Analysis of Manchuria astronomical almanacs of 1933–1945

J. Astrophys. Astr. (2019) 40:45 © Indian Academy of Scienceshttps://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, from1932 to 1945. We examine their contents and analyze the accuracy of the time data by using the almanacs for theyears from 1933 to 1945. We find that the calendar of the Qing dynasty in China, Shixianshu, provided the nameof the almanac. In addition, the reference location of the time data was Xinjing (now known as Changchun) andthe standard meridian was changed from 120◦E to 135◦E, starting with the almanac of 1937. We also find thatsunrise and sunset times were recorded only on days of the 24 solar terms, for several cities, whereas moonriseand moonset times were recorded daily, but only for Xinjing. Moreover, only days were recorded (i.e., thehours are not recorded) in the almanacs of 1933 and 1934 for the 24 solar terms. To estimate the accuracy, wefirst extract 19 kinds of time data and classify them into four groups: rising and setting, solar term, phases ofthe Moon and eclipses. Then, we determine the mean absolute difference (MAD) of the time data between thealmanacs and modern calculations performed using the DE405 ephemeris. Even though most of the time dataare recorded in minutes, we compute the data in seconds. We find that the MAD values are 0.44, 0.42, 0.27and 0.44 min for the time data of the four respective groups. We believe that our findings will contribute to thestudy of the astronomical almanacs of Korea, Japan and Taiwan, which were published during this period.

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

1. Introduction

The astronomical almanac of a nation contains notonly astronomical data, such as sunrise times, butalso its cultural data, such as national holidays (Yanget al. 2008). To prevent social confusions by incon-sistent data, calendar data are produced and compiledby government institutes. This situation was also truein the dynasties of East Asia such as China, Koreaand Japan. One of the exclusive powers and impor-tant duties of a king was to calculate calendar dataand to inform them to the people through the dis-tribution of an almanac. Today, all nations use theGregorian calendar days but calculate the astronom-ical data of the almanac using modern astrophysicalcalculations (i.e., using the newest ephemeris and astro-nomical knowledge). The calendar of East Asia wasthe astronomical system or mathematical astronomyreckoning both calendar days and some astronomicalevents, including the data recorded in the almanac. The

astronomical almanacs of East Asia were noticed early.Maurice Courant, a French bibliographer introduced theKorean astronomical almanac of 1892 in his book, Bib-liographie Coréenne, published in 1894 (see Lee et al.2008). Although there have been some studies of theEast Asian astronomical almanacs since then (e.g., Lee1976; Hurukawa 1988; Wang 1993), many studies havefocused on the calendar rather than the almanac (Need-ham 1959; Nakayama 1969; Sivin 2008; Mihn et al.2014; Martzloff 2016; Choi et al. 2018).

Manchukuo was a Japanese puppet state for 14 years,from 1932 to 1945, in China. Therefore, the astronom-ical almanacs might have been compiled by Japanesescholars, as in Korea, which was occupied by Japanfrom 1910 to 1945 (Lee et al. 2011b). Because it isknown that Japan adopted Western culture from theMeiji restoration of 1896, the Japanese might also haveestablished the methods of calendrical calculation bythe end of the nineteenth century. In the Manchuriaalmanac, 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 NDL2a 1934 Shixianshu for the 1st year of Kangde NLK, NDL2b 1934 Shixianshu for the 3rd year of Datong NLK, NDL3 1935 Shixianshu for the 2nd year of Kangde NLK, NDL4 1936 Shixianshu for the 3rd year of Kangde NLK, NDL5 1937 Shixianshu for the 4th year of Kangde NLK, NDL6 1938 Shixianshu for the 5th year of Kangde NLK, NDL7 1939 Shixianshu for the 6th year of Kangde NLK, NDL8 1940 Shixianshu for the 7th year of Kangde NLK, NDL9 1941 Shixianshu for the 8th year of Kangde NDL10 1942 Shixianshu for the 9th year of Kangde NLK, NDL11 1943 Shixianshu for the 10th year of Kangde NLK, NDL12 1944 Shixianshu for the 11th year of Kangde NLK, NDL13a 1945 Shixianshu for the 12th year of Kangde (Chinese) NLK13b 1945 Shixianshu for the 12th year of Kangde (Mongolian) NDL

whether the atmospheric refraction was considered, andso forth is not mentioned. Additionally, the contents ofthe astronomical almanac differ according to countrydue to political and cultural reasons. In this study, weinvestigate the astronomical almanacs of Manchukuo interms of the contents and accuracies of time data, suchas the sunrise, new moon and eclipse, as a series of stud-ies on the almanacs published by Japanese astronomersin Korea, Manchukuo, Japan and Taiwan. Consideringthat the astronomical almanac for a particular year waspublished in the previous year (e.g., NAO 2017), theastronomical almanacs of Manchukuo were publishedfor 13 years (from 1933 to 1945), which were then usedin our study.

