The Saphea Arzachelis Universal Astrolabe
Many would argue that the highest level ever achieved by the astrolabe was an instrument style introduced by Gemma Frisius (1508-1555) in Louvain, Belgium in the middle of the 16th century. This instrument, called the Astrolabum (sic) Catholicum by Gemma, included innovations in the instrument itself and a standard of artistic execution that greatly influenced European instrument manufacturing. Hans Dorn (1430-1509) of Vienna produced an astrolabe in 1486 with virtually the same format as the Astrolabum Catholicum (the instrument survives and is in Poland). There is no way of knowing whether Gemma ever saw or heard of Dorn's astrolabe and simultaneous inventions in a time of rapid progress are not unusual. In any case, this form of universal astrolabe is usually associated with Gemma Frisius.
Gemma's Astrolabum Catholicum was an attempt to make an astronomical instrument that could be used anywhere by a wide range of users. An ordinary astrolabe requires a separate plate for each latitude, which makes it impractical to produce an instrument that can be used anywhere at reasonable cost and convenience of use. In addition, the ordinary astrolabe, as flexible as it is, is not well suited for certain types of problems, particularly those expressed in celestial latitude and longitude. In order to overcome these shortcomings, Gemma Frisius designed an instrument that had an ordinary astrolabe on one side and adopted a form of astrolabe that can be used at any latitude for the other side and included a magnetic compass in the throne. This form makes a lot of sense, since different problems are better suited for one type of astrolabe or the other.
The latitude independent astrolabe variation was originally described by Ibn al-Zarqālluh of Toledo in the 11th century, probably in about 1048, and had been discussed in several treatises in the Middle Ages. It was called the Saphea Arzachelis by Profat Tibbon (Jacob ben Makir), better known under the name of Prophatius Judaeus, in a treatise dated 1263. The name, which derives from al-Safihat (the plate) of al-Zarqālluh, has endured, although it is often shortened to simply saphea.
As Henri Michel put it, "The Astrolabum Catholicum was definitely not Gemma Frisius' invention and, with the typical lack of concern of the time, the learned cosmographer 'forgot' to say that this instrument had been contrived five centuries earlier". Regardless of the facts, Gemma Frisius is usually credited with the invention. There is certainly no argument that the instruments he inspired had a profound effect on instrument making.
The principle of the saphea is similar to the plane astrolabe. Both instruments use the stereographic projection. The projection origin is at the south celestial pole and the sky is projected onto the equator on the planispheric astrolabe. On the saphea, the projection is from one of the equinoxes and the celestial sphere is projected onto the great circle of the celestial sphere defined by the poles and the solstices (the solsticial colure). That is, the projection is from the "side".
At this point we note that the projection would have exactly the same arcs if the origin of the projection were at the autumnal equinox instead of the vernal equinox. Thus, we can divide the ecliptic for the entire range of solar longitudes and simply imagine that we are looking at the sphere from one side or the other depending on the time of year.
The really clever part of this application of the stereographic projection is, if the projection is rotated so the ecliptic is horizontal, the arcs above the ecliptic represent arcs of celestial latitude and the perpendicular arcs represent celestial longitude. That is, if the horizontal diameter through the center (the equinoctial line) is considered to be the ecliptic, the poles are the ecliptic poles and the arcs are celestial latitude and longitude.
Similarly, if the projection origin is moved to a point on the celestial sphere on the extension of the local horizon then the equinoctial line is the horizon, the poles represent the zenith and nadir of the place and the arcs represent angles of altitude and azimuth or hour angles.
Thus, the projection can represent the celestial coordinates of a point in space in three different coordinate systems at the same time. In fact, the simplest applications of the saphea involve converting between coordinate systems. For example, if the celestial latitude and longitude are known, it is very simple to find the declination and right ascension or the altitude and azimuth of the same point, and vice versa.
The ecliptic is divided by the zodiac on most saphea instruments. These divisions represent the position of the Sun on the ecliptic and require a little imagination to visualize. Recall that the projection arcs are identical whether the projection origin is at the vernal equinox or the autumnal equinox. Therefore, the half of the ecliptic we are considering depends on the origin. We see the half of the ecliptic from Aries 0° to Gemini 30° and Capricorn 0° to Pisces 30° when the origin is the autumnal equinox. These signs are printed above the ecliptic line. We see the half of the ecliptic from Cancer 0° to Sagittarius 30° when the origin is the vernal equinox. These signs are printed upside down and below the ecliptic line. Thus, we can visualize the Sun moving back and forth along the ecliptic over the course of a year if we mentally shift our view of the projection origin. It is much more difficult to describe than it is to do.
The margin of the plate is divided into four 90° quadrants. The sequence of the numbering for a quadrant depends on the use. The numbering in QI proceeds from 0° at the equator to 90° at the north pole. This set of divisions is used when the arcs are interpreted as declinations or latitudes. QII can be divided in the same way or in the reverse order so 0° is at the north pole, increasing in the counterclockwise direction to 90° at the 9 o'clock position. This set of divisions is the polar distance and is used to orient the local horizon. Instrument makers were not particularly consistent in the labeling of the saphea limb. A mental subtraction is needed for certain problems if QII and QIV are not labeled with polar distance.
