J. Astrophys. Astr. (2019) 40:45 © Indian Academy of Sciences https://doi.org/10.1007/s12036-019-9612-3

Analysis of Manchuria astronomical almanacs of 1933–1945

G.-E. CHOI1, K.-W. LEE2,∗ , B.-H. MIHN1,3 and Y. S. AHN1

1Korea Astronomy and Space Science Institute, Daejeon 34055, South Korea. 2Daegu Catholic University, Gyeongsan 38430, South Korea. 3Korea University of Science and Technology, Daejeon 34113, South Korea. ∗Corresponding author. E-mail: [email protected]

MS received 11 May 2019; accepted 2 October 2019

Abstract. We investigate the astronomical almanacs of the Manchukuo state, which lasted for 14 years, from 1932 to 1945. We examine their contents and analyze the accuracy of the time data by using the almanacs for the years from 1933 to 1945. We find that the calendar of the Qing dynasty in China, Shixianshu, provided the name of the almanac. In addition, the reference location of the time data was Xinjing (now known as Changchun) and the standard meridian was changed from 120◦E to 135◦E, starting with the almanac of 1937. We also find that sunrise and sunset times were recorded only on days of the 24 solar terms, for several cities, whereas moonrise and moonset times were recorded daily, but only for Xinjing. Moreover, only days were recorded (i.e., the hours are not recorded) in the almanacs of 1933 and 1934 for the 24 solar terms. To estimate the accuracy, we first extract 19 kinds of time data and classify them into four groups: rising and setting, solar term, phases of the Moon and eclipses. Then, we determine the mean absolute difference (MAD) of the time data between the almanacs and modern calculations performed using the DE405 ephemeris. Even though most of the time data are recorded in minutes, we compute the data in seconds. We find that the MAD values are 0.44, 0.42, 0.27 and 0.44 min for the time data of the four respective groups. We believe that our findings will contribute to the study of the astronomical almanacs of Korea, Japan and Taiwan, which were published during this period.

Keywords. History of astronomy—almanac—ephemeris—Manchukuo.

1. Introduction astronomical almanacs of East Asia were noticed early. Maurice Courant, a French bibliographer introduced the The astronomical almanac of a nation contains not Korean astronomical almanac of 1892 in his book, Bib- only astronomical data, such as sunrise times, but liographie Coréenne, published in 1894 (see Lee et al. also its cultural data, such as national holidays (Yang 2008). Although there have been some studies of the et al. 2008). To prevent social confusions by incon- East Asian astronomical almanacs since then (e.g., Lee sistent data, calendar data are produced and compiled 1976; Hurukawa 1988; Wang 1993), many studies have by government institutes. This situation was also true focused on the calendar rather than the almanac (Need- in the dynasties of East Asia such as China, Korea ham 1959; Nakayama 1969; Sivin 2008; Mihn et al. and Japan. One of the exclusive powers and impor- 2014; Martzloff 2016; Choi et al. 2018). tant duties of a king was to calculate calendar data Manchukuo was a Japanese puppet state for 14 years, and to inform them to the people through the dis- from 1932 to 1945, in China. Therefore, the astronom- tribution of an almanac. Today, all nations use the ical almanacs might have been compiled by Japanese Gregorian calendar days but calculate the astronom- scholars, as in Korea, which was occupied by Japan ical data of the almanac using modern astrophysical from 1910 to 1945 (Lee et al. 2011b). Because it is calculations (i.e., using the newest ephemeris and astro- known that Japan adopted Western culture from the nomical knowledge). The calendar of East Asia was Meiji restoration of 1896, the Japanese might also have the astronomical system or mathematical astronomy established the methods of calendrical calculation by reckoning both calendar days and some astronomical the end of the nineteenth century. In the Manchuria events, including the data recorded in the almanac. The almanac, however, what kind of ephemeris was used,

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Table 1. Summary of Manchuria astronomical almanacs used in this study.

