1. Armillary Spheres NASS Montreal 2001 Roger Bailey
When I travel, I like to enjoy sunsets and search for sundials. This year we enjoyed the sunsets at Cabo Carvoeiro on the Algarve Coast of Portugal. This was our base for searching for sundials

2. Armillary Spheres in Portugal
Armillary spheres are everywhere!
Traffic circle/ fountain
Flag, money, coat of arms
Churches, monasteries, convents, schools, monuments, flagpoles
What is an armillary sphere and why is it the symbol of Portugal?
At first we were disappointed. Sundials did not seem to be part of the culture in Portugal. But armillary spheres were. They were everywhere. This monumental armillary sphere was in the center of a traffic circle in Albufeira. Why?

3. What is an Armillary Sphere?
Sundial ?
Astronomical instrument?
Analogue computer?
Navigation tool?
Horoscope calculator?
Model of the Universe?
Symbol of science, technology and the universe?
First, what is an armillary sphere? What is its function and why is it so common in Portugal? My search for sundials turned into a great research project.

4. Quadrant and Ring
Equatorial Ring identifies time of equinox when the shadow from the upper ring is totally cast on the lower portion of the ring
Quadrant measures noonday altitude of sun
Hipparchus used the bronze equatorial ring in the Square Hall in Alexandria to determine the equinox and precession about 130 BC
St John’s College, Annapolis

5. Greek Armillary Spheres
Greek astronomers devised armillary spheres as observational instruments, models of the universe and the basis for navigation and geography
In his “Almagest”, Ptolemy described the meridian ring (1-12), equatorial ring (3-1), ecliptic observation rings (5-1) and solid celestial sphere (7-4)
The history of the armillary sphere.

6. Hipparchus Equatorial Ring and Equinox Shadow
North Pole
Hipparchus used the large brass ring set at the angle of the latitude in the great hall in Alexandria. Yes they knew how to use latitude to describe locations on the spherical earth. At the equinox, the shadow of the upper ring is cast on the lower ring. This allowed Hipparchus to determine the exact day of the equinox aand to determine that that day was shifting from the day of the year determined by observing the stars. He discovered and measured precession of the nodes of the ecliptic about 150 BC.
Latitude
Hipparchus Equatorial Ring and Equinox Shadow

7. Ptolemy Meridian Ring and Noon Shadow
Zenith
Polar Axis
Ptolemy describes how to build the vertical meridian ring oriented North / South to determine the altitude of the sun at noon and use that to determine the latitude and declination throughout the year.
Altitude
Ptolemy Meridian Ring and Noon Shadow

8. Ecliptic Ring = Equatorial Ring + Declination
Ecliptic Pole
Declination
North Pole
The ecliptic ring showing the plane of the path of the sun moon and planets was the next ring to be added. All these rings were measuring devises, calibrated in degrees and using slots or pegs to sight through. They were often two concentric rings,the one for sighting rotating within the one calibrated for measuring.
Ecliptic Ring = Equatorial Ring + Declination

9. Ptolemy’s Ecliptic Armillary
Ptolemy’s Almagest 5 –1
“On the Construction of the Astrolabe”
Determine ecliptic coordinates of celestial objects
Set meridian and latitude rings to equatorial pole
Sight on Inner Ring
Read ecliptic latitude and longitude rings
Sketch from Regiomontanus
They could get pretty fancy. Ptolemy describes this ring. Regiomontanus drew this sketch over 1000 years later based on that description. This allowed determination of coordinates in the ecliptic plane.

10. Rings of the Magi ?
Armillary used by the ancient astronomers to track the path of the planets, sun and moon and cast horoscopes
Did the Magi, Zoroastrian astrologers, use armillary spheres to track the Star of Bethlehem?
Heliacal rising of conjunction?
Precession to age of Pisces?
Were armillary spheres used by the Magi? I like to think they used armillary spheres to track the Star of Bethlehem. I make these armillary sphere Christmas tree ornaments to celebrate that legend.

