Analysis of Time Data in Korean Almanacs of 1913

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Journal of the Korean Astronomical Society https://doi.org/10.5303/JKAS.2017.50.6.191 50: 191 ∼ 200, 2017 December pISSN: 1225-4614 · eISSN: 2288-890X c 2017. The Korean Astronomical Society. All rights reserved. http://jkas.kas.org

ANALYSIS OF TIME DATA IN KOREAN ALMANACS OF 1913 – 1945 Ki-Won Lee Daegu Catholic University, Hayang-Ro 13-13, Hayang-Eup, Gyeongsan, Gyeongbuk 38430, Korea; [email protected] Received December 7, 2017; accepted December 12, 2017 Abstract: We analyze the time data recorded in Korean astronomical almanacs for the years from 1913 to 1945, which belong to the period in which Japan occupied Korea (1910–1945). 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 1937 to 1942. 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 0.5 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

1. INTRODUCTION which was introduced into Korea in 1896 (KASI 2016). Regarding the accuracy of time data, Choi (2010) inves- An astronomical almanac is a book containing the day tigated the almanacs for the period from 1864 to 1945. and hour data necessary for civil life such as sunrise and However, the study was restricted to the times of sun- sunset times and national holidays (Yang et al. 2008). rise/sunset and new Moon. In this study, we examine Because these data should be standardized in a nation, twelve kinds of time data including moonrise, moonset, historically, a government institute compiles almanacs, and solar terms. generally annually. The oldest extant almanac in Ko- The rest of this paper is organized as follows: In rea is that for the year 1580, which was compiled by Section 2, we briefly introduce the Korean almanacs of the Gwansanggam (The Royal Astronomical Bureau) 1913 to 1945 in terms of organization and content, fo- of the Joseon dynasty (A.D. 1392–1910) (Kim 2002; Lee cusing on the kinds of time data and their definition. et al. 2010). During the period of the Japanese occupa- We describe the modern calculations used for the analy- tion of Korea (i.e., 1910–1945), astronomical almanacs sis of the time data in Section 3 and compare the results for Korea were published by Japanese scholars. Cur- with the data tabulated in the almanacs in Section 4. rently, the Korea Astronomy and Space Science Insti- Finally, we summarize our findings in Section 5. tute (hereafter, KASI) publishes almanacs. We analyze the Korean astronomical almanacs for 2. KOREAN ASTRONOMICAL ALMANACS the period from 1913 to 1945, focusing on the accuracy 2.1. Organization of time data. Even though Japan occupied Korea since 1910, it is known that Japanese scholars compiled Ko- Even though Japan occupied Korea since 1910, it is rean almanacs from 1913 to 1945 (Choi et al. 2015). known that the almanacs for 1911 and 1912 were com- The almanacs of these periods are different from con- piled by Korean astronomers, primarily by Lee Don- ventional Korean almanacs in terms of organization and Su (Choi et al. 2015). Figure 1 shows the first pages content (Lee et al. 2011a) and presumably calendrical of the Korean astronomical almanacs for 1912 (left) methods and the utilized ephemeris. However, the dates and 1913 (right). As shown in the figure, appar- in the almanacs are referred to the Gregorian calendar, ent changes are that the Japanese reign-style, i.e., Daejeong, and the compilation institute, i.e., the Ob- Corresponding author: K.-W. Lee servatory of the Japanese Government-General of Ko- 191 192 Lee