No. Year Title Remark

1 1933 Shixianshu for the 2nd year of Datong NDL 2a 1934 Shixianshu for the 1st year of Kangde NLK, NDL 2b 1934 Shixianshu for the 3rd year of Datong NLK, NDL 3 1935 Shixianshu for the 2nd year of Kangde NLK, NDL 4 1936 Shixianshu for the 3rd year of Kangde NLK, NDL 5 1937 Shixianshu for the 4th year of Kangde NLK, NDL 6 1938 Shixianshu for the 5th year of Kangde NLK, NDL 7 1939 Shixianshu for the 6th year of Kangde NLK, NDL 8 1940 Shixianshu for the 7th year of Kangde NLK, NDL 9 1941 Shixianshu for the 8th year of Kangde NDL 10 1942 Shixianshu for the 9th year of Kangde NLK, NDL 11 1943 Shixianshu for the 10th year of Kangde NLK, NDL 12 1944 Shixianshu for the 11th year of Kangde NLK, NDL 13a 1945 Shixianshu for the 12th year of Kangde (Chinese) NLK 13b 1945 Shixianshu for the 12th year of Kangde (Mongolian) NDL

whether the atmospheric refraction was considered, and This paper is structured as follows. In Section 2,we so forth is not mentioned. Additionally, the contents of list the Manchuria astronomical almanacs used in this the astronomical almanac differ according to country study and examine their contents such as publisher, stan- due to political and cultural reasons. In this study, we dard meridian and reference location. In Section 3,we investigate the astronomical almanacs of Manchukuo in categorize 19 kinds of time data into four groups (i.e., terms of the contents and accuracies of time data, such rising and setting, solar term, phases of the Moon and as the sunrise, new moon and eclipse, as a series of stud- eclipses), and estimate their accuracies by comparing ies on the almanacs published by Japanese astronomers with the results of modern calculations including the in Korea, Manchukuo, Japan and Taiwan. Considering definition of each piece of time data used in the calcula- that the astronomical almanac for a particular year was tions. In both sections, we also discuss the differences published in the previous year (e.g., NAO 2017), the between Manchuria and Korean astronomical almanacs. astronomical almanacs of Manchukuo were published Finally, we summarize our findings in Section 4. for 13 years (from 1933 to 1945), which were then used in our study. Although there have been some studies on the astro- 2. Examination of the contents nomical almanacs of East Asian countries, such as Korea, China and Japan (e.g., Lee 2017), the almanacs In Table 1, we summarize the astronomical almanacs of Manchukuo have not been studied except for the of Manchukuo used in this study together with their work of Jeong (2008). That study was constrained to the geographical location. In the table, columns 1, 2 and almanacs of nine years (from 1934 to 1942) and mostly 3 are the sequential number, year and title, respec- focused on the political implications of the publication tively, of the almanacs expressed using the reign-style of the almanacs in Manchukuo. On the other hand, of Manchukuo. In the last column, we indicate where Choi (2010) studied the Korean almanacs of 1864Ð the collections are housed: NLK and NDL represent the 1945, which included the almanacs published during National Library of Korea and the National Diet Library the period of Japanese occupation of Korea, but mainly of Japan, respectively. As shown in Table 1, NDL pos- focused on the contents of the almanacs. Very recently, sesses all astronomical almanacs of Manchukuo, while Lee (2017) analyzed the Korean almanacs of 1913Ð the astronomical almanacs of the years 1933 and 1941 1945 in terms of the accuracy of their time data. For are missing in NLK. reference, it is known that Korean almanacs were com- From the examination of the contents, we first found piled by Japanese scholars starting from 1912 (i.e., from that the name of Shixianshu was used as the title the almanac of 1913) and not 1911. of the almanacs of Manchukuo. In the Qing dynasty J. Astrophys. Astr. (2019) 40:45 Page 3 of 10 45

Figure 1. The astronomical almanacs of Manchukuo for the year 1945, which were written in Chinese (left) and Mongolian (right).

