Scale Marking Method on the Circumference of Circle Elements for Astronomical Instruments in the Early Joseon Dynasty
 Author: Mihn ByeongHee, Lee KiWon, Ahn Young Sook, Lee Yong Sam
 Publish: Journal of Astronomy and Space Sciences Volume 32, Issue1, p63~71, 15 March 2015

ABSTRACT
During the reign of King
Sejong (世宗, 14181450) in the Joseon Dynasty, there were lots of astronomical instruments, including miniaturized ones. Those instruments utilized the technical knowhow acquired through building contemporary astronomical instruments previously developed in theSong (宋),Jin (金), andYuan (元) dynasties of China. In those days, many astronomical instruments had circles, rings, and spheres carved with a scale of 365.25, 100, and 24 parts, respectively, on their circumference. These were called the celestialcircumference degree, hundredinterval (Baekgak ), and 24 direction, respectively. These scales are marked by the angular distance, not by the angle. Therefore, these circles, rings, and spheres had to be optimized in size to accomodate proper scales. Assuming that the scale system is composed of integer multiples of unit length, we studied the sizes of circles by referring to old articles and investigating existing artifacts. We discovered that the star chart ofCheonsang yeolcha bunyajido was drawn with a royal standard ruler (周尺) based on the unit length of 207 mm. Interestingly, its circumference was marked by the unit scale of 3puns per 1du (or degree) likeHonsang (a celestial globe). We also found thatHyeonju ilgu (a equatorial sundial) has a Baekgak disk on a scale of 1pu n per 1gak (that is an interval of time similar to a quarter). This study contributes to the analysis of specifications of numerous circular elements from old Korean astronomical instruments.

KEYWORD
ancient astronomical instrument , scales of ring , Cheonsang yeolcha bunyaji do , Honsang , Hyeonjuilgua

1. INTRODUCTION
In the 15^{th} century of the Joseon Dynasty, during the reign of King
Sejong (14181450), various astronomical instruments were developed. InSejong sillok (世宗實錄, the veritable record of King Sejong), there is a summary of astronomical instruments made from the period of July 1432 (the 14^{th} year ofSejong ) to January 1438 (the 20^{th }year ofSejong ) by the scholars ofJiphyeonjeon (Hall of Worthies) and the astronomical officials of Gwansanggam (Royal Observatory). Lee Cheon(李蕆), theGanuidae jejo (簡儀 臺提調) took a leading role in making those astronomical instruments in theGanuidae Project , which lasted for about 5.5 years (Nha et al. 1992, Jeon 2011). Those instruments comprisedGanui (簡儀, a simplified armillary sphere),Dae gyupyo( 大圭表, a large measuringscale and gnomon), the waterpoweredHoncheonui (渾天儀, an armillary sphere, in other words,Honui ) andHonsang (渾象, a celestial globe),Angbu ilgu (仰釜日晷, a scaphe sundial),Ilseong jeongsiui (日 星定時儀, a sunandstars timedetermining instrument),So ganui (小簡儀, a small, simplified armillary sphere), andHyeonju ilgu (懸珠日晷, a plummet sundial). Most of these astromical instruments also had markings of angle, time, and direction on their spheres, circles, and rings.There have been several attempts to make replicas of the astronomical instruments from the Joseon Dynasty (Nam 1989, Nha et al. 1992, Lee 1996, Kim 1997, Lee et al. 2006, Lee & Kim 2011, Lee at al. 2011, Lee & Kim 2012). However, the markings on the spheres or circles of these replicas were engraved using modern technology and knowledge. In this paper, some specifications of early Joseonese astronomical instruments are summarized. A scale marking method regarding the circumference of spheres or circles was examined using a stonecarved astronomical chart,
Honsang , andHyeonju ilgu .2. ASTRONOMICAL INSTRUMENTS IN THE REIGN OF KING
SEJONG 2.1 Classification
Astronomical instruments made in the early Joseon Dynasty are categorized into two types: restored astronomical instruments and creative astronomical instruments. The restored astronomical instruments were quite large usually and built based on the astronomical literatures of old Chinese dynasties. In contrast, the creative astronomical ones, which were relatively small in scale, were made using technical knowhow acquired during the process of building the restored astronomical instruments.
