ANALYSIS OF TIME DATA IN KOREAN ALMANACS OF

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1 Journal of the Korean Astronomical Society 5: 9 2, 27 December pissn: eissn: X c 27. The Korean Astronomical Society. All rights reserved. ANALYSIS OF TIME DATA IN KOREAN ALMANACS OF Ki-Won Lee Daegu Catholic University, Hayang-Ro 33, Hayang-Eup, Gyeongsan, Gyeongbuk 3843, Korea; leekw@cu.ac.kr Received December 7, 27; accepted December 2, 27 Abstract: We analyze the time data recorded in Korean astronomical almanacs for the years from 93 to 945, which belong to the period in which Japan occupied Korea (9 945). These almanacs, published by Japanese scholars, differ from previous almanacs in terms of organization, content, and calendrical methods. In this study, we first extract twelve kinds of time data from the almanacs at the following times: solar terms, rising and setting of the Sun and Moon, transit of the Sun, phases of the Moon (i.e., new Moon, first quarter Moon, full Moon, and last quarter Moon), and eclipses of the Sun and Moon. Then, we compare the time data with that obtained from modern calculations. Even though all time data in the almanacs are tabulated in units of minutes, we calculate the data in units of seconds and determine the root mean square (RMS) deviation values for each kind of time data to estimate the accuracy of the data. Our findings are as follows: First, the kind and tabulation method of time data changes several times. For instance, solar transit time is listed only for six years from 937 to 942. Second, the times of two equinoxes and those of a new Moon are considerably close to midnight. Third, there are some typographical errors in the almanacs, particularly in the times of moonrise and moonset. Fourth, the contact times for lunar eclipses represent the times of the umbra and not of the penumbra, which is different from the times for solar eclipses. Finally, the RMS deviation values are approximately.5 min on average in all kinds of time data, even though they show slightly large differences in the times related to the Moon. In conclusion, we believe that this study is useful for investigating the time data in the almanacs of other East Asian countries that were published during the same period, such as China, Japan, and Manchuria. Key words: history and philosophy of astronomy astronomical data bases: almanacs ephemerides time. INTRODUCTION An astronomical almanac is a book containing the day and hour data necessaryfor civil life such assunrise and sunset times and national holidays (Yang et al. 28). Because these data should be standardized in a nation, historically, a government institute compiles almanacs, generally annually. The oldest extant almanac in Korea is that for the year 58, which was compiled by the Gwansanggam (The Royal Astronomical Bureau) of the Joseon dynasty(a.d )(Kim 22; Lee et al. 2). During the period of the Japanese occupation of Korea (i.e., 9 945), astronomical almanacs for Korea were published by Japanese scholars. Currently, the Korea Astronomy and Space Science Institute (hereafter, KASI) publishes almanacs. We analyze the Korean astronomical almanacs for the period from 93 to 945, focusing on the accuracy of time data. Even though Japan occupied Korea since 9, it is known that Japanese scholars compiled Korean almanacs from 93 to 945 (Choi et al. 25). The almanacs of these periods are different from conventional Korean almanacs in terms of organization and content (Lee et al. 2a) and presumably calendrical methods and the utilized ephemeris. However, the dates in the almanacs are referred to the Gregorian calendar, Corresponding author: K.-W. Lee which was introduced into Korea in 896 (KASI 26). Regarding the accuracy of time data, Choi (2) investigated the almanacs for the period from 864 to 945. However, the study was restricted to the times of sunrise/sunset and new Moon. In this study, we examine twelve kinds of time data including moonrise, moonset, and solar terms. The rest of this paper is organized as follows: In Section 2, we briefly introduce the Korean almanacs of 93 to 945 in terms of organization and content, focusing on the kinds of time data and their definition. We describe the modern calculations used for the analysis ofthe time data in Section 3 and comparethe results with the data tabulated in the almanacs in Section 4. Finally, we summarize our findings in Section KOREAN ASTRONOMICAL ALMANACS 2.. Organization Even though Japan occupied Korea since 9, it is known that the almanacs for 9 and 92 were compiled by Korean astronomers, primarily by Lee Don- Su (Choi et al. 25). Figure shows the first pages of the Korean astronomical almanacs for 92 (left) and 93 (right). As shown in the figure, apparent changes are that the Japanese reign-style, i.e., Daejeong, and the compilation institute, i.e., the Observatory of the Japanese Government-General of Ko- 9