(1644Ð1912) of China, the Shixianli were first made by contents of the Korean almanacs were also significantly Adam Schall, a western missionary and his colleagues, changed with the almanac of 1937 (Lee et al. 2011a). which was used from the beginning of the dynasty, Second, the two versions of the almanacs were pub- and later renamed Shixianshu. In Korea, as well as in lished for the year 1934 (2a and 2b in Table 1), as the China, the name of the calendar was used as the title reign-style of Manchukuo was changed from Datong of the almanac and Shixianshu was used during the to Kangde. According to our examination, the almanac period from 1733 until 1894 as title of the almanac in 2b was a newly complied version, not simply a change Korea (Lee 1997). In that sense, the purpose of using of the cover page, because the editing, reign-style and Shixianshu as the title of the almanac of Manchukuo page number are different from each other. However, might be to claim the legitimacy of China, at least the time data are the same in both almanacs. As far as on the surface (Jeong 2008). The Manchuria almanacs we know, two versions were also published for the year were compiled by the Zhongyangguanxiangtai (Central 1945 (13a and 13b in Table 1), which were written in Observatory in our translation) except for the almanac Chinese and Mongolian (see Figure 1). Even though of 1933, which was compiled by the Shiyebu (Industrial we could not examine the contents of the Mongolian Department in our translation). The reference location version almanac, it is expected that both almanacs are of the time data was chosen as Xinjing (nowadays identical, at least in time data. known as Changchun). According to the almanac of Third, we found that time data were recorded in min- 1937, the geographical location of Xinjing is 43◦55N utes in the almanacs except for solar eclipse times after and 125◦18E. We used those coordinates in modern 1935. In addition, the style recording time data varied calculations to estimate the accuracies of the time data over the years. For instance, only days are recorded (i.e., recorded in the almanacs. In addition, the standard the hours are not recorded) in the almanacs of 1933 and meridian was changed from 120◦E to 135◦E starting 1934 for 24 solar terms. Compared with the Korean with the almanac of 1937. It is known that the stan- almanacs at that time, an interesting point is that the dard meridian was changed to 135◦E starting with the sunrise and sunset times were recorded on the days of almanac of 1913 in Korea (Choi 2010) and that the 24 solar terms but for several cities, while moonrise 45 Page 4 of 10 J. Astrophys. Astr. (2019) 40:45

Figure 2. Explanatory notes presented in the Manchuria almanac. For the purpose of illustration, we present the explanatory notes recorded in the almanac of 1934. and moonset times were recorded daily but only for Figure 2). That is, the sunrise and sunset times were the Xinjing. moments when the ‘upper part’ of the Sun reaches the horizon in the rising and setting, respectively. However, it is unclear whether the atmospheric refraction was 3. Analysis of time data considered or not. At present, those times are defined as the moment when the zenith distance of the Sun We extracted 19 kinds of time data from the almanacs ◦  (z)is90 50 considering the apparent solar radius of and classified them into four categories: rising and set- 16 and the atmospheric refraction of 34 (NAO 2017). ting, solar terms, phases of the Moon and eclipses. To On the other hand, the moonrise and moonset times evaluate the accuracy of the time data recorded in the were defined as the moments when the ‘center’ of the almanacs, we compared them with the results of modern Moon reaches the horizon. It is also unclear whether calculations, which employed the DE405 ephemeris of the atmospheric refraction was considered in the calcu- Standish et al. (1997) and the astronomical algorithms lations of moonrise and moonset times. According to the  of Meeus (1998) for the data. We considered T ,the Japanese astronomical almanac of 1915 (private collec- difference between terrestrial time (TT) and universal tion), the moonrise and moonset times were defined as time (UT), using the values presented in the work of mentioned above, and this definition is still used in mod-  NAO (2017). However, T is not critical in this study ern Japanese astronomical almanac (e.g., NAOJ 2013). because its values are less than 1 min during the period Nowadays, the moonrise or moonset time is generally  from 1933 to 1945. For reference, the values of T are defined as the moment when the zenith distance of the +23.95 and +26.77 s in 1933 and 1945, respectively. Moon (z)is90◦34 + π (≡ sin−1(R/r)), where the Then, we converted into the local time at Xinjing by ◦ ◦ ◦ value of 34 is the atmospheric refraction and the param- applying the standard meridian of 120 or 135 Eto eter π is the horizontal parallax defined from the Earth’s UT, i.e., UT+8 or UT+9 h. Finally, we determined the radius, R, and the distance to the Moon, r.InTable2, mean absolute difference (MAD) for each time data. we summarize the definitions of the time data used in The MAD value defined in this study is this study. N 1  The sunrise and sunset times are recorded only on MAD = |T A − T C | , (1) N D D i the days of 24 solar terms for a dozen of cities includ- i=1 ing Xinjing. According to our examination, the number A C of cities increased from 11 to 12 after 1935. A remark- where N is the number of data, and TD and TD are times (T ) obtained from the almanac (A) and modern calcu- able point is that there are no solar transit times that lations (C), respectively, for the time data of kind D. were recorded in Korean almanacs during the period Although time data are given in minutes in the almanacs from 1937 to 1942 (Lee 2017). On the other hand, as mentioned above, we computed the time in seconds the moonrise and moonset times are recorded daily but in modern calculations. only for Xinjing. We extracted the rising and setting times of the Sun and Moon and compared them with 3.1 Rising and setting the results of modern calculations with and without the consideration of the atmospheric refraction. From In the almanac of 1933, the definition of rising and the comparison with modern calculations, we found setting times of the Sun and Moon is explained (see that the atmospheric refraction was considered in the J. Astrophys. Astr. (2019) 40:45 Page 5 of 10 45

Table 2. Summary of the definitions of the time data used in this study.