Typical restored astronomical instruments are
Honsang ,Honui , andDae gyupyo . InSejong sillok , there is no description on the detailed structures or specifications of those instruments. Instead, there are only descriptions of the Chinese literatures referenced and the places where the instruments were installed. Meanwhile, although there is currently a debate on the replica of the originalCheonsang Yeolcha Bunyaji do (Rufus 1913, Koo 2007, Ahn 2010, Ahn 2011),Cheonsang Yeolcha Bunyajido can be classified as one of the restored astronomical instruments because it was made in January 1396 during the early Joseon Dynasty. However, forSo ganui, Ilseong jeongsiui , andHyeonju ilgu , the detailed description of the shapes and dimensions is given inSejong sillok . These astronomical instruments are not mentioned in the Chinese articles from those days and were downsized while being built. Thus, it is speculated that these are creative astronomical instruments.2.2 Composition and Specification
In the Joseon Dynasty, the celestialcircumference degree, also known as the great circle of celestial sphere, was divided into 365.25 dus while the time scale of a day was divided into 100
gaks (a time interval where 1gak corresponds to 14.4 minutes today) prior to the introduction of theShixian calendar. Also, the 24 direction systems were used. However, after the introduction of theShixian calendar, the metrics of degree and time were changed to 360˚ and 96 quarterofanhour(so called 96gaks ), respectively. Moreover, regardless of the calendar system, the twentyeight lunar lodge system of irregular intervals and the twelve doublehour system of uniform scale were traditionally kept for the celestialcircumference degree and time, respectively. These systems were marked on the astronomical instruments of those days.For example, in
Cheonsang Yeolcha Bunyajido , there is a circular star chart with a diameter of 761 mm (Park 1998). The diameter of the circle can be divided into a coordinate circle and an outermost circle . While the degree of celestialcircumference is inscribed on the coordinate circle, twelve zodiac and 12 directions are inscribed on the outermost circle. According to the replica of theCheonsang Yeolcha Bunyajido housed in Korea Astronomy and Space Science Institute (KASI), the longitudinal diameters of the coordinate circle and outermost circle are about 723 mm and 760 mm, respectively (Table 3). Whereas the circular star chart of theCheonsang Yeolcha Bunyajido shows old Chinese constellations on a 2dimensional plane,Honsang shows them on a 3dimensional spherical surface. Also,Sejong sillok describes the circumference of Honsang to be 10.86ja , while there is an assertion that it is a typographical error of 10.96ja (Han et al. 2001).Most Joseonese astronomical instruments had various sizes of rings corresponding to the great circle of the celestial sphere. These rings were used to measure the position, time, and direction of celestial bodies, and those were known as
Jucheon dobun hwan (a celestialcircumference degreeandfractions ring; abbreviated to celestialcircumference ring), Baekgak hwan (a hundredinterval ring), andJipyeong hwan (a horizontal ring). TheJucheon dobun hwan divides the celestial sphere into 365.25 uniform parts according to the total days of a year. Occasionally, twentyeight lunar lodges are marked together. This ring is either marked by a scale of 365.25 equal parts or marked twice by a scale of 182.6 equal parts. For example, theJekdo hwan (an equatorial ring) of Ganui has twentyeight lunar lodges with 365.25 ticks and itsSa yu whan (a declination ring) marks the scale of 182.6 on the northern and southern half circles, respectively.Baekgak hwan is a ring carved with a twelve doublehour system and 100gaks . However, after the introduction of theShixian calendar, the time scale of a day was modified into 96gaks . Also, 24 directions were marked onJipyeong hwan .Honcheonui is an astronomical instrument containing the most number of rings. It is believed thatHoncheonui was made during the reign of KingSejong (世宗, 14191450) and is referred to in the “Compiled Description on theShujing (書纂言)” byWu Cheng (吳澄, 12491333) in theYuan Dynasty.Honcheonui has a 3layered structure ofYukhapui (a fixed celestialcoordinate part),Samsinui (a rotating three celestial body part), andSayuui (a observational part). Each layer is composed of several single or double rings (Lee et al., 2010). The structrure ofHoncheonui is complicated, as described above. However,Ganui (a simplified armillary sphere) was developed for a simpler structure. Moreover, So ganui was developed