A Study for the Restoration of the Sundials in King
- Author: Lee Yong Sam, Kim Sang Hyuk
- Organization: Lee Yong Sam; Kim Sang Hyuk
- Publish: Journal of Astronomy and Space Sciences Volume 28, Issue2, p143~153, 15 June 2011
The sundials produced in King Sejong era had the functions of accurate observation instruments and were fabricated in various forms such as
Angbuilgu(hemispherical sundial). In this study, we investigated the literature, structural characteristics and principles of Hyeonjuilgu, Cheonpyeongilguand Jeongnamilguthat were developed in Joseonto have the unique structures. Additionally, the sundials were reviewed in the perspective of technical history by comparing them with the sundials of China. For the restoration of the sundials, we identified the principle in which the light spots and shade of the sun were used, and drew the variations of the altitude and azimuth by the yearly motion of the sun on the Sibanon the hemispheric and flat surfaces. Based on these results, we completed the design drawings of the three sundials and proposed the restoration models.
Jeongnamilgu , Hyeonjuilgu , Cheonpyeongilgu , sundials , restoration , King Sejong era
Various sundials were produced in King
Sejongera. According to the record for the day of April 15 in the year 1437 in Sejongsillok(Annals of Sejong)1, a 40 Cheok(scale unit) of Gyupyo(gnomon) was produced and it allowed accurate measurement at that time. Gyupyo, the most fundamental instrument to establish an independent astronomical calendar, was a giant sundial that determined the length of a year and 24 subdivisions of the seasons. In addition to Gyupyo, Hyeonjuilgu, Cheonpyeongilguand Jeongnamilguwere produced in King Sejongera (Table 1). Hyeonjuilguand Cheonpyeongilguwere the sundials produced on the basis of the equatorial plane of the celestial sphere. Jeongnamilgu, which had a more complicated structure than that of the equatorial sundials such as Hyeonjuilgu, also had included the characteristics of the observational instrument and the original sundial structure. The structure, method to use, principle and restoration design of Hyeonjuilgu, Cheonpyeongilguand Jeongnamilguwere described in the main text focusing on the accomplishments obtained in the restoration procedures of them.
1Sejong sillok, 77:10a:line 12~10b:line 14.
Hyeonjuilguand Cheonpyeongilguwere portable equatorial sundials. With these sundials, the north-south direction was aligned with a magnet, and the time was measured by looking at the shade on the Sibanface after leveling. Based on the record that Hyeonjuilguand Cheonpyeongilguhad similar shape and size, it is assumed that not only the shape but also the methods to produce and use them were similar. Fig. 1 shows the artifacts of the remaining Ilyeongui(portable equatorial sundial) (a) and the enlarged image of 100- Gak Siban(round plate with one hundred intervals time lines) (b).
A round shaped
Sibanis fixed in the celestial equatorial direction on the base of the artifact. One hundred of angle marks are engraved at both sides of the Siban. There is a round pond under the Siban, which is connected with the water channels at the edge of the base. At the southern part of the base, there is a hole through which a knot can be made (1). The thread knotted at the southern part was to penetrate the center of the Siban(2). This indicates that the thread from the southern part of the base was aligned toward the pillar at the northern part of the base. The thread at the southern part of the base was lost, and only the rectangular groove (3) is remaining currently. The structure of this artifact is almost perfectly matched with Hyeonjuilgumentioned in Sejongsillok. It is highly probable that Ilyeonguimight have been the artifact corresponding to the prototype of Hyeonjuilgu.
Fig. 2 shows the structure of
Hyeonjuilguand the variation of the solar meridian altitude. As shown in Fig. 2a, the thread penetrating the center of the Sibanis laid in the direction of the earth’s axis of rotation (north pole: NP).