Category Kind of time data Definition

◦  Rising and setting Sunrise/sunset z =90 50 in the rising/setting Moonrise/moonset z =90◦ 34 +π in the rising/setting ◦ ◦ ◦ ◦ ◦ ◦ Solar term 24 solar terms λ = 315 , 330 , 345 , ···, 270 , 285 , 300 ◦ Phases of the Moon New moon |λ − λ|=0 ◦ First quarter moon |λ − λ|=90 ◦ Full moon |λ − λ|=180 ◦ Last quarter moon |λ − λ|=270 Eclipses P1/P4 First/last external contacts of penumbra U1/U4 First/last external contacts of umbra U2/U3 First/last internal contacts of umbra GE/GE Greatest solar/lunar eclipses Emag Fraction of the Sun’s diameter obscured by the Moon Umag Fraction of the Moon’s diameter immersed in the Earth’s umbral shadow

2

1

0

-1

-2

Figure 3. Comparison of rising and setting times of the Sun (SR and SS) and Moon (MRand MS) between the almanacs (A) and modern calculations (C). The horizontal axes represent years and the vertical axes represent the differences in units A − C A − C A − C A − C of minutes, TSR TSR (bottom left), TSS TSS (top left), TMR TMR (bottom right) and TMS TMS (top right). rising and setting times of the Sun and the Moon. In MAD values are 0.31 min for both sunrise and sunset this study, the time data used in the comparison are times and 0.43 and 0.46 min for moonrise and moonset those at Xinjing. Figure 3 shows the differences of ris- times, respectively. This is very similar to the values in ing and setting times of the Sun (SRand SS) and Moon Korean almanacs during this period (Lee 2017). (MR and MS) in the almanacs (A) and modern calcu- A − C A − C A − C lations (C), TSR TSR, TSS TSS, TMR TMR and 3.2 Solar term A − C TMS TMS, for the period from 1933 to 1945. In the fig- ure, the horizontal axes are the year and the vertical axes The Chinese calendar, such as Shixianli, is classified as a are the differences given in minutes. As shown in Fig- lunisolar calendar maintaining synchrony of the length ure 3, the moonrise and moonset times show relatively of a year in the lunar calendar with that of a tropical large differences in 1941. We think that further studies year (Urban & Seidelmann 2012). To retrieve the dif- are required to understand the reasons behind this. The ference in both lengths, a leap lunar month was inserted 45 Page 6 of 10 J. Astrophys. Astr. (2019) 40:45 approximately every three years. As a rule, to insert the leap month, the day of the solar term was used in Chinese calendars (refer to KASI 2017 for details). The solar terms consist of twelve minor and major terms, and these names were assigned to represent the season or weather (Urban & Seidelmann 2012). Historically, two types of solar terms have been used in China: ‘mean’ and ‘corrected’ (in literal translation). The mean solar term was obtained by dividing the length of a tropi- cal year into 24 equal intervals. On the other hand, the days of the corrected solar term were obtained by con- Figure 4. Comparison of the times of the 24 solar terms sidering the unequal motions of the Sun and Moon. In (ST) between the almanacs (A) and modern calculations (C). contemporary concepts, the days of the corrected solar The horizontal axis represents years and the vertical axis rep- A − C term were determined by dividing the ecliptic longitude resents the differences in units of minutes, TST TST . into 24 equal intervals. For instance, the day of the win- ter solstice in the corrected solar term is the moment ◦ when the ecliptic longitude of the Sun (λ) is 270 .It respectively. That is, mean new, first quarter, full and is known that the days of the corrected solar term have last quarter moons are obtained by successively adding been used in the almanac since Shixianli or Shixianshu. a quarter of the synodic month to a reference point of However, it is unknown whether or not the methods of time. Alternatively, mean phases of the Moon can be the Shixianli were used in the Manchuria almanacs to obtained by adding the synodic month to each previous calculate the times of the 24 solar terms. In this study, phase of the Moon. For instance, the mean full moon we obtained those times from modern calculations as can be obtained by adding the synodic month to the the moments defined in Table 2. previous mean full moon. On the other hand, the cor- According to our examination, only the days of the 24 rected phases of the Moon are obtained by considering solar terms are recorded (i.e., hours are not recorded) the unequal motion of the Sun and Moon for each of the in the almanacs of 1933 and 1934. We found that all mean phases of the Moon. In Chinese calendars, the day days show exact agreement with modern calculations of the corrected new moon was used as the first day of in these two years. On the other hand, we found that the lunar month before the Shixianli. In terms of modern the MAD value is 0.42 min for the dates of the 24 solar astronomy, the corrected new, first quarter, full and last terms recorded on the remaining almanacs. In addition, quarter moons are the moments when the differences of we found that there were no times of solar terms close the ecliptic longitude between the Sun and the Moon, ◦ ◦ ◦ ◦ to midnight so that the day might be changed due to the |λ − λ|,are0 ,90 , 180 and 270 respectively. In uncertainty in the calculation. Instead, we found that Figure 5, we present the differences of the times of the the time of the 6th solar term, counting from the vernal new moon (NM), first quarter moon (FQ), full moon equinox, in 1939 was the closest to midnight among (FM) and last quarter moon (LQ) between the almanac A − C A − C the 312 solar terms as 23 h 52 min. Figure 4 shows the and modern calculations, TNM TNM, TFQ TFQ, differences of the time of the 24 solar terms (ST)inthe T A − T C and T A − T C . The MAD values are A − C FM FM LQ LQ almanac and modern calculations, TST TST , in units 0.27, 0.27, 0.28 and 0.25 min for new, first quarter, full of minutes. One of the patterns in Figure 4 is that most and last quarter moons, respectively. of the differences show positive values.