and hours of 24 solar terms are the moments when the Sun passes a multiple of 15◦ in the ecliptic starting from the spring equinox. For example, the date and hour of the winter solstice are the times when the ecliptic lon- ◦ gitude of the Sun (λ⊙) is 270 . 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 ◦ ′ zenith distance of the Sun (z⊙) is 90 50 considering the apparent angular radius of the Sun (16′) 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$) is 90◦ 34′ + π, considering an atmospheric reflection of 34′ and the horizontal parallax (π) defined using the Earth’s radius (R) and the Figure 1. First pages of the Korean astronomical almanacs distance to the Moon (r)(i.e., π ≡ sin−1(R/r)). This for 1912 (left) and 1913 (right) (source: KASI). is different from the modern definition, i.e., when the “upper part” of the Moon apparently reaches the hori- rea (hereafter, OJGK) located in Incheon, begin to ap- zon (refer to Urban & Seidelmann 2013). Fourth, the pear in the far right column. From the astronomical times of the phases of the Moon are the moments when point of view, the standard meridian (i.e., 135◦E) and the angular distances between the Sun and Moon in ◦ ◦ the reference location (i.e., Incheon) of time data are the ecliptic (|λ⊙ − λ$|) are 0 (new Moon), 90 (first ◦ ◦ clearly described under the title of Seolmyeong (Ex- quarter Moon), 180 (full Moon), and 270 (last quar- planation) since the almanacs of 1913 (see also Choi ter Moon), even though there is no explanation in the 2010). Moreover, the organization and content of the almanacs. Fifth, the Moon age is the number of days Korean almanacs were significantly changed once again elapsed since the new Moon day (hence, it is an inte- from 1937, along with the change in the title from the ger); however, it is the number of days elapsed since the Yakryeok to the Joseonminryeok. In addition, the com- new Moon time (hence, it is a real number) nowadays. pilation institute was renamed as the Meteorological Therefore, we excluded the time data of the Moon age Observatory of the Japanese Government-General of because it is naturally determined if a new Moon day Korea (hereafter, MOJGK) from 1939. Further, there is obtained. Lastly, the times of three and five stages were minor changes from the almanacs of 1943. are tabulated for solar and lunar eclipses, respectively. In a solar eclipse, Chohu and Bokwon are the first and 2.2. Contents last external contact times of the penumbra (P1 and P4), respectively. On the contrary, in a lunar eclipse, In addition to changes in organization, there were mod- Chohu, Sikgi, Saenggwang, and Bokwon represent the ifications in content, particularly in the appendices. For first external, first internal, last internal, and last ex- instance, the comparison tables for the chronicle, mean ternal contact times of the umbra (U1, U2, U3, and temperatures for several cities, the times of high and U4), respectively (refer to Section 4). In both eclipses, low tides, and so forth were supplemented or eliminated. Siksim is the time of greatest eclipse. In Table 2, we One of the interesting features was that the agricultural summarize the definition of the time data used in this work to be carried out in each month were recorded study. using a Korean auxiliary particle. A notable change in terms of astronomy was the tabulation of moonrise 3.2. Modern Calculation and moonset times from 1915 and of solar transit time from 1937. For details on the changes in the organiza- We utilized the astronomical algorithms of Meeus tion and contents with respect to the period, refer to (1998) and the DE405 ephemeris of Standish et al. the works of Lee (1985), Choi (2010), and Lee et al. (1997) to calculate the time data given in Table 2, ex- (2011a). We have summarized the time data tabulated cept for the eclipse times. We used the values of ∆T , in the almanacs according to the period in Table 1. i.e., the difference between terrestrial time (TT) and universal time (UT), presented in The Astronomical Al- 3. MODERN CALCULATIONS manacs published by Nautical Almanac Office (hereafter, NAO) (NAO 2014). For reference, the values of 3.1. Definition of Time Data ∆T in 1913 and 1945 are 14.65 and 26.77 s, respec- In the almanacs, the definition of time data is not de- tively. Hence, the values of ∆T are not critical for the scribed in detail, even though the standard time and period considered in this study because they are less reference location are clearly mentioned. Therefore, we than 0.5 min. With regard to the calculations of eclipse inferred the definition from the Japanese almanacs pub- times at different stages, we referred to the work of Lee lished at approximately the same time. First, the dates (2008), in which Besselian elements were utilized, for Time Data in Korean Astronomical Almanacs of 1913 – 1945 193

Table 1 Summary of time data presented in Korean astronomical almanacs for the period from 1913 to 1945