Sibanlaid in the perpendicular direction of the thread represents the equator on the celestial sphere (E). Since the solar meridian altitude, the solar declination, is varied by the seasons, the shade of the thread falls on the upper plane or the lower plane of the Siban(Figs. 2b and c, Fig. 3). The shade falls on the mark over the Sibanface from the spring equinox to the autumnal equinox and on the mark below the Sibanface from the autumnal equinox to the spring equinox of the next year. The variation of the solar hour angle in a day determined the shade direction of the thread, announcing the hour. The water channels around the corners of the base was used for the leveling of the astronomical instruments at that time. In particular, the leveling of Hyeonjuilguwas more convenient because, in addition to the water channels, a bead was hung up to align it at the crossed lines below.
Two round ponds were placed on the base of
Cheonpyeongilgu(Fig. 4), which was the structure produced by improving the one-pond structure of Hyeonjuilgu. In Hyeonjuilgu, the north-south direction is aligned by using a round pond at the southern part.2Then, the hour is read according to the direction of the shade on the Sibanface. In summer, however, the time line on the Sibanface was to be read at the northern side (in front of the Siban) and checking out the southern part (behind the Siban) to align the north-south direction was not convenient. Thus, the structure was improved in Cheonpyeongilguto read the time more conveniently; the north-south direction was determined with reference to the pond at the northern part in summer and the pond at the southern part in winter.
The record in
Sejongsillokmentions that the time was measured with Cheonpyeongilguon horseback. The instruments used on horseback usually have a handle. Fig. 5a shows the shape of a drinking cup used on horseback. If Cheonpyeongilguwas used on horseback, it might have been attached to the bottom of a drinking cup with a handle.3 Fig. 5b is the schematic illustration of the handle in Cheonpyeongilguthat is newly suggested based on the basic model of the drinking cup used on horseback. The four legs at the base of Cheonpyeongilguwere removed. Still, it may be almost impossible to have measured the time while riding on a horse. Perhaps the time might have been measured on the back of a stopped horse while not getting off the horse. The accuracy of the time measurement must have been lower than that of other sundials established on the ground such as Ilseongjeongsiuiand Jeongnamilguor Hyeonjuilguthat had cross lines.
Fig. 6 shows the equatorial sundial in the National Palace Museum in Beijing. A sharp perpendicular needle penetrates the center of the
Sibanface. The needle plays the same role of the thread penetrating the center of the Sibanin Hyeonjuilgu. The time marks are engraved on the Siban face. An extra rotating instrument is located on the Sibanface. The extra instrument in the equatorial equipment is the aspect different from Hyeonjuilguand Cheonpyeongilgu, the sundials in King Sejongera. The extra instrument might have been to measure the time at night by observing the celestial bodies and considering the hour angle.
There is nothing known about whether or not there was a portable equatorial sundial in China at that time.
Joseonmay be the only country where a portable equatorial sundial was produced among the East Asian countries.This tradition might have helped the development to the portable Angbuilgusystem in the latter part of JoseonDynasty.
In the equatorial sundials of the traditional society, 30° of angle was divided to both the right and left sides with the solar meridian reference line at the center, allocating the same interval for one
Sigan(corresponding to two hours at present). Each Siganwas divided into Choand Jeongin the same interval, and thus the system was identical to the current 24-hour system. However, the time used in the era was true solar time, not mean solar time that is currently used.
Twelve time lines drawn on the equatorial face were generated by the rotating earth. Thus, even though the solar elevation is varied on the meridian line, the twelve equal intervals are still valid because the earth’s rotation is constant. For example, the solar meridian elevation is 76° on the summer solstice in the location of 37.5° latitude.The earth’s rotation is constant as 30° for each hour with reference to the equatorial plane regardless of the solar elevation, the marks on the Siban face of equatorial planes can be still used. As already shown in the previous studies, the time was measured in the same manner in the observation instruments where the
Baekgakhwanwas installed as the equatorial plane such as Ganui, Soganuiand Ilseongjeongsiui(Lee 1996, Lee & Nam 1998, Lee & Kim 2002, Kim 2007).