11. Chinese Armillary Spheres
Armillary sphere of Guo Shoujing ( ) at the Purple Mountain Observatory at Nanjing.
These instruments predate by 350 years similar instruments at the Beijing Ancient Observatory provided by Jesuits (Schall-1666, Verbiest-1673)

12. The Dark Ages Vandals sack Rome, Alexandria etc
Greek/Roman civilization collapses
Warlords dominate feudal life
Science moves east with Moslems and Hindus
Technology stalled in Europe for over years

13. Henry the Navigator Renaissance man 1394-1460
Third son of João & Phillippa
School of Navigation at Sagres, Cape Vincent, Portugal
Applied Ptolemy’s navigation technology: armillary sphere maps and marine astrolabe
Sponsored “Voyages of Discovery” to Africa, Azores, India, Spice Islands and Brazil
We now get to the connection of armillary spheres with Portugal through Henry the Navigator and his School of Navigation at Sagres.

14. Henry and the Discoverers, Belem
Henry provided the technology base for the Voyages of Discovery, the trip by Portuguese explorers to Africa, India, the Spice Islands and Brazil in the New World. Note the navigators astrolabe and the armillary sphere, just behind the bible and the sword as the tools of of the explorers.

15. Ptolemy's Geography
Celestial sphere defined terrestrial positions on globe
Eratosthenes, inventor of the armillary sphere, calculated the diameter of the earth from shadow angles
Ptolemy's “Geography” gave latitude and longitude for known world from Thule to Ceylon
The concepts of a spherical globe and coordinates of Latitude and Longitude were well known to the Greek astronomers. Ptolmey described the world they knew in his other great book “Geography” It described the positions from “Ultima Thule” in Greenland to Ceylon and Indo-China. They were guessing on longitudes as only local time could be measured with sundials. It took a long time to solve the longitude problem.

16. Ptolemy's Geography
A Renaissance map based on Ptolemy’s Geography.

17. Mariners’ Astrolabe
Mariners’ astrolabe as used by Portuguese navigators to determine the altitude of the sun
Reproduction by Tony Moss
The other essential tool for navigation, later replaced with the sextant.

18. Sacro Bosco’s de Sphaera Mundi
John Holywood of Yorkshire, (Joannis de Sacro Bosco) wrote “de Sphaera Mundi” about 1220
This text updated Ptolemy and explained the use of armillary spheres in astronomy and navigation
“Commentary” by Christoph Clavius 1570
Johanis de Sacrobosco, or John Holywood for Yorkshiremen, reintroduced the armillary sphere to the western world with his book “de Sphaera’ about This was based on Ptolemy’s” Almagest”.

19. Sagres Compass Rose and Sundial
Sagres on the windy south west tip of Europe was the site of Henry’s legendary school of navigation and the point of departure for the “Voyages of Discovery” These artifacts, probably added later, are all that is left behind the fortress wall. Sagres was sacked by that perfidious English privateer, Sir Francis Drake, perhaps as a strategic target but more likely a target of opportunity as the city of Lagos around the corner was too well defended. What we now know of Sagres is based on Drake’s log books.

20. Christopher Colombus Portuguese Caravel
Christopher Columbus rescued from shipwreck at Sagres in 1479
Later he sailed to Madeira, married the daughter of the governor and set up a shipping company
Spanish (Ferdinand and Isabella) provided venture capital for his exploration to the new world in 1492 and gained the benefits
Did he learn navigation from the Portuguese at Sagres?
Christopher Columbus knew Sagres and the Portuguese navigation technology well.
Portuguese Caravel

21. Armillary Spheres and Navigation
Zenith
Armillary Sphere is a model of the Universe
The earth is round. You cannot sail off the edge
The position of the sun and stars can tell you where on earth you are, and how to get back to where you started
The ecliptic ring tells you the declination of the sun
The noon altitude sight and declination determine the latitude
Altitude
Dec
North
Latitude
Co-Latitude
Horizon
Equatorial Ring
What is the secret of the armillary sphere that is the basis for celestial navigation? It is simple. The sphere determines the declination of the sun. The date is marked around the equatorial and ecliptic rings. For each day, determine the solar declination as the angular distance on a meridian between the ecliptic ring and the equatorial ring. Use an astrolabe to determine the altitude of the sun at its highest point at noon, and calculate your latitude.
Ecliptic Ring
Or Zodiac
Lat = 90-Alt+ Dec

22. Declination Error Analysis
Armillary assumes circular orbits vs elliptical. Error?
Estimate is reasonable compared to commonly used equations
Greatest error (0.7°) at equinox when rate of change is greatest (0.4°/day)
Date of equinox is critical
Does it work well? It is a reasonable estimate. There is a periodic error because the orbit of the sun is elliptical and not quite circular. Drop the sphere a couple of times and the error will disappear or more likely get worse.