Although there have been some studies on the astro-nomical almanacs of East Asian countries, such asKorea, China and Japan (e.g., Lee 2017), the almanacsof Manchukuo have not been studied except for thework of Jeong (2008). That study was constrained to thealmanacs of nine years (from 1934 to 1942) and mostlyfocused on the political implications of the publicationof the almanacs in Manchukuo. On the other hand,Choi (2010) studied the Korean almanacs of 1864–1945, which included the almanacs published duringthe period of Japanese occupation of Korea, but mainlyfocused on the contents of the almanacs. Very recently,Lee (2017) analyzed the Korean almanacs of 1913–1945 in terms of the accuracy of their time data. Forreference, it is known that Korean almanacs were com-piled by Japanese scholars starting from 1912 (i.e., fromthe almanac of 1913) and not 1911.

This paper is structured as follows. In Section 2, welist the Manchuria astronomical almanacs used in thisstudy and examine their contents such as publisher, stan-dard meridian and reference location. In Section 3, wecategorize 19 kinds of time data into four groups (i.e.,rising and setting, solar term, phases of the Moon andeclipses), and estimate their accuracies by comparingwith the results of modern calculations including thedefinition of each piece of time data used in the calcula-tions. In both sections, we also discuss the differencesbetween Manchuria and Korean astronomical almanacs.Finally, we summarize our findings in Section 4.

2. Examination of the contents

In Table 1, we summarize the astronomical almanacsof Manchukuo used in this study together with theirgeographical location. In the table, columns 1, 2 and3 are the sequential number, year and title, respec-tively, of the almanacs expressed using the reign-styleof Manchukuo. In the last column, we indicate wherethe collections are housed: NLK and NDL represent theNational Library of Korea and the National Diet Libraryof Japan, respectively. As shown in Table 1, NDL pos-sesses all astronomical almanacs of Manchukuo, whilethe astronomical almanacs of the years 1933 and 1941are missing in NLK.

From the examination of the contents, we first foundthat the name of Shixianshu was used as the titleof 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).

(1644–1912) of China, the Shixianli were first made byAdam Schall, a western missionary and his colleagues,which was used from the beginning of the dynasty,and later renamed Shixianshu. In Korea, as well as inChina, the name of the calendar was used as the titleof the almanac and Shixianshu was used during theperiod from 1733 until 1894 as title of the almanac inKorea (Lee 1997). In that sense, the purpose of usingShixianshu as the title of the almanac of Manchukuomight be to claim the legitimacy of China, at leaston the surface (Jeong 2008). The Manchuria almanacswere compiled by the Zhongyangguanxiangtai (CentralObservatory in our translation) except for the almanacof 1933, which was compiled by the Shiyebu (IndustrialDepartment in our translation). The reference locationof the time data was chosen as Xinjing (nowadaysknown as Changchun). According to the almanac of1937, the geographical location of Xinjing is 43◦55′Nand 125◦18′E. We used those coordinates in moderncalculations to estimate the accuracies of the time datarecorded in the almanacs. In addition, the standardmeridian was changed from 120◦E to 135◦E startingwith the almanac of 1937. It is known that the stan-dard meridian was changed to 135◦E starting with thealmanac of 1913 in Korea (Choi 2010) and that the

contents of the Korean almanacs were also significantlychanged with the almanac of 1937 (Lee et al. 2011a).

Second, the two versions of the almanacs were pub-lished for the year 1934 (2a and 2b in Table 1), as thereign-style of Manchukuo was changed from Datongto Kangde. According to our examination, the almanac2b was a newly complied version, not simply a changeof the cover page, because the editing, reign-style andpage number are different from each other. However,the time data are the same in both almanacs. As far aswe know, two versions were also published for the year1945 (13a and 13b in Table 1), which were written inChinese and Mongolian (see Figure 1). Even thoughwe could not examine the contents of the Mongolianversion almanac, it is expected that both almanacs areidentical, at least in time data.

Third, we found that time data were recorded in min-utes in the almanacs except for solar eclipse times after1935. In addition, the style recording time data variedover the years. For instance, only days are recorded (i.e.,the hours are not recorded) in the almanacs of 1933 and1934 for 24 solar terms. Compared with the Koreanalmanacs at that time, an interesting point is that thesunrise and sunset times were recorded on the days of24 solar terms but for several cities, while moonrise


Figure 2. Explanatory notes presented in the Manchuria almanac. For the purpose of illustration, we present the explanatorynotes recorded in the almanac of 1934.

and moonset times were recorded daily but only forXinjing.