Fig. 7 shows the meridian elevation by the horizontal coordinates system where Z denotes the zenith and H the horizontal plane. The polar axis (south celestial pole: SCP, north celestial pole: NCP) of the celestial sphere rotates the equatorial plane. When the sun is located on the equatorial plane of the celestial sphere, the season corresponds to the spring equinox (SE) and autumnal equinox (AE). On that day, the solar meridian elevation is 52.5° at 37.5° north latitude.4The variation of the solar meridian elevation is +23.5°~-23.5° with the horizontal plane at the center. Thus, the solar meridian elevation is the highest as 76° on the summer solstice (SS) and the lowest as 29° on the winter solstice (WS). In the case of equatorial sundials in which the equatorial plane is fixed, the time is read on the shade line generated by the thread onto the front face and the rear face of the equatorial plane
Sibanbecause the solar meridian elevation is varied up and down.
2The north-south direction alignment method using a magnet floated on the water in a round pond may be the most probable method applied to the instruments that could be established at a certain place such as Ilseongjeongsiui and Jeongnamilgu. However, a more careful approach should be taken about whether or not a magnet (magnet needle) was floated on the water in a round pond for the small, portable instrument to set the north-south direction. The portable instrument, Angbuilgu, used in the latter part of Joseon dynasty provides a clue for that; the compass system of the portable Angbuilgu might have been used as it is fixed in the round pond of Cheonpyeongilgu. This may be applied to the portable sundials such as Hyeonjuilgu and Cheonpyeongilgu. We will analyze this in detail in further studies.
3Mihn Byeong-Hee (Korea Astronomy and Space Science Institute, researcher) suggested the necessity of a handle in Cheonpyeongilgu in the presentation at the Conference of the Korean Space Science Society (October 29, 2010). The suggested model included the pillar of Cheonpyeongilgu extended to the upper direction. Referring this information, we examined the drinking cup used on horseback and assumed the model in which the pillar was extended to the bottom direction.
4Meridian elevation (h) = 90° ? latitude at the observation point (φ) + solar declination (δ⊙)
Jeongnamilgu, the sundial invented in 1437 (the 19 year of King Sejongera), has the features of an observation instrument. Table 2 shows the specifications of Jeongnamilgupresented in Sejongsillok. The name of each part, the scale at that time, the values converted to today’s unit, and the structure characteristics were described.
Sayuhwan(four-displacement ring) axis that links the north-south pillar of Jeongnamilguis to be aligned with the NP direction of the sky which is the rotational axis of the earth. Leveling was to be performed by hanging a weight with a thread at the tip of the Sayuhwanaxis penetrating the northern pillar and aligning it with the cross lines. The Juchoendosumarks are engraved at both sides of Sayuhwanin order to measure Geogeukdo(the angular distance from the NP which is similar to the solar declination value) of the sun. The cross line method is the same with the leveling method of Hyeonjuilgu. The method to align the north-south direction was improved using Sayuhwanand Gyuhyeong.
Jikgeo is placed inside
Sayuhwanand the Gyuhyeonginside it was to be moved so that the solar light could be received by Banhwan(half-ring). In the restoration model of the Korea Research Institute of Standards and Science, based on the research data of Needham et al. (1986), Banhwanwas produced in the shape of an equator belt. However, Sejongsillokstated about Banhwanthat it was installed under Jipyeonghwanaccording to the time of sunrise and sunset on the day of the summer solstice, which is different from the result of Needham et al. (1986).
The time of sunrise and sunset on the day of the summer solstice can give important information that determines the position and shape of
Banhwan. The reference for Banhwanwas set to the summer solstice, which may be actually the SE-AE line or the WE line with reference to the SS line. Thus, Banhwanof Jeongnamilguis assumed to be a Sibanwith a round surface that expresses the position of the sun at 24 subdivisions of the seasons as in Angbuilgu, rather than a belt for the equator on the celestial sphere (Fig. 8). Jeongnamilguhas the similar function with that of Anguiin Chinese Yuandynasty in the sense that the solar light spots are used. Despite the similar function, the measurement method is different: Anguihas the light spot measurement function at the center, while Sayuhwan
Honchonuiwas applied to Jeongnamilgu(Fig. 9).5 Jeongnamilguhas features of the Islamic sundials in that a hemispheric Banhwanwas employed. This Islamic tradition led to Anguiin Chinese Yuandynasty and Angbuilguin Joseon. Hence, Jeongnamilgumay be considered as a fusion sundial for observation in the structure of Angbuilguthat had the features of Islamic sundials.