2 92 Lee Figure. First pages of the Korean astronomical almanacs for 92 (left) and 93 (right) (source: KASI). rea (hereafter, OJGK) located in Incheon, begin to appear in the far right column. From the astronomical point of view, the standard meridian (i.e., 35 E) and the reference location (i.e., Incheon) of time data are clearly described under the title of Seolmyeong (Explanation) since the almanacs of 93 (see also Choi 2). Moreover, the organization and content of the Korean almanacs were significantly changed once again from 937, along with the change in the title from the Yakryeok to the Joseonminryeok. In addition, the compilation institute was renamed as the Meteorological Observatory of the Japanese Government-General of Korea (hereafter, MOJGK) from 939. Further, there were minor changes from the almanacs of Contents In addition to changes in organization, there were modifications in content, particularly in the appendices. For instance, the comparison tables for the chronicle, mean temperatures for several cities, the times of high and low tides, and so forth were supplemented or eliminated. One of the interesting features was that the agricultural work to be carried out in each month were recorded using a Korean auxiliary particle. A notable change in terms of astronomy was the tabulation of moonrise and moonset times from 95 and of solar transit time from 937. For details on the changes in the organization and contents with respect to the period, refer to the works of Lee (985), Choi (2), and Lee et al. (2a). We have summarized the time data tabulated in the almanacs according to the period in Table. 3. MODERN CALCULATIONS 3.. Definition of Time Data In the almanacs, the definition of time data is not described in detail, even though the standard time and reference location are clearly mentioned. Therefore, we inferred the definition from the Japanese almanacs published at approximately the same time. First, the dates and hours of 24 solar terms are the moments when the Sun passesamultiple of5 in the ecliptic startingfrom the spring equinox. For example, the date and hour of the winter solstice are the times when the ecliptic longitude of the Sun (λ ) is 27. Second, the sunrise and sunset times are described as the moments when the upper part of the Sun apparently reaches the horizon. In other words, these times are the moments when the zenithdistanceofthesun(z )is9 5 consideringthe apparent angular radius of the Sun (6 ) and an atmospheric reflection of 34. Third, moonrise and moonset times are described as the moments when the center of the Moon apparently reaches the horizon. In other words, these times are the moments when the zenith distance of the Moon (z ) is π, considering an atmospheric reflection of 34 and the horizontal parallax (π) defined using the Earth s radius (R) and the distance to the Moon (r)(i.e., π sin (R/r)). This is different from the modern definition, i.e., when the upper part of the Moon apparently reaches the horizon (refer to Urban & Seidelmann 23). Fourth, the times of the phases of the Moon are the moments when the angular distances between the Sun and Moon in the ecliptic ( λ λ ) are (new Moon), 9 (first quarter Moon), 8 (full Moon), and 27 (last quarter Moon), even though there is no explanation in the almanacs. Fifth, the Moon age is the number of days elapsed since the new Moon day (hence, it is an integer); however, it is the number of days elapsed since the new Moon time (hence, it is a real number) nowadays. Therefore, we excluded the time data of the Moon age because it is naturally determined if a new Moon day is obtained. Lastly, the times of three