Time data Periods Solar term 1913–1936: 24 solar terms 1937–1941: 4 solar terms (two solstices and equinoxes) 1942: no solar terms 1943–1945: 4 solar terms (two solstices and equinoxes) Sunrise/sunset 1913–1936: on the days of 24 solar terms 1937–1942: on every day including transit time 1943–1945: on about ten days for several cities but without transit time Moonrise/moonset 1915–1936: in turns 1937–1945: on every day Phase of the Moon 1913–1945: new Moon, first quarter Moon, full Moon, last quarter Moon Moon age 1937–1945: on every day Eclipse 1913–1945: solar and lunar eclipses solar eclipses and the work of Liu & Fiala (1992) for manac. lunar eclipses (see also Lee et al. 2016). 4. ANALYSIS OF TIME DATA According to the records of the almanacs, there was 4.1. Solar Terms no change in the standard time (i.e., UT + 9 h). On the contrary, the reference location of time data changed The times of 24 solar terms are listed based on the hour four times, as summarized in Table 3 (see also Choi system in the Chinese Shixian calendar until 1937 and 2010). As mentioned earlier, OJGK was renamed to on the modern system (i.e., a day is 24 hours) subse- MOJGK; hence the reference locations were practically quently. Two hours systems are used in the Shixian changed two times. As the longitude and latitude of the calendar. In the first, a day is divided into 96 Gak and reference locations, we used the values of 126◦ 37′ 39′′ 1 Gak is divided into 15 Bun (hence, 1 Bun is 1 minute E and 37◦ 28′ 29′′ N (listed in the almanac for 1937) in the modern hour system). In the second system, a for OJGK and MOJGK, and 126◦ 58′ E and 37◦ 34′′ N day is divided into 12 Sijin and 1 Sijin is divided into (referring to the almanac for 1953) for Seoul. Cho and Jeong (refer to Lee et al. 2012). In addition, the hours are listed for only four solar terms (i.e., two Except for the times of moonrise and moonset, we solstices and equinoxes) in the almanacs after 1937, ex- reproduced the time data recorded in the Korean al- cept for 1942, even though dates are provided for all manac for 2017 compiled by KASI (KASI 2016) to ver- solar terms. Interestingly, the solar terms are omitted ify our calculations. We reproduced the moonrise and in the almanac for 1942. moonset times recorded in the Japanese almanac for Using modern calculations, we calculate the times 2014 compiled by the National Astronomical Observa- of 24 solar terms in units of seconds and compare the tory of Japan (hereafter, NAOJ) (NAOJ 2013), which results with those of the almanacs; the hours are listed still uses the same definitions as those in this study. We in units of minutes in the almanacs. Figure 2 shows found good agreement within the units given in each al- 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 Table 2 Summary of the definition of time data axis represents years and the vertical axis represents the difference between the times in units of minutes. The Time data Definition number of data is small during the period after 1937 ◦ ◦ ◦ ◦ and there are no data in 1942 for the reasons mentioned Solar terms λ⊙ = 0 , 15 , · · ·, 330 , 345 ◦ ′ above. Sunrise z⊙ = 90 50 in the rising Solar transit passage of Sun across a meridian In the analysis of solar terms, the largest differ- ◦ ′ Sunset z⊙ = 90 50 in the setting ence was approximately 1.06 min on October 8, 1928 Moonrise z$ = 90◦ 34′ + π in the rising and the root mean square (RMS) deviation (i.e., RMS Moonset z$ = 90◦ 34′ + π in the setting of the differences between the times in the almanacs ◦ New Moon |λ⊙ − λ$| = 0 and modern calculations) was 0.46 min. Moreover, we ◦ First quarter Moon |λ⊙ − λ$| = 90 found that the times of the autumnal equinox in 1917 λ λ ◦ Full Moon | ⊙ − $| = 180 (September 24) and the spring equinox in 1927 (March λ λ ◦ Last quarter Moon | ⊙ − $| = 270 21) were very close to midnight. The times of the for- Greatest eclipse midpoint of the eclipse mer and latter equinoxes were 0 h 0 min 13.2 s and 23 h Eclipse begins first contact of penumbra/umbra 59 min 6.7 s, respectively. However, in case of the year Eclipse ends last contact of penumbra/umbra 1917, there is no change in the day of the Malbok (Late 194 Lee

1 1

0.5 0.5

0 0

-0.5 -0.5

-1 -1 1 1915 1920 1925 1930 1935 1940 1945

0.5 Figure 2. Comparison of the times of 24 solar terms (T ) be- A C tween the almanacs ( ) and modern calculations ( ). The 0 horizontal axis represents years and the vertical axis represents the diﬀerences (T A – T C ) in units of minutes. -0.5

Hot Day), which is determined based on the day of the -1 autumnal equinox (refer to Mihn et al. 2014), even if 1915 1920 1925 1930 1935 1940 1945 the day was September 23. For reference, the values of ∆T were +19.06 s and +24.49 s in 1917 and 1927, Figure 3. Comparison of the times of rising (r) and setting respectively. (s) of the Sun (S) between the almanacs (A) and modern calculations (C). The horizontal axis represents years and 4.2. Rising, Transit, and Setting the vertical axes represent the differences in units of minutes, A C A C As shown in Table 1, the intervals of sunrise and sun- Sr − Sr (upper panel) and Ss − Ss (lower panel). set times listed in the almanacs vary with respect to the period. These times are listed on the days of 24 solar terms from 1913 to 1936, every day from 1937 to 1942 including the transit time of the Sun, and ap- min. proximately ten days afterwards for eight cities (sixteen cities since 1943) but without the transit time. In Fig- The times of moonrise and moonset are listed on al- ure 3, we present the difference between the almanacs ternate days in the almanacs of 1915 to 1936. Moonrise and modern calculations in terms of the rising (r) and time is for the period between new Moon and full Moon setting (s) times of the Sun (S) in units of minutes. days and moonset time is between full Moon and next A C For instance, Sr − Sr indicates the difference between new Moon days. However, these times were recorded the sunrise times in the almanacs and modern calcu- every day in the almanacs from 1937 to 1945. Different lations. The horizontal axis represents years and the from the times of sunrise and sunset, there are a few A C A C vertical axes represent Sr − Sr and Ss − Ss in the typographical errors in moonrise and moonset times. upper and lower panels, respectively. Even though we Table 4 lists the dates for which the difference between do not present the transit time of the Sun, its trend the moonrise times in the almanacs and modern calcu- is considerably similar to the rising or setting time in lations is larger than 2 min. Table 5 lists these data the same period. The RMS deviation values for the with respect to moonset times. We consider that the times of the rising, transit, and setting of the Sun are times with differences larger than 5 min are typograph- 0.31, 0.28, and 0.32 min, respectively; these values are ical errors in the almanacs. For instance, the moonrise slightly smaller than the times in 24 solar terms. In ad- time on March 15, 1933, is listed as 10 h 33 min a.m. dition, there are no times with differences larger than 1 not p.m.; this is clearly a typographical error (see Ta- ble 4). In addition, the errors are concentrated in 1915 and 1916, which were first two years beginning to sup- Table 3 port moonrise and moonset times (refer to Tables 4 and Summary of the reference locations of time data 5). Adopting the results of modern calculations for the Period Reference location times with differences larger than 5 min, the RMS deviation values are 0.48 min for both types of time data. 1913–1926 Observatory of the Japanese In Figure 4, we present the differences between the ris- Government-General of Korea ing and setting times of the Moon (M) in the almanacs A C 1927–1929 Seoul and modern calculations, Mr − Mr (upper panel) and A C 1930–1939 Observatory of the Japanese Ms − Ms (lower panel). One of the most distinctive Government-General of Korea features is that the differences in the almanacs up to 1932 are relatively large compared with subsequent al- 1940–1945 Meteorological Observatory of the Japanese manacs. For this reason, we think that further studies Government-General of Korea are needed. Time Data in Korean Astronomical Almanacs of 1913 – 1945 195