3.3 Phases of the Moon 3.4 Eclipses

The four phases of the Moon were utilized in Chinese An eclipse, particularly a total solar eclipse, is one of calendars: new, first quarter, full and last quarter moons. the most dramatic astronomical events. In addition, it For each of the phases of the Moon, two kinds were used was one of most ominous phenomena in East Asia in just like for the solar term: ‘mean’ and ‘corrected’ (in terms of astrology. Hence, it was an important task of a literal translation) simply using the synodic month, i.e., king to predict the eclipse event precisely. It can be said the average period between two successive lunar phases that the history of the calendar in China was an effort to (e.g., new moons or full moons), and additionally con- predict the eclipse more accurately. The decisive reason sidering the unequal motions of the Sun and Moon, for the Qing dynasty introducing Shixianli in 1644 was J. Astrophys. Astr. (2019) 40:45 Page 7 of 10 45

Figure 5. Comparison of the times of new moon (NM), first quarter moon (FQ), full moon (FM) and last quarter moon (LQ) between the almanacs (A) and modern calculations (C). The horizontal axes represent years and the vertical axes A − C A − C A − C represent the differences in units of minutes, TNM TNM (bottom right), TFQ TFQ (bottom left), TFM TFM (top right), A − C and TLQ TLQ (top left).

Table 3. Comparison of solar eclipse times recorded in the almanacs with those obtained from modern calculations.

Calendar Almanac (A) Modern calculations (C) Difference (A − C)

Date P1 GE P4 Emag P1 GE P4 Emag P1 GE P4 Emag h:min:s h:min:s h:min:s h:min:s h:min:s h:min:s min min min