and five stages are tabulated for solar and lunar eclipses, respectively. In a solar eclipse, Chohu and Bokwon are the first and last external contact times of the penumbra (P and P4), respectively. On the contrary, in a lunar eclipse, Chohu, Sikgi, Saenggwang, and Bokwon represent the first external, first internal, last internal, and last external contact times of the umbra (U, U2, U3, and U4), respectively (refer to Section 4). In both eclipses, Siksim is the time of greatest eclipse. In Table 2, we summarize the definition of the time data used in this study Modern Calculation We utilized the astronomical algorithms of Meeus (998) and the DE45 ephemeris of Standish et al. (997) to calculate the time data given in Table 2, except for the eclipse times. We used the values of T, i.e., the difference between terrestrial time (TT) and universal time (UT), presented in The Astronomical Almanacs published by Nautical Almanac Office (hereafter, NAO) (NAO 24). For reference, the values of T in 93 and 945 are 4.65 and s, respectively. Hence, the values of T are not critical for the period considered in this study because they are less than.5 min. With regard to the calculations of eclipse times at different stages, we referred to the work of Lee (28), in which Besselian elements were utilized, for

3 Time Data in Korean Astronomical Almanacs of Table Summary of time data presented in Korean astronomical almanacs for the period from 93 to 945 Time data Solar term Sunrise/sunset Periods : 24 solar terms : 4 solar terms (two solstices and equinoxes) 942: no solar terms : 4 solar terms (two solstices and equinoxes) : on the days of 24 solar terms : on every day including transit time : on about ten days for several cities but without transit time Moonrise/moonset : in turns : on every day Phase of the Moon : new Moon, first quarter Moon, full Moon, last quarter Moon Moon age Eclipse : on every day : solar and lunar eclipses solar eclipses and the work of Liu & Fiala (992) for lunar eclipses (see also Lee et al. 26). According to the records of the almanacs, there was no changein the standardtime (i.e., UT + 9 h). On the contrary, the reference location of time data changed four times, as summarized in Table 3 (see also Choi 2). As mentioned earlier, OJGK was renamed to MOJGK; hence the reference locations were practically changed two times. As the longitude and latitude of the reference locations, we used the values of E and N (listed in the almanac for 937) for OJGK and MOJGK, and E and N (referring to the almanac for 953) for Seoul. Except for the times of moonrise and moonset, we reproduced the time data recorded in the Korean almanac for 27 compiled by KASI (KASI 26) to verify our calculations. We reproduced the moonrise and moonset times recorded in the Japanese almanac for 24 compiled by the National Astronomical Observatory of Japan (hereafter, NAOJ) (NAOJ 23), which still uses the same definitions as those in this study. We found good agreement within the units given in each al- Table 2 Summary of the definition of time data Time data Definition Solar terms λ =, 5,, 33, 345 Sunrise z = 9 5 in the rising Solar transit passage of Sun across a meridian Sunset z = 9 5 in the setting Moonrise Moonset z = π in the rising z = π in the setting New Moon λ λ = First quarter Moon λ λ = 9 Full Moon λ λ = 8 Last quarter Moon λ λ = 27 Greatest eclipse midpoint of the eclipse Eclipse begins first contact of penumbra/umbra Eclipse ends last contact of penumbra/umbra manac. 4. ANALYSIS OF TIME DATA 4.. Solar Terms The times of 24 solar terms are listed based on the hour system in the Chinese Shixian calendar until 937 and on the modern system (i.e., a day is 24 hours) subsequently. Two hours systems are used in the Shixian calendar. In the first, a day is divided into 96 Gak and Gak is divided into 5 Bun (hence, Bun is minute in the modern hour system). In the second system, a day is divided into 2 Sijin and Sijin is divided into Cho and Jeong (refer to Lee et al. 22). In addition, the hours are listed for only four solar terms (i.e., two solstices and equinoxes) in the almanacs after 937, except for 942, even though dates are provided for all solar terms. Interestingly, the solar terms are omitted in the almanac for 942. Using modern