for a much simpler and smaller structure. The records ofGanui andYangyi (仰儀, a scaphe sundial) are listed in the Yuan History’s (元史) section ofJega ryeoksangjib (諸家曆象集, collections of astronomy from all Chinese dynasties). According to this record,Ganui has aBaekgak hwan ,Jekdo hwan , andSa yu ssanghwan . In particular, theJekdo hwan rotates on the inner cross section of the LshapedBaekgak hwan (Lee 1996). Most of the existingAngbu ilgus (仰釜日晷, a scaphe sundial) from Joseon originated from the 17^{th} century or later. However, the prototype of the Angbuilgus from the early Joseon Dynasty is presumed to be a downsized Yangyi according to the description ofXuanjiban (旋璣板, a pinpoint plate) in the inscription ofAngbu ilgus written byKim Don (金墩, 13851440).As mentioned above,
So ganui in theSejong era is a simplified form ofGanui and it has three rings ofJekdo hwan ,Baekgak hwan , andSa yu hwan . Even though their sizes are not known, according to the inscription ofSo ganui in the KingSeongjong era, the diameters ofJekdo hwan andSa yu hwan are the same as those of 2ja , which are based on the Soganui of theSejong era (Lee & Moon 2004).Lastly,
Ilseong jeongsiui is a typical creative astronomical instrument and detailed dimensions are shown in theSejong sillok . According to this record, the rings ofIlseong jeongsiui consist of aJucheon dobun hwan (a celestialcircumference ring) and twoBaekgak hwans (hundredinterval rings). Also, the record shows thatSo Ilseongjeongsiui was made to be almost similar toIlseongjeongsiui . We can presume that the SoIlseongjeongsiui has three rings and the same dimensions.Various small scale sundials were made in King
Sejong ’s era, for example,Hyeonju ilgu ,Cheonpyeong ilgu (a ruletheworld sundial or a plummet sundial), and Jeongnam ilgu. According to Sejong sillok , there is aBaekgak disk with a diameter of 0.32ja in theHyeonju ilgu and the structure and dimension ofCheonpyeong ilgu are similar toHyeonju ilgu .Cheonpyeong ilgu , which was developed to determine the time in the middle of horse riding, has aBaekgak disk similar toHyeonju ilgu . UnlikeHyeonju ilgu , it has irrigable pools at both the south and north sides and a rope attached to the top of the post in order to grip it while winding a rope around a wrist.Jeongnam ilgu measures the time usingSa yu ssanghwan (a declination double ring). However, the exact dimensions ofSa yu ssanghwan are not known.Table 1 shows the dimensions of astronomical instruments according to the category of restored astronomical instruments (I) and creative astronomical instruments (II). The rings of each astronomical instrument are divided into
Jucheon dobun hwan (celestialcircumference), Baekgak hwan (hundredinterval rings), andJipyeong hwan (horizontal ring). In this table, the unit length of specifications isja (refer to Section 3.2). The star charts ofCheonsang yeolcha bunyajido andHonsang are classified as celestialcircumference rings and theBaekgak disks ofHyeonju ilgu andCheonpyeong ilgu are classified as hundredinterval rings for convenience.3. METHOD FOR DRAWING SCALE
3.1 Circumference and scale
In ancient China, the
du in the celestialcircumference degree is a unit of length rather than of angle. This unit has been used in astronomical instruments (Zhang 2000). According toZhoubi suanjing (周脾算經, arithmetic classic of circles and gnomons), the circle of diameter, 121.75ja , has a circumference of 365.25ja which makes 1du equal 1ja . According to this method, the circle is equally divided by using the celestialcircumference degree, and the ratio of the circumference used was 3. Thus, the scales of a circle or a sphere were marked as angular distance.While the ratio of circumference was 3 in
Zhoubi suanjing ,Liu Hu i (劉徽) from the Wei Dynasty (魏, 220~265) of China used 157/50(=3.14) andZhao Chong Zhi (趙冲之, 429~500) of theLiu’s Song (劉宋, 420~479) used 3.1415926 (Needham 1959, Kim 2006). It seems that the ratio ocircumference varies depending on the precision of the scales and the convenience of calculation. However, as astronomical instruments require precise measurement of the position of the celestial body, it is believed that the value of 3.14 was used in marking the scales on the circumferences.Similar to China, the units of length used in Joseon are
jang ,ja ,chi ,pun ,li , andho , where, 0.1jang = 1ja = 10chi = 100pun = 1000li = 10000ho . In particular,Ju cheok (周尺, a royal standard ruler) was used in Joseon and 1ja of this ruler was 207 mm (Nam 1995). In contrast, 1ja of the astronomical instruments from China was 245 mm (Kim 1993, Lee et al. 2011)3.2 Diameter of the Circle, Sphere, and Ring