1934 Feb 14 07:41:Ð 08:19:Ð 08:59:Ð 0.16 07:41:13 08:19:19 08:59:04 0.16 −0.22 −0.32 −0.06 0.00 1936 Jun 19 12:30:04 14:03:06 15:16:05 0.81 12:43:17 14:03:31 15:16:30 0.82 −0.22 −0.42 −0.42 −0.01 1938 Nov 22 08:09:Ð 0.13 08:09:02 0.11 −0.03 0.02 1941 Sep 21 12:10:08 13:24:07 14:36:06 0.57 12:10:46 13:24:38 14:36:29 0.57 −0.63 −0.51 −0.39 0.00 1943 Feb 05 08:44:05 0.81 08:44.38 0.72 −0.54 0.09 1945 Jul 20 14:53:02 15:21:02 15:48:05 0.05 14:52:59 15:21:03 15:48:22 0.05 −0.04 −0.02 −0.28 0.00 that the calendar was more precise than previous calen- Shengguang, Fuyuan and Shishen including the umbral dars in predicting when the solar eclipse would occur magnitude (Umag). In modern terminology, each stage in the year. is the first external and internal contacts of the umbra In astronomical almanacs referring to this study, (U1 and U2), the last internal and external contacts of six solar eclipses1 are recorded for three stages, i.e., the umbra (U3 and U4), and greatest eclipse (GE), Chukui, Fuyuan and Shishen together with the eclipse respectively. We utilized the algorithms used in the magnitude (Emag). Each stage is the first and last works of Lee (2008)andLee et al. (2016) in the modern external contacts of the penumbra (P1 and P4), and calculations for solar and lunar eclipses, respectively. greatest eclipse (GE), respectively, in modern termi- In Table 3, we present the solar eclipse times recorded nology (Lee 2017). On the other hand, twelve lunar in the almanacs and obtained from modern calcula- eclipses2 are recorded in five stages, i.e., Chukui, Shigi, tions at Xinjing but in units of minutes, for clarity of the table. Including the solar eclipse of 1941 Septem-

1 ber 21 observed in Korea by Yumi, a Japanese scholar, Actually, eight solar eclipses, including two eclipses (unobservable all eclipses were recorded on the Korean astronomical at Xinjing) in 1933 and 1937. almanacs at corresponding times, i.e., visible in Korea 2Actually, 14 lunar eclipses, including two eclipses (unobservable at Xinjing) in 1939 and 1942. as well. According to our calculations, the MAD value 45 Page 8 of 10 J. Astrophys. Astr. (2019) 40:45

figure, red asterisk and black cross symbols represent the geographical regions of greatest eclipse and of Xin- jing, respectively. In Table 4, we present lunar eclipse times at Xinjing from the almanacs. The symbol ‘T’ in the 9th column of the table indicates the total lunar eclipse as recorded on the almanac. Although we do not present the lunar eclipse times obtained from modern calculations for clarity of the table, those times can also be found on the NASA eclipse website3 providing the times in units of TT. Because the circumstances of a lunar eclipse event is the same over all areas of the Earth if the Moon is visible, the lunar eclipse times at Xinjing can easily be obtained by considering the standard meridians used in Manchukuo (i.e., 120◦ or 135◦E). For reference, the average differences of the lunar eclipse times between this study and those on the NASA website are less than 10 s for all stages. According to our study, the MAD val- Figure 6. Diagram of the solar eclipse that occurred in 1936 ues for all lunar eclipse times and umbral magnitudes June 19. The asterisk and cross symbols indicate the point of are 0.49 min and 0.008 mag, respectively. In Figure 7, greatest eclipse and the location of Xinjing, respectively. we present the lunar eclipse map showing the visibility areas at five stages for the lunar eclipse that occurred in 1936 January 9, which was total. In the figure, the for the times of the three stages is 0.29 min and the entire eclipse was observed in the unshaded area while solar eclipse that occurred in 1936 June 19 had the there was no eclipse in the darkest area. In the remaining largest magnitude, 0.82, among six eclipses, In addi- shaded areas, some phases of the eclipse were visible tion, it seems that the solar eclipse magnitude of 0.81 during progress. The axis of the shadow of the Earth occurred in 1943 February 5 is a typographic error of and the geographical location of Xinjing are denoted 0.71 considering the MAD value of 0.021 in magnitude. by the red asterisk and black cross symbols, respec- In Figure 6, we present a diagram showing the eclipse tively. magnitude with respect to longitude and latitude for the eclipse of 1936 using a T value of 23.73 s. In the 3http://eclipse.gsfc.gov/lunar.html.

Table 4. Comparison of lunar eclipse times recorded in the almanacs with those obtained from modern calculations.