Table 4 2 Dates on which the diﬀerences between the moonrise times in almanacs and modern calculations is larger than 2 min 1 A C A C Date MR MR MR − MR Year Month day h:min h:min min 0 1915 Mar 03 20:22 20:20 2.28 − -1 1915 Jun 28 21:15 21:17 2.07 1915 Jul 28 20:53 20:55 −2.48 1915 Oct 24 18:08 18:05 3.44 -2 1916 Jan 28 01:02 00:59 3.23 2 1916 Feb 01 05:24 05:35 −11.39 1916 Feb 21 20:28 20:39 −10.61 1 1916 Feb 27 02:18 02:20 −2.33 1916 May 30 03:47 03:43 3.93 1916 Jun 17 21:31 21:33 −2.08 0 1916 Aug 13 19:14 19:16 −2.06 1916 Dec 10 17:41 17:43 −2.22 -1 1922 Dec 14 01:34 02:33 −59.29 1930 Dec 14 01:21 01:16 5.01

-2 1933 Mar 15 10:33 22:33 −719.77 1915 1920 1925 1930 1935 1940 1945 1945 Apr 19 11:39 11:29 10.08

Table 5 Figure 4. Comparison of the times of rising (r) and setting Dates on which the differences between the moonset times (s) of the Moon (M) between the almanacs (A) and modern in almanacs and modern calculations is larger than 2 min calculations (C). The horizontal axis represents years and the vertical axes represent the differences in units of minutes, A C A C A C A C Date MS MS MS − MS Mr − Mr (upper panel) and Ms − Ms (lower panel). Year Month day h:min h:min min 1915 Jan 16 18:19 18:17 2.23 4.3. Phases of the Moon 1915 Apr 16 20:50 21:04 −14.05 The times of the phases of the Moon, i.e., new Moon 1916 Jan 18 06:11 06:17 −5.61 (NM), first quarter Moon (FQ), full Moon (FM), and 1916 Feb 08 23:18 23:16 2.01 last quarter Moon (LQ), were recorded during the en- 1916 May 16 03:37 03:52 −14.61 tire period considered in this study. Because the first 1916 Sep 30 19:36 19:33 3.24 1916 Oct 08 02:54 02:52 2.17 day in a lunar month is a new Moon day, its time is 1916 Nov 06 01:41 01:51 −10.33 very important in Korea, where the conventional lu- 1916 Nov 26 17:54 17:48 6.01 nisolar calendar is still used. According to this study, the new Moon time closest to midnight was 23 h 58 min on December 27, 1913. In addition, the new Moon time the solar eclipses are listed for three stages, i.e., Chohu, of 12 h 15 min on May 4, 1939, is a typographical error Bokwon, and Siksim. From the almanac of 1937, the for 00 h 15 min. With regard to first quarter Moon, the times are tabulated for several cities including Incheon. time on December 31, 1916, is omitted in the almanac In modern terminology, each stage is the first and last of that year and the time of 21 h 39 min on April 9, external contacts of the penumbra (P1 and P4) and 1919, is a typographical error for 7 h 39 min. Finally, greatest eclipse (GE⊙). Table 6 lists the solar eclipse “p.m.” is a typographical error (instead of “a.m.”) in times in the almanacs and modern calculations and the the last quarter Moon on June 17, 1941 (i.e., the time differences between them. Column 1 shows the date, is not 12 h 45 min but 0 h 45 min). After correcting columns 2, 3, 4, and 5 are the times for P1, GE⊙, these errors, we obtained the time differences between P4, and the penumbral magnitude (Pmag) from the al- the almanacs and modern calculations for the phases of manacs, respectively, and columns 6, 7, 8, and 9 provide the Moon (P ), which are shown in Figure 5. The hori- these values obtained from the modern calculations for zontal axis represents years and the vertical axes repre- a given location (refer to Table 3). Columns 10, 11, A − C sent the differences for new Moon (PNM PNM ), first 12, and 13 are differences between the values in the A − C A − C quarter Moon (PF Q PF Q), full Moon (PF M PF M ), almanacs and modern calculations. The accuracy in A − C and last quarter Moon (PLQ PLQ). The RMS values solar eclipse times and magnitude are less than 1 min of these differences are 0.36, 0.41, 0.38 and 0.35 min, and 0.01 mag on average, respectively. In this sense, respectively. the penumbral magnitude of 0.08 on December 3, 1937, seems to be a typographical error for 0.002 mag. In 4.4. Eclipses addition, Yumi, a Japanese scholar, observed the solar Sixteen solar eclipses are recorded in the almanacs from eclipse that occurred on September 21, 1941 (refer to 1913 to 1945, and all eclipses are partial. The times of Lee et al. 2011b). In Figure 6, we present the diagram 196 Lee