calculations, we calculate the times of 24 solar terms in units of seconds and compare the results with those of the almanacs; the hours are listed in units of minutes in the almanacs. Figure 2 shows the difference between the times in the almanacs (A) and modern calculations (C) (in units of minutes) for 24 solar terms (T), i.e., T A and T C. The horizontal axis represents years and the vertical axis represents the difference between the times in units of minutes. The number of data is small during the period after 937 and there are no data in 942for the reasonsmentioned above. In the analysis of solar terms, the largest difference was approximately.6 min on October 8, 928 and the root mean square (RMS) deviation (i.e., RMS of the differences between the times in the almanacs and modern calculations) was.46 min. Moreover, we found that the times of the autumnal equinox in 97 (September 24) and the spring equinox in 927 (March 2) were very close to midnight. The times of the former and latter equinoxes were h min 3.2 s and 23 h 59 min 6.7 s, respectively. However, in case of the year 97, there is no change in the day of the Malbok (Late

4 94 Lee Figure 2. Comparison of the times of 24 solar terms (T) between the almanacs (A) and modern calculations (C). The horizontal axis represents years and the vertical axis represents the differences (T A T C ) in units of minutes. Hot Day), which is determined based on the day of the autumnal equinox (refer to Mihn et al. 24), even if the day was September 23. For reference, the values of T were +9.6 s and s in 97 and 927, respectively Rising, Transit, and Setting As shown in Table, the intervals of sunrise and sunset times listed in the almanacs vary with respect to the period. These times are listed on the days of 24 solar terms from 93 to 936, every day from 937 to 942 including the transit time of the Sun, and approximately ten days afterwards for eight cities (sixteen cities since 943) but without the transit time. In Figure 3, we present the difference between the almanacs and modern calculations in terms of the rising (r) and setting (s) times of the Sun (S) in units of minutes. For instance, S A r S C r indicates the difference between the sunrise times in the almanacs and modern calculations. The horizontal axis represents years and the vertical axes represent S A r S C r and S A s S C s in the upper and lower panels, respectively. Even though we do not present the transit time of the Sun, its trend is considerably similar to the rising or setting time in the same period. The RMS deviation values for the times of the rising, transit, and setting of the Sun are.3,.28, and.32 min, respectively; these values are slightly smaller than the times in 24 solar terms. In addition, there are no times with differences larger than Table 3 Summary of the reference locations of time data Period Reference location Observatory of the Japanese Government-General of Korea Seoul Observatory of the Japanese Government-General of Korea Meteorological Observatory of the Japanese Government-General of Korea Figure 3. Comparison of the times of rising (r) and setting (s) of the Sun (S) between the almanacs (A) and modern calculations (C). The horizontal axis represents years and the vertical axes represent the differences in units of minutes, S A r S C r (upper panel) and S A s S C s (lower panel). min. Thetimesofmoonriseandmoonsetarelistedonalternate days in the almanacs of 95 to 936. Moonrise time is for the period between new Moon and full Moon days and moonset time is between full Moon and next new Moon days. However, these times were recorded every day in the almanacs from 937 to 945. Different from the times of sunrise and sunset, there are a few typographical errors in moonrise and moonset times. Table 4 lists the dates for which the difference between the moonrise times in the almanacs and modern calculations is larger than 2 min. Table 5 lists these data with respect to moonset times. We consider that the times with differences larger than 5 min are typographical errors in the almanacs. For instance, the moonrise time on March 5, 933, is listed as h 33 min a.m. not p.m.; this is clearly a typographical error (see Table 4). In addition, the errors are concentrated in 95 and 96, which