Calendar Almanac Difference

Date U1 U2 GE U3 U4 Umag U1 U2 GE U3 U4 Umag h:min h:min h:min h:min h:min min min min min min

1934 Jan 31 00:01 00:43 01:24 0.12 −0.83 0.60 1.10 0.008 1934 Jul 26 20:15 09:36 0.67 −0.15 0.33 0.008 1935 Jan 19 21:53 23:04 23:47 24:31 25:41 T −0.82 0.00 −0.10 0.65 0.46 1936 Jan 09 00:28 01:58 02:10 02:21 03:51 T −0.25 −0.97 0.52 0.88 0.18 1936 Jul 05 00:27 01:25 02:24 0.27 0.11 0.10 0.73 0.003 1937 Nov 18 17:19 18:01 0.15 −0.11 1.24 0.005 1938 Nov 08 05:41 06:45 T −0.21 −0.57 1939 May 03 22:28 23:40 24:11 24:43 25:55 T 0.28 −0.04 −0.22 0.48 0.16 1941 Mar 13 19:55 20:55 21:56 0.33 −0.50 −0.28 0.67 0.007 1941 Sep 06 02:19 02:47 03:15 0.06 −0.94 0.26 1.49 0.009 1943 Aug 16 02:59 04:29 0.88 −0.10 0.75 0.010 1945 Jun 25 22:37 24:14 25:51 0.87 −0.57 0.17 0.67 0.010 J. Astrophys. Astr. (2019) 40:45 Page 9 of 10 45

Figure 7. Diagram showing the areas of visibility of the lunar eclipse that occurred in 1936 January 9, at different stages. The horizontal and vertical axes represent the longitude and latitude, respectively. The red asterisk and black cross symbols represent the geographical location of greatest eclipse and of Xinjing, respectively.

4. Summary and hours in the almanacs afterwards. For the period of 1933Ð1934, the days show good agreement with We investigated the astronomical almanacs of Manchu- modern calculations. On the other hand, the MAD kuo, a puppet Japanese state that lasted for 14 years values are 0.41 min for the remaining period. According from 1932 to 1945, in terms of the contents and the to our study, there were no days of the 24 solar terms for accuracy of the time data. Considering that the annual which the day might be changed due to the uncertainty almanac for each year was published in the previous in modern calculations such as the uncertainty in the year, the Manchuria almanacs were published for 13 value of T . years from 1933 to 1945, which were used in this study. From the examination of the contents, we found that Phases of the Moon: The MAD values for the times of the name of the almanacs was Shixianshu, the name of the phases of the Moon show the minimum accuracy the calendar used in the Qing dynasty of China. The among four groups: 0.27, 0.27, 0.28 and 0.25 min for reference location of time data was Xinjing, nowadays new, first quarter, full and last quarter moons, respec- known as Changchun, and the standard meridian was tively. ◦ ◦ changed from 120 E to 135 E, the standard meridian Eclipses: Six solar and twelve lunar eclipses are of Japan, starting from the almanac of 1937. In addi- recorded in the almanacs together with the eclipse mag- tion, two kinds of the almanac were published in 1934, nitude. All these were visible in Korea, hence they as the reign-style was changed from Datong to Kangde, were recorded on Korean almanacs at that time as well. and in 1945 written in both Chinese and Mongolian, as Except for the almanacs of 1933 and 1934, the solar far as we know. We classified the time data into four eclipse times were recorded in seconds, different from groups and the summary of our finding for each group other time data such as the lunar eclipse times. The times is as follows: for the three and five stages are recorded for solar and Rising and setting: The sunrise and sunset times are lunar eclipses, and the MAD values are 0.29 and 0.49 recorded only on the days of the 24 solar terms at Xin- min, respectively. jing, while moonrise and moonset times are recorded In conclusion, we think that our findings will con- on a daily basis, but for a dozen of cities. In addition, tribute to the study of astronomical almanacs of Japan the atmospheric refraction was considered for calculat- and Taiwan and to the comparison of the astronomical ing the rising and setting times of the Sun and Moon almanacs of East Asia that were published during this compared with the results of modern calculations. In period. particular, the moonrise and moonset times show rel- atively large differences with modern calculations for 1941. The MAD values are 0.31 min for the sunrise and Acknowledgements sunset times, and 0.43 and 0.46 min for the moonrise and moonset times, respectively. The second author was supported by the National Re- Solar term: Solar terms are presented only in terms of search Foundation of Korea (NRF) grant funded by the days in the almanacs of 1933 and 1934, and both days Korea government (MSIP) (No. 2016R1A2B4010887). 45 Page 10 of 10 J. Astrophys. Astr. (2019) 40:45

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