To help understand the evolution of the armillary sphere into the equatorial mounting of a telescope, the pure technical evolution into Guo Shoujing’s Jian Yi(Simplified Instrument), also called an equatorial torquetum, will be discussed in this chapter.
Armillary spheres can be divided into observational armillary spheres and the demonstrational instruments. Only observational armillaries will be discussed, since the others are technically non-functional and often mere copies for representation.
The armillary sphere consists of a number of armillae[1] that correspond to the various great circles of the celestial sphere, for example, the celestial equator, the ecliptic and the horizon. The instrument was used by astronomers to determine the celestial positions of celestial bodies. There are basically two types of armillary spheres: the equatorial armillary sphere and the ecliptic armillary sphere, which use different coordinate systems to determine the positions of the celestial bodies.
The equatorial armillary sphere, as its name implies, uses declination and right ascension which determine the positions of the heavenly bodies with respect to the celestial equator, whereas the ecliptic armillary sphere uses latitude and longitude which determine the positions of the heavenly bodies with respect to the ecliptic[2].
Note that to differentiate between the two types of armillary spheres, we just need to see the number of axes they have. The equatorial armillary sphere has only one axis that the various rings move about, while the ecliptic armillary sphere has two axes that the various rings can move about.
Chinese astronomers had always used equatorial armillary spheres because of their loyalty towards the use of the equatorial coordinates, which happens to be the standard coordinate system that is used by astronomers today around the world. European and Arabic astronomers, however, started out with the ecliptic armillary spheres and used the ecliptic coordinates to determine the positions of the heavenly bodies, but later modified them into equatorial armillary spheres and switched to the equatorial coordinates. One of the reasons that led to this modification was that more accurate readings can be achieved using the equatorial coordinates than ecliptic coordinates.
The equatorial armillary sphere basically contains three rings, with an additional ring to support the whole structure. The axis CD is made to point towards the north celestial pole, which will in turn make the plane that ring FG lies on parallel to the plane of the celestial equator. The axis can be made to point towards the north celestial pole by making use of the north polestar. By pointing this axis directly towards the north polestar, the axis will then point towards the north celestial pole. Ring E is mobile, which makes it possible to move about the axis that it is mounted to.
It also has the sight H and I on it which astronomers line up with the star under observation and the sight A (often presented by a globe) on the axis FG. In this way, the proper bearing of the star can be obtained. Both ring E and FG contain graduations, and thus when the required heavenly body is targeted using the sights, astronomers can then read off the north polar distance (the Chinese form of declination) of the heavenly body from the graduations on ring E and the position of the heavenly body in a xiu[1] from the graduations on ring FG. Thus the positions of the heavenly bodies with respect to the equatorial coordinates can be determined. Later an ecliptic ring is added to the equatorial armillary sphere, but its function has always being secondary, mainly for demonstrational purposes.
[1]宿, the Chinese form of right ascension. There are 28 xiu. Cfr. Introduction Minganto: Specifications and they are similar to constellations on the celestial equatorial.
The ecliptic armillary sphere, on the other hand, has a slightly different structure from that of the equatorial armillary sphere. Ring B and C contain graduations, and ring B itself contains an inner mobile ring which can be turned around. It also has two sights S and T, which astronomers can use to target the required heavenly body. The axis HK is still made to point towards the north celestial pole, and ring A and C are pivoted round the axis HK (note that ring A and C are connected together, which make up the inner framework). The angle between the axis HK and PQ is made to be the same as the angle between the ecliptic and the equator, and thus it is possible for ring C to swing into the plane of the ecliptic. To fix the position of this particular armillary sphere, the inner framework of ring A and C is turned about HK until the shadow of one half of ring C falls on the other half. This will make ring C parallel to the ecliptic. Then the ring B together with its inner ring D, are individually moved until the sights are lined up with the targeted heavenly bodies. Once the required heavenly body is targeted, the sights will indicate the latitude of the heavenly body on the graduations on ring B, and the reading of ring B itself on the graduations on ring C will give the particular heavenly body's longitude. The latitude and longitude of the heavenly body determine its position with respect to the ecliptic.
The developments of the armillary spheres also included the introduction of various rings that correspond to other great circles of the celestial sphere. Guo Shoujing built an equatorial armillary sphere which had rings representing many of the great circles of the celestial sphere.
However, the main contribution that Guo Shoujing had on the development of the armillary sphere was not to build such a complicated armillary sphere, but to modify its structure into a more simplified form.
The new form of armillary “sphere” that Guo Shoujing built, was called the equatorial torquetum. Clearly, it was no longer in a spherical form, however the equatorial torquetum still contains some familiar features of the equatorial armillary sphere. Ring f is the mobile declination ring or meridian double circle, which graduates on both sides in degrees and minutes. It carries a sighting-tube, tube i, which can be moved around ring f, and is used for the determination of the declination of the required heavenly body. The sighting tube is pointed at one end to clearly mark out the reading on the ring f. The stretchers g, g’, and the double brace h are built to prevent the deformation of the declination ring f. Ring j is the mobile equatorial circle, which is also graduated in degrees and minutes, and has markings that mark out the boundaries of the 28 xiu[1]. Like the declination ring f, it is also strengthened by cross-stretchers. The right ascension of the heavenly body is read off from this equatorial circle, and there are two independently movable radial pointers k, k’, which have pointed ends to mark off the boundaries of the xiu which are situated on the equatorial circle.
Apart from these usual features of the equatorial armillary sphere, this modified armillary contains some new features. The ring l is the pole determining circle, which has a cross-piece inside it with a central hole. Observation of the pole star is effected through a small hole in a bronze plate attached to the South Pole cloud frame standards d, d’. The function of this pole determining circle is to determine the moment of culmination of the pole star. Also, it has the fixed terrestrial coordinate azimuth circle, m, and the revolving vertical circle n, for the measurement of altitudes. These two rings will give the positions of the heavenly bodies with respect to the horizon. Thus, the equatorial torquetum is able to provide two systems of coordinates (the equatorial coordinates and the coordinates with respect to the horizon) to determine the positions of the heavenly bodies.
The advantage that this equatorial torquetum has over an equatorial armillary sphere is that it separates the various rings, thus avoiding confusion over the functions of the various rings. Also, the readings on the graduations of the rings can be taken easily compared to that of the armillary sphere. Furthermore, the construction of this equatorial torquetum makes it more stable than the equatorial armillary sphere and resists deformation better, which is important since deformation in the structure of these instruments will lead to inaccuracy in the readings of the heavenly bodies’ positions. On the whole, Guo Shoujing was able to innovate when it came to the building of their instruments for measurements, and this brought about an increase in the accuracy of the observational results. Combined with the new mathematical methods[2] that he had derived, more accurate calculations could be made based on these results.