were first two years beginning to support moonrise and moonset times (refer to Tables 4 and 5). Adopting the results of modern calculations for the times with differences larger than 5 min, the RMS deviation values are.48 min for both types of time data. In Figure 4, we present the differences between the rising and setting times of the Moon (M) in the almanacs and modern calculations, Mr A MC r (upper panel) and Ms A Ms C (lower panel). One of the most distinctive features is that the differences in the almanacs up to 932 are relatively large compared with subsequent almanacs. For this reason, we think that further studies are needed.

5 Time Data in Korean Astronomical Almanacs of Table 4 Dates on which the differences between the moonrise times in almanacs and modern calculations is larger than 2 min Date MR A MR C MR A MR C Year Month day h:min h:min min 95 Mar 3 2:22 2: Jun 28 2:5 2: Jul 28 2:53 2: Oct 24 8:8 8: Jan 28 :2 : Feb 5:24 5: Feb 2 2:28 2: Feb 27 2:8 2: May 3 3:47 3: Jun 7 2:3 2: Aug 3 9:4 9: Dec 7:4 7: Dec 4 :34 2: Dec 4 :2 : Mar 5 :33 22: Apr 9 :39 :29.8 Figure 4. Comparison of the times of rising (r) and setting (s) of the Moon (M) between the almanacs (A) and modern calculations (C). The horizontal axis represents years and the vertical axes represent the differences in units of minutes, M A r M C r (upper panel) and M A s M C s (lower panel) Phases of the Moon The times of the phases of the Moon, i.e., new Moon (NM), first quarter Moon (FQ), full Moon (FM), and last quarter Moon (LQ), were recorded during the entire period considered in this study. Because the first day in a lunar month is a new Moon day, its time is very important in Korea, where the conventional lunisolar calendar is still used. According to this study, the new Moon time closest to midnight was 23 h 58 min on December 27, 93. In addition, the new Moon time of 2 h 5 min on May 4, 939, is a typographical error for h 5 min. With regard to first quarter Moon, the time on December 3, 96, is omitted in the almanac of that year and the time of 2 h 39 min on April 9, 99, is a typographical error for 7 h 39 min. Finally, p.m. is a typographical error (instead of a.m. ) in the last quarter Moon on June 7, 94 (i.e., the time is not 2 h 45 min but h 45 min). After correcting these errors, we obtained the time differences between the almanacs and modern calculations for the phases of the Moon (P), which are shown in Figure 5. The horizontal axis represents years and the vertical axes represent the differences for new Moon (PNM A PC NM ), first quarter Moon (PFQ A PC FQ ), full Moon (PA FM PC FM ), and last quarter Moon (PLQ A PC LQ ). The RMS values of these differences are.36,.4,.38 and.35 min, respectively Eclipses Sixteen solar eclipses are recorded in the almanacs from 93 to 945, and all eclipses are partial. The times of Table 5 Dates on which the differences between the moonset times in almanacs and modern calculations is larger than 2 min Date MS A MS C MS A MS C Year Month day h:min h:min min 95 Jan 6 8:9 8: Apr 6 2:5 2: Jan 8 6: 6: Feb 8 23:8 23: May 6 3:37 3: Sep 3 9:36 9: Oct 8 2:54 2: Nov 6 :4 : Nov 26 7:54 7:48 6. the solar eclipses are listed for three stages, i.e., Chohu, Bokwon, and Siksim. From the almanac of 937, the times are tabulated for several cities including Incheon. In modern terminology, each stage is the first and last external contacts of the penumbra (P and P4) and greatest eclipse (GE ). Table 6 lists the solar eclipse times in the almanacs and modern calculations and the differences between them. Column shows the date, columns 2, 3, 4, and 5 are the times for P, GE, P4, and the penumbral magnitude (P mag ) from the almanacs, respectively, and columns 6, 7, 8, and 9 provide these values obtained from the modern calculations for a given location (refer to Table 3). Columns,, 2, and 3 are differences between the values in the almanacs and modern calculations. The accuracy in solar eclipse times and magnitude are less than min and. mag on average, respectively. In this sense, the penumbral magnitude of.8 on December 3, 937, seems to be a typographical error for.2 mag. In addition, Yumi, a Japanese scholar, observed the solar eclipse that occurred on September 2, 94 (refer to Lee et al. 2b). In Figure 6, we present the diagram