23. Wenger Uniglobe
Modern armillary sphere for teaching celestial navigation
Adds angle measuring spanner to meridian, great circle and equatorial (time) rings
Adds solution of the navigation triangle to traditional uses
The idea is still useful. Daniel Wenger has reintroduced it, adding an extra arm and building it from modern materials to teach navigation and solve the navigation triangle spherical geometry.

24. Armillary Sphere As Astronomical Instrument
Ptolemy's brass rings
Tycho Brahe’s instruments of 1581
Beijing Ancient Observatory of 1670
Location at zenith
Sighting points on meridian ring
Determines celestial coordinates: right ascension and declination
Tycho Brahe built this one as an observational instrument based on Ptolemy’s description. It was too diffucult to build, too clumsy to use and too inaccurate to measure the celestial coordinates well.

25. Equatorial Armillary Tycho’s great equatorial armillary of 1531
Abandoned as too complex and inaccurate
Replaced with giant quadrant
He simplified it to just the equatorial ring but abandoned this as well.

26. Armillary Sphere as a Model of the Universe
Ptolemy's geocentric model
Earth is a sphere at the center of the universe
Stars on celestial sphere rotating around the earth
Copernicus: Earth and planets rotate around sun
Sun moon and planets rotate on the ecliptic path
Anomalies as epicycles
Kepler: Elliptical orbits
Armillaries had removable centers!
The sphere described the geocentric model of the circular spheres of the universe. It did not describe the sun centered elliptical universe of the Copernican Revolution. No problem, it still works well describing the perceived motions of the sun for sundial designers.

27. Armillary as a Model of the Universe
Demonstrate motions of celestial objects
Show ecliptic path of sun, moon and planets
Explain equinox and precession
Explain solstice and tropics
It still is useful as a model of the universe to determine those things listed on this slide.

28. Armillary as a Computer
Translate coordinate systems
Horizon/Zenith: Alt/Az
Polar/equatorial: Dec & RA
Ecliptic: Latitude/Longitude
Determine position of celestial objects
Determine declination from date
Determine latitude from declination and altitude
Determine rise / set times and azimuth
It is still useful as a computer.

29. Armillary as a Symbol Symbol of Science in art
Typically a learned man with an armillary, the epitome of knowledge
Here Descartes teaches science to Queen Christina of Sweden
“Triumph of Faith” at Jeronimos Monastery, Lisbon shows an armillary sphere as the guide to salvation.
It has become an icon of “Science”.

30. “Triumph of Faith”

31. Portuguese Royal Symbol
Portuguese gain control of the spice trade
Wealth and power flows to Portugal
Dom Manuel I adopts the armillary as the Royal symbol
Manueline architecture uses the Royal Armillary in palaces, churches, monasteries, built with taxes on spices
It’s importance as the technology for navigation is honoured by its adoption as the Royal Symbol for Portugal This is why armillary spheres are so common in Portugal.
Azulejos tile from Sintra Palace

32. Portuguese Flag
The armillary sphere:
The armillary sphere is a main element in Portuguese heraldry, being incorporated in the modern flag and in a number of historical flags of both Portugal and Brazil. It was an astronomical and navigation instrument made of wood or metal rings ("armilas") interconnected around a central axe to form parallels, meridians and the ecliptic, allowing to calculate one's position on the earth surface by examining the stars. It is usually depicted in heraldry in simplified form, with only one meridian (viewed in a 180 deg. position, as a circle), and only three parallel circles, the equator and the tropics. The ecliptic (sometimes bearing four to six zodiacal signs on it), in descending position on the modern flag's obverse, is usually wider than the other circles. The central axe is also visible, sometimes overlapping the meridian (and in that case we could consider it to be a 0 degrees meridian, viewed as a vertical line...). Anyway, the parallel circles overlap the meridians, and the ecliptic overlaps them all. Older depictions show usually the instrument's "feet", a rotative "stool", as in a modern classroom globes, and sometimes a smaller globe in the center or on the North Pole. The modern version consists of the sphere only, and all the elements are samewhat wider and bearing detailed edges. The width difference between the ecliptic and the other rings is much smaller. António Martins, 28 May 1997