As shown in Fig. 1, it is assumed that the scales of a circle, sphere, or ring in the astronomical instruments of China or Joseon were inscribed by dividing the circumference equally with the integer multiple of unit length. First, if we designate the circumference as
l , the ratio of circumference asπ , and the ratio of the division asĸ , the diameter of a ring can be expressed as follows:where
is the size of the unit scale.a Although it is possible to express
orl in the unit ofd ja , can have the unit of chi or pun. Ifa is a positive number andn is a conversion constant, it is possible to expressc asn =n /n . For example, ifc = 1, the unit ofc isn ja , and if = 100, the unit ofc isn pun . If the unit length of adu fromJucheon du (the celestialcircumference degree) or agak fromBaekgak (the hundredinterval) is 1chi ( =10), the diameter and circumference of a circle can be obtained by multiplying 10 to the value of Table 2.c 4. COMPARISON WITH THE RECORDS AND RELICS
4.1
Cheonsang yeolcha bunyajido (天象列次分野之圖) andHonsang Although there is no record on this in
Taejo sillok (Veritable Record of the KingTaejo ), the originalCheonsang yeolcha bunyajido appeared to have been made at the end of the 4^{th} year ofTaejo (1395). Using the replica in KASI, the diameter of the coordinate circle ofJucheon dobun was measured to find the northsouth diameter of 723 mm. When this value is converted using the royal standard ruler of theSejong era, the diameter is about 3.49ja . Furthermore, theChunyou star chart (淳祐天文圖) in China, which has a circular star chart on the top, was made 150 years earlier than theCheonsang yeolcha bunyajido . According to the rubbing of the Chunyou star chart at KASI, the measurements of the northsouth diameter from the coordinate circle, on whichJucheon du is marked, is 844 mm, which is 3.44ja in units from old China.The value of 3.490
ja in Table 3 is quite similar to the diameter of the coordinate cicle with = 3 in Jucheonn du ’s column of Table 2. Although the physical sizes of both star charts are different from each other, it is clear that the sizes of those charts in units ofja are similar and that the diameter of the star chart inCheonsang yeolcha bunyajido is 3.49ja based on the royal standard ruler of theSejong era. In the two star charts mentioned above, the total degree ofXu lunar lodge (虛宿) is about 9 1/4du . However, it is actually 9du . Therefore, the circumference can be uniformly divided into 365 parts rather than 365.25 parts and the circumference is calculated to be about 10.95ja based on the scale of 3pun per 1du .In
Cheonsang yeolcha bunyajido , the center of the chart is the north pole and the radius of the coordinate circle is the boundary of seeing a star at an observatory. Thus, that boundary depends on the latitude (φ , the altitude of north pole) of the observer. The boundary circle indicates – (91.3125 –φ )du in the declination and (182.625 –φ )du in polar distance. In Table 3, the radius of equatorial circle is about 1.08ja and the radius of the coordinate circle is 1.745ja . Hence,φ is calculated to be (182.625 – 91.3125)du ㆍ(1.745/1.08) = 35.09du . Converting this value into a 360˚system gives us 34.58˚, which is close to the latitude ofYangcheng (陽城) of theZhuo Dynasty (周) or the currentDengfeng (登封) where theZhougong cejing tai (周公測景 臺) andGuanxing tai (觀星臺) are located. InCheonsang yeolcha bunyajido , 91.3125du corresponds to 1.08ja , so 1du in declination is about 1.2 pun for scale marking. On the contrary, if we fix 1 du as 1.2pun in declination, the radius of the equatorial circle is about 1.096ja while that of the coordinate circle is 1.758pun , which shows a difference of about 1.5pun each.Ahn (2010) suggested that the
Cheonsang yeolcha bunyajido was made according to the method described inTianwen zhi (天文志, the treatise on astronomy) ofXin tangshu (新唐書, the new book of Tang history). If the star chart followed the method ofXin tangshu , the right ascension should have been marked by 3pun per 1du on the basis of the circumference of the coordinate circle and polar distance being 1.2pun per 1du or 6pun per 5du , which is like a polar coordinate with the origin as the north pole. According toXin Tangshu , the ruler made the skin of a bamboo tree have 147 scales from a hole at one end of it (Ahn 2010). 147 scales of that ruler agrees well with those of the radius of the coordinate circle ofCheonsang yeolcha bunyajido (181.625du – 35 du=146.625du ).According to