1 1

0 0

-1 -1

1 1

0 0

-1 -1

1915 1920 1925 1930 1935 1940 1945 1915 1920 1925 1930 1935 1940 1945

Figure 5. Comparison of the times of the phases (P ) of the Moon between the almanacs (A) and modern calculations (C). A C The horizontal axis represents years and the vertical axes represent the diﬀerences in in units of minutes, PNM − PNM A C A C A C (bottom left), PFM − PFM (top left), PF Q − PF Q (bottom right), and PLQ − PLQ (top right).

(GE$). It should be noted that Chohu and Bokwon in lunar eclipse time are the contact times of the umbra not the penumbra, unlike in a solar eclipse. Table 7 presents the lunar eclipse times recorded in the almanacs for 35 events and those obtained from modern calculations. Column 1 lists the date, and columns 2, 3, 4, 5, 6, and 7 list the times for U1, U2, GE$, U3, and U4 and the umbral magnitude (Umag) 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 10, 11, 12, 13, 14, and 15 show the differences between the values in almanacs and those obtained from modern calculations. We do not present Figure 6. Diagram of the solar eclipse that occurred on September 21, 1941. The horizontal and vertical axes rep- the eclipse times and magnitude obtained from our cal- resent the longitude and latitude, respectively. culations since they can be found on the NASA web- site,1 in which times are given in units of TT. Because the circumference of a lunar eclipse event is the same of the solar eclipse that occurred on this day using the over all parts of the Earth if the Moon is visible, times value of ∆T as 15 s (see also Park 1999). As seen in in units of Korean Standard Time can be easily ob- the figure, this solar eclipse was also visible in Japan. tained by adding 9 h to TT and correcting the value According to the Japanese almanac of 1941, the penum- of ∆T . As mentioned in the work of Lee et al. (2016), bral magnitude was estimated as 0.59 in Tokyo. the difference between our calculation and NASA is approximately 9 s on average; this is presumably due to Thirty-six lunar eclipses were recorded in the al- the adoption of different ephemeris. manacs, including one event on May 14, 1938, which Among the lunar eclipses given in Table 7, the was not visible in Incheon. The lunar eclipse times longest duration of totality is 98 min on August 15, are listed for the following five stages: Chohu, Sikgi, 1924. However, all eclipse stages were unobservable Saenggwang, and Bokwon including Siksim. These in Korea owing to moonset. However, another lunar stages represent the first external contact (U1), first in- eclipse that occurred in the same year (i.e., February ternal contact (U2), last internal contact (U3), and last external contact (U4) of the umbra and greatest eclipse 1https://eclipse.gsfc.nasa.gov/lunar.html Time Data in Korean Astronomical Almanacs of 1913 – 1945 197

Figure 7. Areas of visibility for the lunar eclipse that occurred on October 27, 1920, at diﬀerent stages. The horizontal and vertical axes represent the longitude and latitude, respectively.

