator to improve the astrolabe for the Portuguese so that it worked better below the equator. [Possibly he refined the star chart on the plate so that it matched the southern sky. That would have required him to adjust the rete to match the new chart.]

Once the scientific experiments were completed, Diogo Cão could continue to the Congo, where he sailed upriver to look for the emissaries he had left behind in 1484. He also wanted to find out if the river led to Ethiopia and the Kingdom of Prester John. The ship was able to navigate as far as Yellala Falls, where Diogo Cão or one of his party left an inscription on a rock. The inscription still existed when the photo shown below was taken in 1910. [The inscriptions were filled in with white chalk to make them more readable for the photo. If you read Portuguese, maybe you can tell us what it says.]

Inscription of Diogo Cão on a stone in Jelala [Yellala Falls] Congo. Photo 1910.(4)

Along the way upriver and downriver, Diogo Cão placed his Order of the Cross pillars and met with native Congolese who accepted his Christian religion. After returning to the rivermouth, he coasted south again. [The records do not say whether or not Diogo retrieved the four emissaries.]

According to João Afonso de Aveiro, who made it back to Portugal safely, the expedition reached Cape Cross in today’s Namibia, where Diogo Cão got sick and died.

Meanwhile, the Portuguese were heading to India by a different route than under Africa.


  1. Zacuto, Abraham. Almanach Perpetuum, Salamanca, Castile, bet.1473 and 1478. {{PD-Old}} This work is in the public domain in the USA and Spain. The document is over a hundred years old. Image source: Brown University. http://www.brown.edu/Facilities/John_Carter_Brown_Library
  2. It is possible that Martin Behaim and or João Afonso de Aveiro made a separate expedition from Diogo Cão’s. Possibly they were part of the expedition sent by King Joao’s Junta Matemático with José Vizinho.
  3. Zacuto, Abraham. Almanach Perpetuum, Portugal, Castile, c1489. {{PD-Old}} This work is in the public domain in the USA and Spain. The document is over a hundred years old. Image source: http://tipografos.net/blowups/zacuto-tabelas-big.jpg
  4. Photo by Victor Couto, “Inscription of Diogo Cão on the stone of Jelala/Ielele,” Congo, 1910. Image source: http://commons.wikimedia.org/wiki/ File:Matadi,_Congo,_pedra_de_Ielala,_Diogo_C%C3%A3o.jpg

Next Article: The Overland Route East to Abyssinia [Ethiopia]