6 96 Lee Figure 5. Comparison of the times of the phases (P) of the Moon between the almanacs (A) and modern calculations (C). The horizontal axis represents years and the vertical axes represent the differences in in units of minutes, P A NM P C NM (bottom left), P A FM P C FM (top left), P A FQ P C FQ (bottom right), and P A LQ P C LQ (top right). Figure 6. Diagram of the solar eclipse that occurred on September 2, 94. The horizontal and vertical axes represent the longitude and latitude, respectively. of the solar eclipse that occurred on this day using the value of T as 5 s (see also Park 999). As seen in the figure, this solar eclipse was also visible in Japan. According to the Japanese almanac of 94, the penumbral magnitude was estimated as.59 in Tokyo. Thirty-six lunar eclipses were recorded in the almanacs, including one event on May 4, 938, which was not visible in Incheon. The lunar eclipse times are listed for the following five stages: Chohu, Sikgi, Saenggwang, and Bokwon including Siksim. These stages represent the first external contact (U), first internal contact (U2), last internal contact (U3), and last external contact (U4) of the umbra and greatest eclipse (GE ). It should be noted that Chohu and Bokwon in lunar eclipse time are the contact times of the umbra not the penumbra, unlike in a solar eclipse. Table 7 presents the lunar eclipse times recorded in the almanacs for 35 events and those obtained from modern calculations. Column lists the date, and columns 2, 3, 4, 5, 6, and 7 list the times for U, U2, GE, U3, and U4 and the umbral magnitude (U mag ) from the almanacs, respectively. In columns 3, 4, 5, and 6, we add 24 to the times for the stages that occurred after midnight. In case of a total lunar eclipse, the umbral magnitude is not given but recorded as a total eclipse. Hence, we indicate a total eclipse with symbol T in column 7. Columns 8 and 9 provide the moonrise and moonset times obtained from our calculations. Columns,, 2, 3, 4, and 5 show the differences between the values in almanacs and those obtained from modern calculations. We do not present the eclipse times and magnitude obtained from our calculations since they can be found on the NASA website, in which times are given in units of TT. Because the circumference of a lunar eclipse event is the same over all parts of the Earth if the Moon is visible, times in units of Korean Standard Time can be easily obtained by adding 9 h to TT and correcting the value of T. As mentioned in the work of Lee et al. (26), the difference between our calculation and NASA is approximately 9 s on average; this is presumably due to the adoption of different ephemeris. Among the lunar eclipses given in Table 7, the longest duration of totality is 98 min on August 5, 924. However, all eclipse stages were unobservable in Korea owing to moonset. However, another lunar eclipse that occurred in the same year (i.e., February

7 Time Data in Korean Astronomical Almanacs of Figure 7. Areas of visibility for the lunar eclipse that occurred on October 27, 92, at different stages. The horizontal and vertical axes represent the longitude and latitude, respectively. 2, 924) was observable at all stages of the eclipse and its duration of totality was 97 min. Figure 7 shows the lunar eclipse diagram showing the areas of visibility at different stages for the eclipse that occurred on October 27, 92 using the T value of 2.6 s. The darkest, shaded, and white areas indicate that no eclipse is visible, the eclipse is visible at moonrise or moonset, and all eclipse stages are visible, respectively, and the solid red circle indicates the sub-lunar point. As seen in the figure, all stages of the eclipse were observable in Korea and Japan. The RMS deviation values of U, U2, GE, U3, and U4 are.58,.76,.35,.96, and.74 min, respectively, and U mag is.. According to our study, the maximum difference is 2.53 min in the time of the last internal contact (U3) on December 28, 97, which is therefore likely to be a typographical error. 