20, 1924) was observable at all stages of the eclipse and 135◦E (i.e., UT + 9 h) throughout the period. We clas- its duration of totality was 97 min. Figure 7 shows the sified twelve kinds of time data into the following four lunar eclipse diagram showing the areas of visibility at groups: solar terms, rising, transit, and setting, phases different stages for the eclipse that occurred on October of the Moon, and eclipse. The summary of our findings 27, 1920 using the ∆T value of 21.16 s. The darkest, for each group is as follows: shaded, and white areas indicate that no eclipse is vis- Solar terms. The times of 24 solar terms were ible, the eclipse is visible at moonrise or moonset, and recorded in the almanacs until 1936, while those of all eclipse stages are visible, respectively, and the solid only four solar terms (two solstices and equinoxes) were red circle indicates the sub-lunar point. As seen in the recorded subsequently, except in 1942. Interesting facts figure, all stages of the eclipse were observable in Ko- are that the times of solar terms were recorded in the rea and Japan. The RMS deviation values of U1, U2, hour system in the Shixian calendar until 1937 and in GE$, U3, and U4 are 0.58, 0.76, 0.35, 0.96, and 0.74 the modern system subsequently. There were no times min, respectively, and Umag is 0.01. According to our of solar terms in the almanac of 1942. Compared with study, the maximum difference is 2.53 min in the time modern calculations, the RMS deviation value was ap- of the last internal contact (U3) on December 28, 1917, proximately 0.46 min. In addition, the times of the which is therefore likely to be a typographical error. autumnal equinox (September 24) in 1917 and of the 5. SUMMARY spring equinox (March 21) in 1927 were very close to midnight. The times of the former and latter equinoxes It is known that the Korean astronomical almanacs for were 0 h 0 min 13.2 s and 23 h 59 min 6.7 s, respectively. the years from 1913 to 1945 were published by Japanese scholars. Hence, the almanacs of these periods are dif- Rising, transit, and setting. The method of record- ferent from conventional Korean almanacs in terms of ing rising, transit, and setting times changed according their organization, content, calendrical methods, etc. to the period. Transit times were listed only for the We studied the accuracy of the time data listed in Ko- Sun, for six years from 1937 to 1942. The RMS de- rean almanacs by comparing the data with the results viation values were approximately 0.30 min for sunrise of modern calculations. We first investigated the def- and sunset times and 0.48 min for moonrise and moon- inition of each type of time data and the reference lo- set times. In the case of moonrise and moonset times, cation of observation. We found that the definition of there were several typographical errors and errors were the time data are the same as modern definitions except relatively large compared to other time data. for the rising and setting times of the Moon, which were Phases of the Moon. Different from other groups, defined as the moments when the center of the Moon the times of four phases of the Moon were listed dur- reached the horizon, considering atmospheric reflection ing the entire period. According to our calculations, and horizontal parallax. The reference location of the the RMS deviation values for the times of new Moon, time data was Incheon except for three years from 1927 first quarter Moon, full Moon, and last quarter Moon to 1929, in which it was Seoul. The time zone was were almost the same at ∼0.40 min. In Korea, where 198 Lee the lunisolar calendar is still used, new Moon time is Lee, K.-W., Ahn, Y. S., & Mihn, B.-H. 2011a, Database extremely important because the first day in the calen- Construction and Textual Analysis of Korean Astronom- dar is determined by this time. The new Moon time on ical Almanacs, PKAS, 26, 1 December 27, 1913, was considerably close to midnight Lee, K.-W., Ahn, Y. S., Mihn, B.-H., & Kim, B.