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).

• Byeong-Hee Mihn(Korea Astronomy and Space Science Institute, Daejeon 34055, Korea, Korea University of Science and Technology, Daejeon 34113, Korea) Corresponding Author
• Goeun Choi(Korea Astronomy and Space Science Institute, Daejeon 34055, Korea, Korea University of Science and Technology, Daejeon 34113, Korea)
• Yong Sam Lee(Department of Astronomy and Space Science, Chungbuk National University, Cheongju 28644, Korea)