5. SUMMARY It is known that the Korean astronomical almanacs for the yearsfrom 93to 945werepublished by Japanese scholars. Hence, the almanacs of these periods are different from conventional Korean almanacs in terms of their organization, content, calendrical methods, etc. We studied the accuracy of the time data listed in Korean almanacs by comparing the data with the results of modern calculations. We first investigated the definition of each type of time data and the reference location of observation. We found that the definition of the time data arethe sameas modern definitions except for the rising and setting times of the Moon, which were defined as the moments when the center of the Moon reached the horizon, considering atmospheric reflection and horizontal parallax. The reference location of the time data was Incheon except for three years from 927 to 929, in which it was Seoul. The time zone was 35 E (i.e., UT + 9 h) throughout the period. We classified twelve kinds of time data into the following four groups: solar terms, rising, transit, and setting, phases of the Moon, and eclipse. The summary of our findings for each group is as follows: Solar terms. The times of 24 solar terms were recorded in the almanacs until 936, while those of only four solar terms (two solstices and equinoxes) were recorded subsequently, except in 942. Interesting facts are that the times of solar terms were recorded in the hour system in the Shixian calendar until 937 and in the modern system subsequently. There were no times of solar terms in the almanac of 942. Compared with modern calculations, the RMS deviation value was approximately.46 min. In addition, the times of the autumnal equinox (September 24) in 97 and of the spring equinox (March 2) in 927 were very close to midnight. The times of the former and latter equinoxes werehmin 3.2sand23h59min 6.7s, respectively. Rising, transit, and setting. The method of recording rising, transit, and setting times changed according to the period. Transit times were listed only for the Sun, for six years from 937 to 942. The RMS deviation values were approximately.3 min for sunrise and sunset times and.48 min for moonrise and moonset times. In the case of moonrise and moonset times, there were several typographical errors and errors were relatively large compared to other time data. Phases of the Moon. Different from other groups, the times of four phases of the Moon were listed during the entire period. According to our calculations, the RMS deviation values for the times of new Moon, first quarter Moon, full Moon, and last quarter Moon were almost the same at.4 min. In Korea, where

8 98 Lee the lunisolar calendar is still used, new Moon time is extremely important because the first day in the calendar is determined by this time. The new Moon time on December 27, 93, was considerably close to midnight (23 h 58 min), and the new Moon time of 2 h 5 min on May 4, 939, was a typographical error of h 5 min. Eclipse. Sixteen solar eclipse were tabulated in the almanacs. The accuracy of solar eclipse time and the penumbral magnitude were less than min and approximately. mag on average, respectively. Yumi, a Japanese scholar, observed the solar eclipse that occurred on September 2, 94, using a telescope. Thirty-six lunar eclipses, including an eclipse that was unobservable in Incheon, were recorded for the following five stages: Chohu, Sikgi, Saenggwang, Bokwon, and Siksim. However, in case of lunar eclipse time, Chohu and Bokwon were the contact times of the umbra and not the penumbra as in the case of solar eclipses. In addition, greatest eclipse times were relatively more accurate compared with the times of other stages. ACKNOWLEDGMENTS This study was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 26RA2B4887). REFERENCES Choi, G.-E. 2, Study of Korean Astronomical Almanacs for , MSc Thesis, Chungbuk National University, Cheongju Choi, G.-E., Mihn, B.-H., & Lee, Y. S. 25, Changes of the Compilation Institute of Korean Astronomical Almanacs and of Its Organization around 9, PKAS, 3, 8 Kim, J.-D. 22, A Look at the Kyeongjinnyeon Daetongryeok, Saenghwalmunmul-yeongu, 7, 69 Korea Astronomy and Space Science Institute(KASI), 26, Korean Almanac 27 (Seoul: Namsandang) Lee, E.-S. 985, Analysis of the Principle of Calendrical Method (Seoul: Jeongeumsa) Lee, K.-W. 28, A Study of Solar Eclipse Records during the Three Kingdoms Period in Korea, Journal of Korean Earth Science Society, 29, 48 Lee, K.-W., Ahn, Y. S., & Mihn, B.