We studied the hour-lines of six extant Yangcheon-cheoks in Korea. To find whether Yangcheon-cheok was used in the whole area of Korea, we calculated the length of shadows of Yangcheon-cheok on the Korean Peninsula, Nanjing and Beijing as well as Hanyang (Seoul), according to 24 solar terms. Comparing the length of shadows with hour-lines of those relics, we could find that Yangcheon-cheok was suitable for use at limited times (from 9:00 to 15:00) during the year. Also, this sundial is more appropriate for use at low latitudes than high ones. Among existing relics, that of Seoul Museum of History made with porcelain was much more suitable to use at Hanyang and its higher latitude. Lee’s collection was also suitable to use at Nanjing. It is certain that Yangcheon-cheok was a portable sundial which could be used from nine to fifteen of clock all the year around except for the winter season.

This study examines the scale unique instruments used for astronomical observation during the Joseon dynasty. The Small Simplified Armillary Sphere (小簡儀, So-ganui) and the Sun-and-Stars Time-Determining Instrument (日星定時儀, Ilseong-jeongsi-ui) are minimized astronomical instruments, which can be characterized, respectively, as an observational instrument and a clock, and were influenced by the Simplified Armilla (簡儀, Jianyi) of the Yuan dynasty. These two instruments were equipped with several rings, and the rings of one were similar both in size and in scale to those of the other. Using the classic method of drawing the scale on the circumference of a ring, we analyze the scales of the Small Simplified Armillary Sphere and the Sun-and-Stars Time-Determining Instrument. Like the scale feature of the Simplified Armilla, we find that these two instruments selected the specific circumference which can be drawn by two kinds of scales. If Joseon’s astronomical instruments is applied by the dual scale drawing on one circumference, we suggest that 3.14 was used as the ratio of the circumference of circle, not 3 like China, when the ring’s size was calculated in that time. From the size of Hundred-interval disk of the extant Simplified Sundial in Korea, we make a conclusion that the three rings’ diameter of the Sun-and-Stars Time-Determining Instrument described in the Sejiong Sillok (世宗實錄, Veritable Records of the King Sejong) refers to that of the middle circle of every ring, not the outer circle. As analyzing the degree of 28 lunar lodges (lunar mansions) in the equator written by Chiljeongsan-naepyeon (七政算內篇, the Inner Volume of Calculation of the Motions of the Seven Celestial Determinants), we also obtain the result that the scale of the Celestial-circumference-degree in the Small Simplified Armillary Sphere was made with a scale error about 0.1 du in root mean square (RMS).

We analyze the design and specifications of the Sun-and-Stars Time-Determining group of instruments (Ilseong-jeongsi-ui, 日星定時儀) made during the Joseon dynasty. According to the records of the Sejong Sillok (Veritable Records of King Sejong), Sun-and-Stars Time-Determining Instruments measure the solar time of day and the sidereal time of night through three rings and an alidade. One such instrument, the Simplified Time-Determining Instrument (So-jeongsi-ui, 小定時儀), is made without the essential component for alignment with the celestial north pole. Among this group of instruments, only two bronze Hundred-Interval-Ring Sundials (Baekgak-hwan-Ilgu, 百刻環日晷) currently exist. A comparison of the functions of these two relics with two Time-Determining Instruments suggests that the Hundred-Interval-Ring Sundial is a Simplified Sundial (So-ilyeong, 小日影), as recorded in the Sejong Sillok and the Seongjong Sillok (Veritable Records of King Seongjong). Furthermore, the Simplified Sundial is a model derived from the Simplified Time-Determining Instrument. During the King Sejong reign, the Sun-and-Stars Time-Determining Instruments were used in military camps of the kingdom’s frontiers, in royal ancestral rituals, and in royal astronomical observatories.

We investigated the six remaining Yang-cheon-cheoks (量天尺), which were first described in the Veritable Record of King Sukjong (肅宗實錄). These woodblock sundials from Korea are structurally very similar to a Gyupyo (圭表, gnomon) or an altitude sundial and are light, compact, and portable. The front side of a Yang-cheon-cheok has two holes for styluses and several hour-lines. We compared the intervals of the hour-lines from the originating point of the stylus placement on all Yang-cheon-cheoks and found that two of the relics had the same hour-lines using the standard of the unit of 1 chon (寸). These two were actually the same sundial although the physical size was different. In spite of the lack of time accuracy, we hypothesize that various-sized Yang-cheon-cheoks were made and widely distributed throughout the public in the late Joseon Dynasty.

The Yang-gyeong-gyu-il-ui (兩景揆日儀) is a kind of elevation sundial using three wooden plates. Sang-hyeok Lee (李尙爀, 1810~?) and Byeong-cheol Nam (南秉哲, 1817~1863) gave descriptions of this sundial and explained how to use it in their Gyu-il-go (揆日考) and Ui-gi-jip-seol (儀器輯說), respectively. According to Gyu-il-go (揆日考) there are two horizontal plates and two vertical plates that have lines of season and time. Subseasonal (節候) lines are engraved between seasonal (節氣) lines, subdividing the interval into three equal lines of Cho-hu (初候, early subseason), Jung-hu (中候, mid subseason) and Mal-hu (末候, late subseason); there are 13 seasonal lines for a year, thus resulting in 37 subseasonal lines; also, there are 12 double-hour (時辰) lines for a day engraved on these plates. The only remaining artifact of Yang-gyeong-gyu-il-ui was made in 1849 (the 15th year of Heon-jong) and is kept at the Korea University Museum. We have compared and analyzed Yanggyeong- gyu-il-ui and similar western sundials. Also, we have reviewed the scientific aspect of this artifact and built a replica. Yang-gyeong-gyu-il-ui is a new model enhanced from the miniaturization development in the early Joseon Dynasty and can be applied to the southern part of the tropic line through a structure change.

During the reign of King Sejong (世宗, 1418-1450) in the Joseon Dynasty, there were lots of astronomical instruments, including miniaturized ones. Those instruments utilized the technical know-how acquired through building contemporary astronomical instruments previously developed in the Song(宋), Jin(金), and Yuan(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 celestial-circumference degree, hundred-interval (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 of Cheonsang 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 3 puns per 1 du (or degree) like Honsang (a celestial globe). We also found that Hyeonju ilgu (a equatorial sundial) has a Baekgak disk on a scale of 1 pun per 1 gak (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.