33. Manueline Architecture
Royal symbols over convent doorway at Estremoz

34. Manueline Monasteries
Steeple at Jeronimos, Belem
Cloister tracery at Batalha

35. Batalha Cloister Noon Mark
But if you look closely you can still find a few sundials in Portugal.

36. Typical Portuguese Church
Armillary on the steeple of Nossa Senhora da Conceição, Ferragudo

37. Armillary on Sintra Town Hall

38. Portuguese Boom as a High Tech venture
Navigation technology conquered the universe
Voyages of Discovery gave Portugal the wealth and power of a colonial empire
Rapid expansion led to huge venture capital requirements for ships, navies, armies, weapons etc
Profits diverted to palaces and cathedrals
Competitive spin offs like Columbus and Spain
Lost technological edge with introduction of the Inquisition and expulsion of the knowledge workers
Lure and cost of colonies bankrupted Portugal
1492 was the year in history that marked the start of the new world order. It was the year that Columbus “discovered” America and the year the Catholic rulers expelled the Jews and Moslems from Spain and Portugal.

39. Armillary Spheres and Sundials
Waugh armillary at Mystic, CT
Armillary spheres lead to sundial designs
Equatorial
Polar
Analemmatic
Horizontal / Vertical
Wenger Globe
Back on topic, armillary sphere are the basis for almost all types and styles of sundials. Everything I need to know about sundial design, I learned from armillary spheres.

40. Armillary Spheres and Equatorial Sundials
Schmoyer Dial by Tony Moss for Mike Shaw
Gnomon is polar axis
EQT correction in gnomon
Hour scale on equatorial ring
Linear scale 15°/hour
Ring opened to avoid equinox shadows

41. Roger’s Equatorial Stainless steel (316L) 12” pipe sections
Hand crafted with hack saw and files
Port Elgin, Ont
Lat N 45:28:00
Long W 81:24:30

42. Armillary Sphere and Polar Sundials
Flatten the equatorial ring in the plane of the polar axis
Distance = r Tan t t r

43. Armillary Spheres and Planar Sundials
The blue ring represents the plane of the sundial in relation to the celestial sphere. Look at the hour lines from the center to the ring intersecting the meridian rings. Rotate the ring or the sphere to get the hour lines for any planar sundial for any location.
Luke Coletti gcstudio.com

44. Armillary and Analemmatic Sundial
Project equatorial ring on plane for ellipse
Project gnomon on plane for zodiac
Declination on gnomon determines zodiac positions
Image by Frans Maes
Project the armillary sphere equatorial ring and the gnomon onto a plane to design an analemmatic sundial. The concept is that simple.

45. Armillary Sphere and Analemmatic Sundials
Equatorial ring projects as an ellipse
Shape depends on latitude
- D L
Gnomon projects as Zodiac
on north south axis for
various solar declinations
This is an engineering type drawing of two plane views showing the projection of the ring and gnomon to the ellipse and zodiac.
Zodiac N

46. Wenger Sundial Glass sphere inscribed with armillary rings
Hour meridians
Horizon
Tropics and analemmas
Location at Zenith
Shadow on center point gives time
Design by Daniel Wenger
Another great and novel sundial design by Daniel Wenger based on the armillary sphere.

47. Modern Armillary Spheres
Prime market is for symbolic ornaments like garden variety sundials
Lots of junk is offered for sale
Rings should represent the universe
Equatorial, ecliptic, meridian, horizon etc
Ecliptic ring should rotate
Must be set for latitude
Should have scales for hours, degrees and date
There is lots of junk out there!

48. Classic Armillary Sphere
Meridian ring engraved for declination and latitude
Equatorial ring
Rotating ecliptic ring with engraved zodiac
Tropic and polar circles
But also some proper instruments.
Horizon ring engraved for degrees and date
Colure rings through pole
Source: Classical Science