-H. 2a, Database Construction and Textual Analysis of Korean Astronomical Almanacs, PKAS, 26, Lee, K.-W., Ahn, Y. S., Mihn, B.-H., & Kim, B.-G. 2b, The Incheon Meteorological Observatory and Its Astronomical Activity, In Kakamura, T., Orchiston, W., and Strom, R. (eds), Proceedings of the Seventh International Conference on Oriental Astronomy, September 6, 2 (Tokyo: National Astronomical Observatory of Japan) Lee, K.-W., Ahn, Y.-S., Mihn, B.-H., & Lim, Y.-R. 2, Study on the Period of the Use of Datong-li in Korea, JASS, 27, 55 Lee, K.-W., Ahn, Y. S., & Yang, H. J. 22, Study on the System of Night Hours for Decoding Korean Astronomical Records of , AdSpR, 48, 592 Lee, K.-W., Mihn, B.-H., Ahn, Y. S., & Ahn, S.-H. 26, Analysis of the Lunar Eclipse Records from the Goryeosa, JKAS, 49, 63 Liu, B.-L., & Fiala, A. D. 992, Canon of Lunar Eclipses 5 B.C. - A.D. 3 (Richmond: Willmann-Bell Inc.) Meeus, J. 998, Astronomical Algorithms (Richmond: Willmann-Bell Inc.) Mihn, B.-H., Lee, K.-W., Ahn, Y. S., Ahn, S.-H., & Lee, Y. S. 24, Analysis of Sambok in Korea, PKAS, 29, National Astronomical Observatory of Japan (NAOJ), 23, Calendar and Ephemeris for the Year 24 (Tokyo: National Astronomical Observatory of Japan) Nautical Almanac Office (NAO), 24, The Astronomical Almanacs for the Year 25 (Washington: U.S. Government Printing Office) Park, C. 999, Canon of Solar Eclipses in East Asia: From B.C. 8 to A.D. 22 (Seoul: Seoul National University Press) Standish, E. M., Newhall, X. X., Williams, J. G., & Folkner, W. F. 997, JPL Planetary and Lunar Ephemeris (CD- ROM) (Richmond: Willmann-Bell Inc.) Urban, S. E., & Seidelmann, P. K. 23, Explanatory Supplement to the Astronomical Almanac (Mill Valley: University Science Books) Yang, H.-J., Ahn, Y.-S., & Lee, K.-W. 28, Analysis of Astronomical Almanac Data for National Standard Reference Data, PKAS, 23, 53

9 Table 6 Comparison of solar eclipse time and penumbral magnitude Date Almanac (A) Modern calculations (C) Difference (A C) Year Month Day P GE P4 P mag P GE P4 P mag P GE P4 P mag h:min h:min h:min h:min h:min h:min min min min 95 Aug 6:6 7:4.56 5:2:42.9 6: :3: Jun 9 5:56 6: :55:24.5 5:45:28. 6:39: Aug 3 8:2 8:33 8:53.6 8::4.2 8:32:36.5 8:53: Jan 4 6:25 7:3.9 6:24:35.6 7:2:43.8 7:38: Jul 6: 6:4 7:3.2 6:9:47.3 6:4:33.5 7:2: Jun 29 6:7 6:5 7:3.9 6:6:32.8 6:5:6. 7:3: May 9 6: 6:34 7:7.3 6::25.8 6:34:33. 7:7: Apr 4 8:24 8:52 9:2.7 8:24:3. 8:52:25.7 9:2: Aug 2 4:4 4:58 5:7.2 4:39:8.6 4:58:3.5 5:7: Feb 4 8:24 9:9 9: :23:29.9 9:9:9.5 9:58: Jun 9 3:57 5:6 6: : :5:39.2 6:25: Dec 3 7:37.8 5:22:4.7 7:35:2.5 7:37: Nov 22 7:23 7:26 7:29. 7:22:4.5 7:26:6.3 7:29: Sep 2 2:4 3:35 4: :3:59.5 3:34:56.7 4:52: Feb 5 8:35 6:35:7.2 7:39:39.8 8:35: Jul 2 4:39 5:32 6:22.9 4:39:2.7 5:32:2.4 6:2: RMS deviation The reference locations are Seoul for the three years from 927 to 929 and Incheon for the other years. Time Data in Korean Astronomical Almanacs of

10 Table 7 Comparison of lunar eclipse time and umbral magnitude Date Almanac (A) Modern calculations (C) Difference (A C) Year Month Day U U2 GE U3 U4 U mag moonrise moonset U U2 GE U3 U4 U mag h:min h:min h:min h:min h:min h:min h:min min min min min min 93 Mar 22 9:3 2: 2:58 2:45 22:48 T 8:37 6: Sep 5 9:53 2: 2:48 22:36 23:44 T 8:38 5: Sep 4 2:7 22:55 24: :5 5: Jan 2 7:4 8:24.4 7:38 7: Jan 8 8:39 T 7:3 7: Jul 5 4:52 T 2:22 5: Dec 28 8:38 8:46 8:55 2:27 T 7:8 7: Jul 24 2:.4 9:52 4: Jan 27 2:8 22:29 23: :58 T 7:29 6: Oct 7 6:4.94 8: 6: Aug 28 9:4 2:27.7 9:6 5: Feb 2 23:8 24:2 25: :59 T 7:57 6: Aug 5 3:3 4:3 5:2 T 9:49 5: Feb 9 5:9 6: :28 7: Aug 4 2:35 22:8.75 9:37 4: Dec 9 :52 :45 2:35 3:5 4:8 T 7:44 7: Jul 3 2:3 2:9 2:48 23:2 T 9:43 4: Nov 27 7:33 8: 8:29 9:39 T 7: 6: Oct 8 3:46 4:7 4:27.3 8:24 6: Apr 3 3:23 4:22 5:7 5:53 T 9:37 6: Sep 27 2:54 4:6 4:48 5:3 T 8:36 6: Mar 22 9:59 2:32 23:5.97 8:36 6: Sep 5 4:8 6:.98 8:5 6: Jan 3 : :43 2:24.2 8:32 7: Jul 26 9:54 2:5 22: :46 4: Jan 9 22:53 24:3 24:7 25:3 26:4 T 7:2 7: Jan 9 :28 2:58 3:9 3:2 4:5 T 8:8 7: Jul 5 :27 2:25 3: :23 5: Nov 8 7:9 8:.5 7:5 6: Nov 8 5:4 6:45 7:46 7: May :4 24: 24:43 25:55 9:8 5: Mar 3 9: : :3 6: Sep 6 2:9 2:47 3:5.6 9:4 6: Aug 6 2:59 4:28 5:58 9:55 5: Jun 25 22:37 24:4 25:5 9:43 4: RMS deviation Lee The reference locations are Seoul for the years from 927 to 929 and Incheon for the other years.