The method to align the north-south direction in
Jeongnamilguis as follows: for the initial installment of Jeongnamilgu, the Gegeokdovalue of the day should be known.6 After aligning the instrument according to the Gegeokdovalue of the sun, the solar light spot should fall on the Sayuhwanface or Siban. For this, the instrument should maintain the leveling-off state. If the Sayuhwansurrounding Gyuhyeongis rotated, tuning the left and right sides of the Jeongnamilgubase, the moment when the solar light falls on the face occurs. At that moment, Jeongnamilguis rightly aligned to the north-south direction.Then, the time can be measured by freely moving Gyuhyeong. The astronomical information including the sunrise time and sunset time at each subdivision of the seasons can be obtained using the seasonal subdivision lines.
In sundials, the shade of the needle falls on the
Sibanface. However, if the needle is long, the needle shade at the tip becomes faint and thus the mark cannot be read clearly with the shade. In the case of Jeongnamilgu, the solar light is introduced using the Gyuhyeongas shown in Fig. 8, not reading the shade. A tiny hole is made at the tip of the front side of the Gyuhyeongso that a bright image of the sun, which is the light spot, can fall on the Sibanface on the basis of the pinhole camera’s principle.
The focal length (
f) of a pinhole camera is the distance from the pinhole face to the focal plane. The depth of field is infinite. Generally, a more clearly image can be seen as the diameter of the pinhole is smaller. However, as the pinhole diameter is decreased, the image is seen darker. Hence, the image may be bright if the object is the sun, but the image may be faint by diffraction if the pinhole is too small.
The optimal pinhole diameter should be calculated after determining the focal length. The optimal pinhole diameter,which is determined by the diffraction pattern on the focal plane and light intensity of the solar light from the pinhole, is the distance from the center of the Airy disk to the first dark diffraction pattern. Based on this optimal pinhole diameter (d) condition, the following relation by Lee et al. (2006) assumed that the approximate mean solar wavelength observed by naked eyes is 5,500 A:
where the focal length (f) is the distance from the pinhole to the focal plane. Since the size of the restored Jeongnamilgu was three times larger than that of the actual one, the size of Gyuhyeong, 440 mm, corresponds to the focal distance and the optimal pinhole diameter (d) is 0.8 mm. The diameter of the solar image on the Siban face is calculated as in the following equation using the apparent diameter of the sun, 32 arcminute:
The diameter of the solar image, which is the light spot, is about 4.1 mm by Eq. (2).
5It seems that the shape of Gyuhyeong in Sayuhwan was an application of the Gyuhyeong in Honchonui that was widely used at that time. While the Gyuhyeong in Ganui has the structure that rotates at the side of Sayuhwan, the Gyuhyeong in Jeongnamilgu was described to move between a pair of Sayuhwan of Honchonui.
6If the accurate Gegeokdo value is not known, the north-south direction can be aligned by fine tuning using the approximate solar Gegeokdo value.
Hyeonjuilguand Cheonpyeongilguare the sundials that have an equator Siban, they do not have the function to measure the subdivisions of the seasons as in Angbuilgu. However, they are convenient, portable sundials in which the yearly variation of the solar meridian elevation and the daily variation of the solar hour angle are expressed as the shade on the Siban. We prepared the restoration design drawing for the fabrication of Hyeonjuilguand Cheonpyeongilgu(Fig. 10; drawing: Korean Traditional Technology and Culture Co., Seoul, Korea). The design of Hyeonjuilguwas based on that of Ilyeongui, and Cheonpyeongilguwas designed referring to Hyeonjuilgu. The handle for Cheonpyeongilgusuggested in the main text was not included in the design and thus it has the structure to be put on a floor.7
Fig. 11 shows the restoration models of
Hyeonjuilguand Cheonpyeongilguproduced according to the design
drawings (production: Korean Traditional Technology and Culture Co.). In
Hyeonjuilgu, two dragons hold the supportive pillars, and a bead is hung on the thread that penetrates the mouths of the dragons for leveling of the instrument.8The pillar of Cheonpyeongilguwas built to be biased to the northern part from the center. The optimized position of the pillar was chosen, because Siban
would be too small if the pillar were located at the center.