Sejong sillok , the circumference ofHonsang is 10.86ja , as shown in Table 1. However, the circumference of a circle with =3, as shown in the Jucheonn du column of Table 2, is 10.958 ja. If we assume that the record ofSejong sillok is a typo of 10.96ja (Han et al. 2001), the diameter of the coordinate circle inCheonsang yeolcha bunyajido is the same as that ofHonsang . The difference fromCheonsang yeolcha bunyajido is thatHonsang is 3pun per 1du in the declination scales, which are similar to the right ascention ones. If the bamboo ruler described inXin Tanshu (新唐書) was used to put stars on the surface ofHonsang , it would have had 147 scales of 3pun and not 1.2pun .Sejong sillok described inHonsang as being installed withHonui in the pavilion and powered by water force. The diameter ofHonui is more than twice of the diameter of theHonsang shown in Table 1, so the volumes differ by 8 times or more.The royal standard ruler did not exist in the Goryeo Dynasty and it was newly introduced in the
Sejong era of the Joseon Dynasty (Lee 2001). This does not agree with the date ofCheonsang yeolcha bunyajido ofTaejo era, the 228^{th} Korea national treasure. In order to find out whether this treasure is from theTaejo era or not, or whether a ruler similar to the royal standard ruler was used or not, archeological study is necessary. It is wellknown that stone carved astronomical charts were built in theSejong era (Koo 2007). The epilogue ofJega ryeoksangjib said that an astronomical chart in theSejong era was inscribed to a stone based on theShoushi calendar. If so, at that time, the new engraving ofCheonsang yeolcha bunyajido might be reproduced by the originals. InCheonsang yeolcha bunyajido , the width of stele in theTaejo era was 122, which is 8 cm wider than that of theSukjong era (the 837^{th} Korea Treasure). Its configuration of the planisphere and the inscription are not in the middle of the stele and leftward drawing(Jeon et al. 1984).4.2.
Hyeonju ilgu andJeongnam ilgu Hyeonju ilgu andCheonpyeong ilgu are downscaled astronomical instruments from theSejong era and could be classified as equatorial sundials. As indicated in Table 1, there is aBaekgak disk with the diameter ofHyeonju ilgu being 0.32ja . The diameter of this disk corresponds with =1 in then Baekgak column shown in Table 2 where 1gak is 1pun . There is an artefact known asHyeonju ilgu and the diameter of itsBaekgak disk is 7.1 cm (Song et al. 1994), which is 0.34ja in the unit of the royal standard ruler from theSejong era. Assuming the ratio of circumference as 3 rather than 3.14, this can be interpreted to be the diameter of a circle with 1gak per 1pun .Applying Equation (1), we can predict whether the ratio of circumference applied to astronomical instruments is 3.14 or 3. If we let
π _{1} andπ _{2} be 3 and 3.14, respectively, and the corresponding diameters based on Equation (1) are _{1} andd _{2} , the difference of diameters is calculated as follows:d Where,
π _{2}^{1}−π _{1}^{1}=14.86×10^{−3}. If we mark the scale of 100 gak ( =100), Δκ ≈ −1.49_{n⋅ c}^{−1}. In the cased is 100, Δc becomes 1.49d pun (about 3 mm) per unit scale of 1pun . However, when the unit of 1gak ischi orja ( c is 10 or 1), becomes 1.49chi (about 3 cm) or 1.49ja (about 30 cm). Thus, it is difficult to build astromical instruments based on the circular constant of 3.If we let
π _{1} andπ _{2} be 3.14 and 3.1415926, respectively, and the corresponding diameters are _{1} andd _{2}, assuming thatd Jucheon du is marked on the circumference, Δ ≈ −5.89×10^{−2} n⋅c^{−1} according to Equation (2). Althoughd is 1, Δc has little discrepancy of 5.89d pun (about 12.2 mm) per unit scale of 1ja . Since the difference is excessively small, it is speculated that astronomical instruments are built based on the circular constant of 3.14.Jeongnam ilgu is also one of the downscaled sundials and has a special shape of sundial, which was described inSejong sillok .Sa yu hwan , halfBaekgak hwan , andJipyeong hwan , which are rings ofJeongnam ilgu , have a scale of the celestialcircumference degree, a hundredinterval, and 24 directions, repectively. Though the dimension of these rings was not recorded, it is estimated that the diameter ofJipyeong hwan is greater than 1.0ja and the diameter of halfBaekgak hwan is between 1.0ja and 0.9ja, while the diameter ofSa yu whan is between 0.9ja and 0.67ja .The length of the bottom plate of