3. Analysis of time data

We extracted 19 kinds of time data from the almanacsand classified them into four categories: rising and set-ting, solar terms, phases of the Moon and eclipses. Toevaluate the accuracy of the time data recorded in thealmanacs, we compared them with the results of moderncalculations, which employed the DE405 ephemeris ofStandish et al. (1997) and the astronomical algorithmsof Meeus (1998) for the data. We considered �T , thedifference between terrestrial time (TT) and universaltime (UT), using the values presented in the work ofNAO (2017). However, �T is not critical in this studybecause its values are less than 1 min during the periodfrom 1933 to 1945. For reference, the values of �T are+23.95 and +26.77 s in 1933 and 1945, respectively.Then, we converted into the local time at Xinjing byapplying the standard meridian of 120◦ or 135◦E toUT, i.e., UT+8 or UT+9 h. Finally, we determined themean absolute difference (MAD) for each time data.The MAD value defined in this study is

MAD = 1

N

N∑

i=1

|T AD − TC

D |i , (1)

where N is the number of data, and T AD and TC

D are times(T ) obtained from the almanac (A) and modern calcu-lations (C), respectively, for the time data of kind D.Although time data are given in minutes in the almanacsas mentioned above, we computed the time in secondsin modern calculations.

3.1 Rising and setting

In the almanac of 1933, the definition of rising andsetting times of the Sun and Moon is explained (see

Figure 2). That is, the sunrise and sunset times were themoments when the ‘upper part’ of the Sun reaches thehorizon in the rising and setting, respectively. However,it is unclear whether the atmospheric refraction wasconsidered or not. At present, those times are definedas the moment when the zenith distance of the Sun(z�) is 90◦50′ considering the apparent solar radius of16′ and the atmospheric refraction of 34′ (NAO 2017).On the other hand, the moonrise and moonset timeswere defined as the moments when the ‘center’ of theMoon reaches the horizon. It is also unclear whetherthe atmospheric refraction was considered in the calcu-lations of moonrise and moonset times. According to theJapanese astronomical almanac of 1915 (private collec-tion), the moonrise and moonset times were defined asmentioned above, and this definition is still used in mod-ern Japanese astronomical almanac (e.g., NAOJ 2013).Nowadays, the moonrise or moonset time is generallydefined as the moment when the zenith distance of theMoon (z�) is 90◦34′ + π (≡ sin−1(R/r)), where thevalue of 34◦ is the atmospheric refraction and the param-eter π is the horizontal parallax defined from the Earth’sradius, R, and the distance to the Moon, r . In Table 2,we summarize the definitions of the time data used inthis study.

The sunrise and sunset times are recorded only onthe days of 24 solar terms for a dozen of cities includ-ing Xinjing. According to our examination, the numberof cities increased from 11 to 12 after 1935. A remark-able point is that there are no solar transit times thatwere recorded in Korean almanacs during the periodfrom 1937 to 1942 (Lee 2017). On the other hand,the moonrise and moonset times are recorded daily butonly for Xinjing. We extracted the rising and settingtimes of the Sun and Moon and compared them withthe results of modern calculations with and withoutthe consideration of the atmospheric refraction. Fromthe comparison with modern calculations, we foundthat the atmospheric refraction was considered in the


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/settingMoonrise/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 penumbraU1/U4 First/last external contacts of umbraU2/U3 First/last internal contacts of umbraGE�/GE� Greatest solar/lunar eclipsesEmag Fraction of the Sun’s diameter obscured by the MoonUmag 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 (MR and MS) between the almanacs(A) and modern calculations (C). The horizontal axes represent years and the vertical axes represent the differences in unitsof minutes, T A

SR − TCSR (bottom left), T A

SS − TCSS (top left), T A

MR − TCMR (bottom right) and T A

MS − TCMS (top right).

rising and setting times of the Sun and the Moon. Inthis study, the time data used in the comparison arethose at Xinjing. Figure 3 shows the differences of ris-ing and setting times of the Sun (SR and SS) and Moon(MR and MS) in the almanacs (A) and modern calcu-lations (C), T A

SR − TCSR , T A

SS − TCSS , T A

MR − TCMR and

T AMS−TC

MS , for the period from 1933 to 1945. In the fig-ure, the horizontal axes are the year and the vertical axesare the differences given in minutes. As shown in Fig-ure 3, the moonrise and moonset times show relativelylarge differences in 1941. We think that further studiesare required to understand the reasons behind this. The

MAD values are 0.31 min for both sunrise and sunsettimes and 0.43 and 0.46 min for moonrise and moonsettimes, respectively. This is very similar to the values inKorean almanacs during this period (Lee 2017).