In the newly restored
Jeongnamilgu, the values that are observed by Angbuilgucan be measured in the same manner because it also has a round Sibanjust like that in Angbuilgu. The time and seasonal subdivisions can be measured and the sunrise and sunset times can be predicted in advance with Jeongnamilgu. The design
Jeongnamilguwas prepared by enlarging the size by three times for outdoor display (Fig. 12; drawing: Korean Traditional Technology and Culture Co.).9The Jeongnamilgumodels produced in this way are exhibited at Yeongreung(the tomb of King Sejong) and the National Science Museum.
Banhwanstructure in Needham et al. (1986) was replaced by a round spherical surface applying the hour lines and the seasonal subdivision lines of Angbuilgu. This structure from the hemisphere shape of Angbuilguprovides the advantage to measure the time and seasons simultaneously. Twelve hours were marked under the Siban plane to read the time. The pillars with dragon patterns were used for the restoration of the northern and southern pillars because Jeongnamilguis the instrument that was used by the royal family. The base was produced considering the stability of the instrument (Fig. 13; product: Korean Traditional Technology and Culture Co.).
7The schematic illustration of the handle attached to the bottom of Cheonpyeongilgu was provided in the main text. The restoration design and model did not reflect the presumption and just provided the basic model to be put on a palm or plane. We will provide the design and restoration model for Cheonpyeongilgu in further studies.
8The pillar in Hyeonjuilgu may be expressed with one pillar from the functional viewpoint, but two dragon pillars were built in the restoration model designing process so that a bead can be hung.
9It was produced as to be three times larger than the actual size for outdoor display. However, there is not a functional problem because the size was increased while understanding the working principle and structure of the original one. The only structural change was made while enlarging by three times for the base in order to install the instrument stably.
Among the sundials produced in King
Sejongera, we analyzed two portable equatorial sundials and one sundial for observation that has Sayuhwan. The principle of the solar movement on the celestial sphere at the rate of 15°/1 hr (the hour in today’s concept) was applied to the equatorial portable sundials. This represents the solar movement at arbitrary latitude along the equatorial plane of the celestial sphere. The actual celestial move ment is by the rotation of the earth’s equatorial plane around the rotational axis one a day. Thus, the solar elevation may be varied between WS and SS, but the hour lines on the equatorial plane can be still used because the earth’s rotational axis is not changed. This indicates that the horizontal coordinates system sundials reflected the accurate understanding of the equatorial coordinate system in which the time can be read on any day despite the variation of the solar hour angle.
However, both sides of the
Sibanshould be used since the solar meridian elevation is varied by the seasons with reference to the equatorial plane of the celestial sphere. In other words, the upper side of the Sibanis read from the SE to the AE and the lower side from the AE to the SE of the next year. Cheonpyeongilgumight have a different shape from that of Hyeonjuilgubecause it was used on horseback and had two round ponds. However, both Cheonpyeongilguand Hyeonjuilgudid not have the function to measure the seasonal subdivisions, different from previous Angbuilguand Jeongnamilgu. According to the investigation until now, the only East Asian country that produced a portable equatorial sundial was Joseonat that time. Regarding this, a more detailed investigation should be carried out about the artifacts of the surrounding countries. Jeongnamilguapplied the method using Geogeukdofor the alignment of the north-south direction, different from the magnet-based method in the previous equatorial sundials. The time of the solar meridian elevation is changed every day. If Geogeukdoof the measurement day is known, the north-south direction was aligned by moving Gyuhyeongso that the solar light spot can fall on the Sayuhwanface (or Sibanface). Such direct observation of the solar spot in sundials was also applied in Anguiof China; the method of Joseonthat employs Sayuhwanis basically different in the structure from the Chinese method that uses the tip of a needle.
