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.

1. INTRODUCTION
 2. ASTRONOMICAL INSTRUMENTS IN THE REIGNOF KING SEJONG
  2.1 Classification
  2.2 Composition and Specification
 3. METHOD FOR DRAWING SCALE
  3.1 Circumference and scale
  3.2 Diameter of the Circle, Sphere, and Ring
 4. COMPARISON WITH THE RECORDS AND RELICS
  4.1 Cheonsang yeolcha bunyajido(天象列次分野之圖) andHonsang
  4.2. Hyeonju ilgu and Jeongnam ilgu
 5. CONCLUSIONS
 ACKNOWLEDGEMENTS
 REFERENCES

• Byeong-Hee Mihn(Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea, Chungbuk National University Observatory, Cheongju 361-763, Korea, Korea University of Science & Technology, Daejeon 305-350, Korea) Corresponding author
• Ki-Won Lee(Catholic University of Daegu, Gyeongsan 712-702, Korea)
• Young Sook Ahn(Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea)
• Yong Sam Lee(Chungbuk National University Observatory, Cheongju 361-763, Korea)