Jeongnam ilgu is 1.25ja and the distance between the two posts in the south and north is about 1.0ja . Because the summer solstice is the longest day, halfBaekgak hwan is aligned along the line of the summer solstice and the scales of 100gak are marked on it. The heights of the northern post and southern post are 1.1ja and 0.59ja , respectively. The inclined axis ofSa yu whan passes through two posts, and the intersection occurs at the height of 0.99ja in the northern post while that occurs at 0.21ja in the southern post. The intersection point of the northern post is 0.78ja higher than that of the southern post. The latitude of Hanyang (the old name of Seoul), the capital of Joseon, was set as 38du (37.45°) while the tan (37.45°) was about 0.766. In other words, the distance between the two posts and the height difference between the two intersections of the axis and post were designed to closely correspond to the latitude of Hanyang. While it is not certain how they determined 0.766 in those days, it can be estimated from the table inLizhi (曆志, Treatise of the Calender) ofMingshi (明史, History of Ming Dynasty). According toMingshi , values corresponding to the adjacent leg and opposite leg of a right triangle are obtained usingHushi geyuan (弧矢割圓, Calculation of the arc and sagitta in the secant of the circle ) andZhehui (折會術, Trapezium Method of the secant of the circle ) ofShen Gua (沈括, 1031  1095). Based on these, the ecliptic opposite leg (黃道半弧弦) is 36.7486 du and the ecliptic adjacent leg(黃道大股) is 48.5316 du. Thus, the ecliptic tangent is 0.7572.The arm of the
Baekgak disk ofHyeonju ilgu is slantly fixed to the right triangle shaped socket which soars from the bottom (Song et al. 1994). If the lengths of the adjacent leg and opposite leg in the right triangle are 3 and 4, respectively, the slanting angle will be tan^{1}(4/3)=53.13° (53.9du ). Fortunately, it is similar to the intersection angle between the horizontal plane and the equatorial plane, which is about 52.55° (53.3du ) at Hanyang. For example, if we set the adjacent leg and the opposite leg of the socket to 0.12ja and 0.16ja , respectively, theBaekgak disk ofHyeonju ilgu could be installed to fit the latitude of Hanyang.5. CONCLUSIONS
Various astronomical instruments were made through the construction of an observatory during the
Sejong era. Some of these instruments were replicas of astronomical instruments from old Chinese dynasties while others were newly developed instruments. There are circular components in these instruments indicating the great circle of the celestial sphere, and there are scale inscriptions of the celestialcircumference degree, a hundredinterval, and 24 directions. Circles, spheres, and rings having these scales do not have arbitrary sizes, but specific sizes of circles, which could be divided into equal parts of 365.25, 100, or 24. That is, the angular distance on the circumference of a circle is subdivided instead of the angle itself in order to mark scales.In this paper, simple cases of marking scales in integer multiple unit intervals were analyzed through the articles from the Joseon dynasty and the extant artifacts of astronomical instruments. The star chart of
Cheonsang yeolcha bunyajido in the early Joseon Dynasty and theHonsang ofSejong era drew the celestialcircumference degrees on a circle whose circumference is 10.96ja in a unit scale of 3pun per 1du . While the declination is on a scale of 1.2pun per 1du in the star chart ofCheonsang yeolcha bunyajido , the declination ofHonsang is on a scale of 3pun per 1du . In this analysis, it was found that the planisphere ofCheonsang yeolcha bunyajido was designed with a royal standard ruler. If the roral standard ruler did not exist in theTaejo era of Joseon, the 228^{th} national treasure ofCheonsang yeolcha bunyajido might be a stone copy of the original made after theSejong era.According to the record,
Hyeonju ilgu andCheonpyeong ilgu had aBaekgak disk with a diameter of 0.32ja , of whose circumference divided hundred ticks by 1gak per 1pun and corresponds to the size of the existing artifacts. Although there is no record about the dimension of rings inJeongnam ilgu , it is estimated that the diameter ofJipyeong hwan is greater than 1.0ja , the diameter of halfBaekgak hwan is between 0.9ja and 1.0ja , and the diameter ofSa yu whan is between 0.67ja and 0.9ja . There is a right triangle socket for theBaekgak disk in the existing artifact ofHyeonju ilgu , making it possible to build theBaekgak disk to fit the latitude of Seoul by using the Pythagorean’s theorem.

[Table 1.] Specifications of astronomical instruments developed in the early Joseon Dynasty (1 ja = 207 mm).

[]

[Fig. 1.] The scale by dividing a circumferance into equal angular distances.

[Table 2.] Diameter and circumference of a circle with the integer multiple scale of unit length in Jucheon du, 100 gak, 24 direction (where, π= 3.14).

[Table 3.] Specifications of the outer circles of Cheonsang yeolcha bunyaji do and Chunyou star chart

[]