As a round
Sibanof Angbuilguwas adopted for the restoration model of Jeongnamilgu, the variation of the solar Geogeukdoand the seasons could be easily measured after the initial installation of Jeongnamilgu. The tradition of spherical surface may be associated with the technological development from the Islamic tradition, to Anguiof Yuandynasty and Angbuilguof Joseon. The measurement of the seasonal subdivisions using a spherical surface was possible only by the accumulated astronomical knowledge that enabled to express the theoretical principle of the astronomy at that time to the observation instruments.
We prepared the design drawings of
Hyeonjuilgu, Cheonpyeongilguand Jeongnamilguby studying the structure, method to use, principle and produced the restoration models. We hope that the sundials could be restored more stably in the future by improving the models through continued experiment with them.
Gak Siban百刻時盤, round plate with one hundred intervals time lines Angbuilgu仰釜日晷, hemispherical sundial Angui仰儀, upward hemisphere Baekgakhwan百刻環, one hundred intervals time lines ring Banhwan半環, half-ring Bu趺, stand; base Cheonpyeongilgu天平日晷, portable equatorial sundial Cho初, beginnings double hours Chou-Cheok周尺, scale unit (1 Chou-Cheok= 207 mm, 1 Chon= 20.7 mm, 1 Bun= 2.07 mm) Ganui簡儀, simplified armillary sphere Geogeukdo去極度, the angular distance from the north pole which is similar to the solar declination value Gyuhyeong窺衡, sighting alidade Gyupyo圭表, gnomon Honui渾儀, armillary sphere; also called Honcheonui渾天儀 Hyeonjuilgu懸珠日晷, portable equatorial sundial; plummet sundial Ilseongjeongsiui日星定時儀, sun-and-star time determining instrument Ilyeongui日影儀, portable equatorial sundial Jagyeongnu自擊漏, striking clepsydra Jeong正, mid-points double hours Jeongnamilgu定南日晷, south-fixing sundial Jikgeo直距 Jipyeonghwan地平環, horizontal ring Jucheondosu周天度數, 365.25度 Sayuhwan四游環, four-displacements ring Sejong世宗, King Sejong (1418~1450) of Joseon Sejongsillok世宗實錄, Annals of Sejong Siban時盤, round plate with time lines Sigan時間, corresponding to two hours at present Soganui小簡儀, small size simplified armillary sphere
[Fig. 1.] Ilyeongui (a) and magnify 100-gak time dial (b) (Song et al. 1994).
[Table 1.] Features on the Hyeonjuilgu Cheonpyeongilgu Jeongnamilgu.
[Fig.2.] Structure of Hyeonjuilgu (a and b) and solar meridian altitude transition (c).
[Fig. 3.] Hyeonjuilgu Siban’s 100-gak graduations: summer season (a) and winter season (b).
[Fig. 4.] Keys map of Cheonpyeongilgu.
[Fig. 5.] Horseback cup (a) and Cheonpyeongilgu handle (b).
[Fig. 6.] Equatorial sundial in China (Beijing National Palace Museum).
[Fig. 7.] Solar meridian in horizontal coordinates.
[Table 2.] Jeongnamilgu’s specifications (1 Chou-Cheok = 207 mm).
[Fig. 8.] Keys map of Jeongnamilgu and optical principle.
[Fig. 9.] China’s Angui model (Wang et al. 2006).
[Fig. 10.] Section of Hyeongjuilgu (a) and Cheonpyeongilgu (b) blueprint.
[Fig. 11.] Restoration models of Hyeonjuilgu (a) and Cheonpyeongilgu (b).
[Fig. 12.] Section of Jeongnamilgu blueprint.
[Fig. 13.] Restoration model of Jeongnamilgu.