-G. 2011b, (23 h 58 min), and the new Moon time of 12 h 15 min The Incheon Meteorological Observatory and Its Astro- nomical Activity, In Kakamura, T., Orchiston, W., and on May 4, 1939, was a typographical error of 00 h 15 Strom, R. (eds), Proceedings of the Seventh International min. Conference on Oriental Astronomy, September 6–10, 2010 Eclipse. Sixteen solar eclipse were tabulated in the (Tokyo: National Astronomical Observatory of Japan) almanacs. The accuracy of solar eclipse time and the Lee, K.-W., Ahn, Y.-S., Mihn, B.-H., & Lim, Y.-R. 2010, penumbral magnitude were less than 1 min and ap- Study on the Period of the Use of Datong-li in Korea, proximately 0.01 mag on average, respectively. Yumi, JASS, 27, 55 a Japanese scholar, observed the solar eclipse that Lee, K.-W., Ahn, Y. S., & Yang, H. J. 2012, Study on the occurred on September 21, 1941, using a telescope. System of Night Hours for Decoding Korean Astronomical Thirty-six lunar eclipses, including an eclipse that was Records of 1625–1787, AdSpR, 48, 592 unobservable in Incheon, were recorded for the following Lee, K.-W., Mihn, B.-H., Ahn, Y. S., & Ahn, S.-H. 2016, five stages: Chohu, Sikgi, Saenggwang, Bokwon, and Analysis of the Lunar Eclipse Records from the Goryeosa, JKAS, 49, 163 Siksim. However, in case of lunar eclipse time, Chohu Liu, B.-L., & Fiala, A. D. 1992, Canon of Lunar Eclipses and Bokwon were the contact times of the umbra and 1500 B.C. - A.D. 3000 (Richmond: Willmann-Bell Inc.) not the penumbra as in the case of solar eclipses. In Meeus, J. 1998, Astronomical Algorithms (Richmond: addition, greatest eclipse times were relatively more ac- Willmann-Bell Inc.) curate compared with the times of other stages. Mihn, B.-H., Lee, K.-W., Ahn, Y. S., Ahn, S.-H., & Lee, Y. S. 2014, Analysis of Sambok in Korea, PKAS, 29, 1 ACKNOWLEDGMENTS National Astronomical Observatory of Japan (NAOJ), 2013, This study was supported by the National Research Calendar and Ephemeris for the Year 2014 (Tokyo: Na- Foundation of Korea (NRF) grant funded by the Ko- tional Astronomical Observatory of Japan) rea government (MSIP) (No. 2016R1A2B4010887). Nautical Almanac Office (NAO), 2014, The Astronomical Almanacs for the Year 2015 (Washington: U.S. Govern- REFERENCES ment Printing Office) Choi, G.-E. 2010, Study of Korean Astronomical Almanacs Park, C. 1999, Canon of Solar Eclipses in East Asia: From for 1864–1945, MSc Thesis, Chungbuk National Univer- B.C. 800 to A.D. 2200 (Seoul: Seoul National University sity, Cheongju Press) Choi, G.-E., Mihn, B.-H., & Lee, Y. S. 2015, Changes of the Standish, E. M., Newhall, X. X., Williams, J. G., & Folkner, Compilation Institute of Korean Astronomical Almanacs W. F. 1997, JPL Planetary and Lunar Ephemeris (CD- and of Its Organization around 1900, PKAS, 30, 801 ROM) (Richmond: Willmann-Bell Inc.) Kim, J.-D. 2002, A Look at the Kyeongjinnyeon Daeton- Urban, S. E., & Seidelmann, P. K. 2013, Explanatory Sup- gryeok, Saenghwalmunmul-yeongu, 7, 69 plement to the Astronomical Almanac (Mill Valley: Uni- Korea Astronomy and Space Science Institute (KASI), 2016, versity Science Books) Korean Almanac 2017 (Seoul: Namsandang) Yang, H.-J., Ahn, Y.-S., & Lee, K.-W. 2008, Analysis of Lee, E.-S. 1985, Analysis of the Principle of Calendrical Astronomical Almanac Data for National Standard Ref- Method (Seoul: Jeongeumsa) erence Data, PKAS, 23, 53 Lee, K.-W. 2008, A Study of Solar Eclipse Records during the Three Kingdoms Period in Korea, Journal of Korean Earth Science Society, 29, 408 Time Data in Korean Astronomical Almanacs of 1913 – 1945 199 mag 0.003 0.005 0.004 0.004 0.003 0.002 0.001 − − − − − − − ) C − P4 P 0.14 0.058 0.34 0.001 0.66 0.000 0.46 — 0.04 0.001 0.27 0.000 0.51 0.27 0.28 0.06 A − − − − − − − − − − ⊙ 0.27 0.32 0.34 0.27 0.003 0.43 0.53 0.55 0.27 0.07 0.56 0.18 − − − − − − − − P1 GE 0.05 0.29 0.35 0.34 0.52 0.43 0.40 0.38 0.32 0.015 − − − − 1 — — mag † .022 — — ) Difference ( 3.4 0.186 0.41 0.27 — 0.004 3.76.8 0.558 0.722 — — 0.01 0.53 0.11 0.002 C P4 P 29:39.6 0.001 0.32 52:20.6 0.689 0.00 0.06 21:43.7 0.187 58:02.3 0.229 0.50 25:39.4 0.663 21:15.9 0.070 17:30.7 0.025 0.69 07:16.4 0.134 30:55.7 0.194 0.45 12:49.4 0.123 0.21 53:03.8 0.061 0.33 0.39 ⊙ Table 6 P1 GE 27 to 1929 and Incheon for the other years. mag ) Modern calculations ( A RMS deviation P4 P Comparison of solar eclipse time