The meridians are generally not labeled along the equinoctial line for two reasons: the labels would have to be very small in order to be consistent and the polar arcs can have a variety of meanings. Among the meanings are right ascension, hour angles, equal hours, longitudes and azimuths. It would not be possible to label all of these uses in a coherent way. The hours (equal hours, hour angles, right ascensions) are labeled near the tropics since they are used rather often and would otherwise be difficult to locate. One hour is 15° on the celestial sphere. The labels along the 30° parallel identify the equal hour associated with each 15° and can be converted to right ascension.
Two additional accessories are required to solve problems with the saphea plate. A rule that is free to rotate around the center of the instrument having one edge as a diameter is called the regula. "Regula" is Latin for "rule" and we use the term to differentiate this device from the rule used on the ordinary astrolabe. The regula may be divided by degrees. Connected to the regula is an articulated arm of two or three sections called the brachiolus (Latin for "little arm"). Some old instruments did not have a brachiolus but had an auxiliary rule oriented 90° to the regula that could slide up and down the regula and point to any location on the plate. Others had both, with the brachiolus attached to the cursor.
Some old instruments showed some stars on the saphea plate even though they were of limited use. Stars shown on the projection plate were located in the equatorial coordinate system by their declination and right ascension. Stars visible from the vernal equinox were sometimes shown as a solid star figure with stars visible from the autumnal equinox shown as a star outline.
The saphea is a very versatile device. Problems involving conversion of coordinate systems are very easy. Thus, if the user has an ephemeris that lists celestial positions by latitude and longitude, which are very awkward on a planispheric astrolabe, it is very easy to convert the positions to declination and right ascension, which are very convenient on a plane astrolabe.
The saphea can be used to find the time of sunrise and sunset, and thus the length of the day, for any latitude. It can also be used to find the latitude from the Sun's meridian altitude, although this is such a simple problem arithmetically that it is unlikely anyone would go to the trouble to use an astrolabe to solve it [Sun's noon altitude = (90° - latitude)+ declination].
Time cannot be found directly on the saphea but requires an iterative procedure. This shortcoming of the saphea is very likely the reason Gemma included a regular plane astrolabe on the instrument.
For the mathematically inclined, the saphea can be used to solve spherical triangles. It is unlikely that the instrument saw much use in this area even though such problems could be solved by a user with little knowledge of spherical trigonometry. As John North points out, such instruments were not very popular since it is unlikely that people with no knowledge of spherical trigonometry would be interested in solving spherical trigonometry problems.
Gemma Frisius was a professor of medicine in Louvain who apparently became interested in astronomy and astronomical instruments through the astrological aspects of medicine as it was practiced at that time. He wanted to create an instrument that would be attractive to users ranging from astronomers and astrologers to surveyors and sailors and named it the Astrolabum Catholicum (Latin for "Universal Astrolabe" ) to convey idea that he had succeeded. Whether he did, in fact, succeed in creating a truly universal astrolabe is arguable, but the quality, flexibility and ingenious design of the instrument assured success for the makers and fame for the designer.
The original instruments are identified with the workshop of Gemma's nephew, Gualterus (Walter) Arsenius. Gemma Frisius probably did not actually make any instruments himself, but he designed many. It is not clear whether he managed a workshop or inspired his nephew to establish one, but the resulting instruments set a new and enduring standard for quality and artistic workmanship. Arsenius clearly ran his own operation after Gemma's early death at the age of 47.
Some of the workers from the Arsenius shop revolutionized calligraphic engraving and artistic design and raised European map and instrument making to an esthetic level that is still admired. Thomas Gemini, a Protestant who worked with Gemma in Louvain as a journeyman , migrated (or was banished for heresy) to England where he had enormous influence on the English instrument making tradition. The beautiful maps, globes and instruments made by Gerard Mercator, who began his career in Louvain, are still admired as among the finest ever made. The elegant and artistic Louvain style introduced by Gemma Frisius and Arsenius was adopted by instrument makers in England, Spain, Italy and Germany. A notable practitioner was the German, Erasmus Habermel, whose beautiful and delicate instruments rivaled and even exceeded the Louvain products in quality and style. Artisans such as Gemini, Habermel and Humphry Cole had dramatic influence on the future of European instrument making.
It should be noted that the arcs on the saphea tend to be rather close together and congested. A rather large instrument is required in order to achieve anywhere near the accuracy of a normal plane astrolabe. Surviving universal astrolabes of this type were exquisitely executed and were quite large and heavy. They must have been incredibly expensive, another reason why this type of instrument never gained a lot of popularity.
Two other forms of universal astrolabe were developed. In 1550, Juan de Rojas Sarmiento of Monzón, Spain, published a commentary on a universal astrolabe based on the orthographic projection of the celestial sphere onto the solsticial colure. Rojas had studied under Gemma Frisius in Louvain where he met Hugo Helt who assisted in the commentary and wrote the section on the instrument's construction. Astrolabes based on the orthographic construction had been discussed earlier and Rojas did not claim to invent the method or assert that he was the first to apply it to the astrolabe, but this form did not gain much attention until Rojas' publication. Phillipe de la Hire (1640-1718) published a third form of universal astrolabe in late 17th century that attempted to resolve some difficulties of both the saphea and Rojas versions. This method was described by Nicholas Bion (1652-1733) in 1702 but apparently no la Hire astrolabes were ever made of metal as interest in the astrolabe had declined by this time.