and penumbral magnitude ⊙ h:min h:min h:min h:min h:min h:min min min min Date Almanac ( The reference locations are Seoul for the three years from 19 1937 Dec 03 — — 07:37 0.80 05:22:40.7 07:35:20.5 07:37:08.5 0 1938 Nov 22 07:23 07:26 07:29 0.00 07:22:40.5 07:26:16.3 07: 1943 Feb 05 — — 08:35 — 06:35:17.2 07:39:39.8 08:35:27.8 0.78 1941 Sep 21 12:14 13:35 14:52 0.69 12:13:59.5 13:34:56.7 14: 1944 Jul 20 14:39 15:32 16:22 0.19 14:39:02.7 15:32:20.4 16: 1934 Feb 14 08:24 09:09 09:58 0.23 08:23:29.9 09:09:19.5 09: 1936 Jun 19 13:57 15:16 16:26 0.66 13:57.17.2 15:15:39.2 16: 1931 Apr 14 08:24 08:52 09:21 0.07 08:24:31.1 08:52:25.7 09: 1933 Aug 21 14:40 14:58 15:17 0.02 14:39:18.6 14:58:31.5 15: 1929 May 09 16:00 16:34 17:07 0.13 16:00:25.8 16:34:33.1 17: 1927 Jun 29 16:07 16:50 17:31 0.19 16:06:32.8 16:50:16.1 17: 19261926 Jan Jul 14 10 16:25 06:10 17:03 06:40 — 07:13 0.19 0.12 16:24:35.6 06:09:47.3 17:02:43.8 06:40:33.5 17:38:4 07: Year Month Day1918 P1 Jun GE 09 — 05:56 06:39 0.72 04:55:24.5 05:45:28.1 06:39:1 1915 Aug 11 — 06:06 07:04 0.56 05:12:42.9 06:05.59.2 07:03:5 † 1924 Aug 30 18:12 18:33 18:53 0.60 18:11:40.2 18:32:36.5 18: 200 Lee mag .73 0.00 .33 0.00 0.35 — − ) C − 0.14 0.59 — U3 U4 U A − $ 0.25 — 0.45 — 0.28 — 0.67 0.01 0.15 — 0.32 0.01 0.10 0.65 0.46 — 0.48 0.880.11 0.18 — — 1.24 0.01 0.22 0.48 0.16 — 0.17 — 0.03 0.00 0.43 0.65 — — 0.03 — — — 0.47 0.75 0.92 — 0.29 0.17 0.51 — 0.10 2.53 0.20 0.17 1.10 – − − − − − − − − − − − − − − 24 0.57 — — — — 1.00 0.97 0.04 0.68 0.840.87 0.31 0.33 0.43 — 0.93 0.150.29 0.51 0.01 1.01 1.14 0.711.85 0.63 — — − − − − − − − − − − − 0.57 — 0.17 — 0.67 — 0.940.10 — — 0.26 — 1.49 0.01 0.21 0.50 — 0.550.830.80 — — 0.49 — 0.60 — — — 1.10 0.00 0.01 0.82 0.25 0.580.57 0.09 — 0.00 0.75 — — 0.11 — 0.11 — — 0.01 1.540.57 — 0.31 — 0.83 0.00 0.36 — — — — — 0.58 0.76 0.35 0.96 0.74 0.01 0.09 — — — — 0.01 0.64 0.06 0.67 0.06 0.56 † − − − − − − − − − − − − − − − − − − − ) Difference ( C moonrise moonset U1 U2 GE Table 7 mag 929 and Incheon for the other years. ) Modern calculations ( A U3 U4 U Comparison of lunar eclipse time and umbral magnitude $ RMS deviation h:min h:min h:min h:min h:min h:min h:min min min min min min Date Almanac ( The reference locations are Seoul for the years from 1927 to 1 1945 Jun 25 22:37 — 24:14 — 25:51 — 19:43 04:41 19411943 Sep Aug 06 16 02:19 02:59 — — 02:47 04:28 — — 03:15 05:58 0.06 — 19:14 19:55 06:19 05:54 1935 Jan 19 22:53 24:03 24:17 25:31 26:41 T 17:21 07:25 1936 Jan 09 01:28 02:58 03:09 03:21 04:51 T 18:08 07:57 19361937 Jul1938 Nov Nov 05 18 01:27 08 — 05:41 — 06:45 — 02:25 — 17:19 — — — 03:24 0.27 18:01 — 0.15 20:23 — 17:15 05:30 17:46 06:51 0.11 07:07 — — 0.10 — — 0 1939 May 03 22.28 23:40 24:11 24:43 25:55 — 19:08 05:09 0.28 1941 Mar 13 19:55 — 20.55 — 21:56 0.33 18:31 06:23 19321934 Sep1934 Jan Jul 15 31 04:18 26 01:01 — 19:54 — 06:01 — 01:43 — 21:15 — — — 02:24 22:36 0.12 0.98 0.67 18:32 18:50 19:46 07:53 06:18 04:41 19311932 Sep Mar 27 22 02:54 19:59 04:06 — 04:48 05:31 21:32 — — 23:05 T 0.97 18:36 18:36 06:30 06:17 19251925 Feb1927 Aug1928 Dec 09 Jul 04 05:09 09 — — 00:52 03 01:45 — 06:42 — 02:35 20:31 — 20:35 03:15 21:09 04:18 — — 21:48 T 22:18 23:02 0.74 0.75 T 17:44 18:28 19:37 19:43 07:51 07:37 04:55 04:50 0.06 — — — 0.52 — 0.99 0.00 1928 Nov 27 — 17:33 18:01 18:29 19:39 T 17:10 06:53 — Year Month Day U1 U2 GE 19301931 Oct Apr 08 03 03:46 03:23 — 04:22 05:07 04:07 05:53 — — 04:27 0.03 T 18:24 19:37 06:42 06:23 19131914 Sep1916 Sep1917 Jan1917 Jan 151917 Jul 04 19:53 Dec 20 21:07 21:01 08 — 21:48 05 — — 28 22:36 04:52 22:55 — 23:44 — — — — 17:40 18:38 T — — 24:33 18:46 — 18:38 18:55 0.86 18:24 — — 20:27 18:51 0.14 18:39 05:40 T — 17:38 T 05:25 17:18 T 0.23 17:30 07:39 20:22 0.39 07:26 07:38 — — 05:16 — 0.41 — — — 0.53 — 0 — — 0.67 0.01 — 0.81 — 1913 Mar 22 19:13 20:11 20:58 21:45 22:48 T 18:37 06:21 0.16 † 19181920 Jul Jan 24 27 — 21:18 22:29 — 23:11 23.54 — 24:58 — T 20:10 17:29 0.14 19:52 06:11 04:43 0.30 0. — — — — 0.91 0.01 19211923 Oct1924 Aug Feb 17 28 06:14 20 — — 23:18 24:20 — — 25:09 19:40 25.57 — 26:59 — T — 20:27 0.17 0.94 17:57 19:06 18:10 06:50 05:28 06:41 — — 0.61 — 0.44 0.01 1924 Aug 15 03:31 04:31 05:20 — — T 19:49 05:53