3.2 Solar term

The Chinese calendar, such as Shixianli, is classified as alunisolar calendar maintaining synchrony of the lengthof a year in the lunar calendar with that of a tropicalyear (Urban & Seidelmann 2012). To retrieve the dif-ference in both lengths, a leap lunar month was inserted


approximately every three years. As a rule, to insertthe leap month, the day of the solar term was used inChinese calendars (refer to KASI 2017 for details). Thesolar terms consist of twelve minor and major terms, andthese names were assigned to represent the season orweather (Urban & Seidelmann 2012). Historically, twotypes of solar terms have been used in China: ‘mean’and ‘corrected’ (in literal translation). The mean solarterm was obtained by dividing the length of a tropi-cal year into 24 equal intervals. On the other hand, thedays of the corrected solar term were obtained by con-sidering the unequal motions of the Sun and Moon. Incontemporary concepts, the days of the corrected solarterm were determined by dividing the ecliptic longitudeinto 24 equal intervals. For instance, the day of the win-ter solstice in the corrected solar term is the momentwhen the ecliptic longitude of the Sun (λ�) is 270◦. Itis known that the days of the corrected solar term havebeen used in the almanac since Shixianli or Shixianshu.However, it is unknown whether or not the methods ofthe Shixianli were used in the Manchuria almanacs tocalculate the times of the 24 solar terms. In this study,we obtained those times from modern calculations asthe moments defined in Table 2.

According to our examination, only the days of the 24solar terms are recorded (i.e., hours are not recorded)in the almanacs of 1933 and 1934. We found that alldays show exact agreement with modern calculationsin these two years. On the other hand, we found thatthe MAD value is 0.42 min for the dates of the 24 solarterms recorded on the remaining almanacs. In addition,we found that there were no times of solar terms closeto midnight so that the day might be changed due to theuncertainty in the calculation. Instead, we found thatthe time of the 6th solar term, counting from the vernalequinox, in 1939 was the closest to midnight amongthe 312 solar terms as 23 h 52 min. Figure 4 shows thedifferences of the time of the 24 solar terms (ST ) in thealmanac and modern calculations, T A

ST − TCST , in units

of minutes. One of the patterns in Figure 4 is that mostof the differences show positive values.

3.3 Phases of the Moon

The four phases of the Moon were utilized in Chinesecalendars: new, first quarter, full and last quarter moons.For each of the phases of the Moon, two kinds were usedjust like for the solar term: ‘mean’ and ‘corrected’ (inliteral translation) simply using the synodic month, i.e.,the average period between two successive lunar phases(e.g., new moons or full moons), and additionally con-sidering the unequal motions of the Sun and Moon,

Figure 4. Comparison of the times of the 24 solar terms(ST ) between the almanacs (A) and modern calculations (C).The horizontal axis represents years and the vertical axis rep-resents the differences in units of minutes, T A

ST − TCST .

respectively. That is, mean new, first quarter, full andlast quarter moons are obtained by successively addinga quarter of the synodic month to a reference point oftime. Alternatively, mean phases of the Moon can beobtained by adding the synodic month to each previousphase of the Moon. For instance, the mean full mooncan be obtained by adding the synodic month to theprevious mean full moon. On the other hand, the cor-rected phases of the Moon are obtained by consideringthe unequal motion of the Sun and Moon for each of themean phases of the Moon. In Chinese calendars, the dayof the corrected new moon was used as the first day ofthe lunar month before the Shixianli. In terms of modernastronomy, the corrected new, first quarter, full and lastquarter moons are the moments when the differences ofthe ecliptic longitude between the Sun and the Moon,|λ� − λ�|, are 0◦, 90◦, 180◦ and 270◦ respectively. InFigure 5, we present the differences of the times of thenew moon (NM), first quarter moon (FQ), full moon(FM) and last quarter moon (LQ) between the almanacand modern calculations, T A

NM − TCNM , T A

FQ − TCFQ ,

T AFM − TC

FM and T ALQ − TC

LQ . The MAD values are0.27, 0.27, 0.28 and 0.25 min for new, first quarter, fulland last quarter moons, respectively.

3.4 Eclipses

An eclipse, particularly a total solar eclipse, is one ofthe most dramatic astronomical events. In addition, itwas one of most ominous phenomena in East Asia interms of astrology. Hence, it was an important task of aking to predict the eclipse event precisely. It can be saidthat the history of the calendar in China was an effort topredict the eclipse more accurately. The decisive reasonfor the Qing dynasty introducing Shixianli in 1644 was


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 axesrepresent the differences in units of minutes, T A

NM − TCNM (bottom right), T A

FQ − TCFQ (bottom left), T A

FM − TCFM (top right),

and T ALQ − TC

LQ (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 Emagh: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:– 08:19:– 08:59:– 0.16 07:41:13 08:19:19 08:59:04 0.16 −0.22 −0.32 −0.06 0.001936 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 −0.011938 Nov 22 08:09:– 0.13 08:09:02 0.11 −0.03 0.021941 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 0.001943 Feb 05 08:44:05 0.81 08:44.38 0.72 −0.54 0.091945 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-dars in predicting when the solar eclipse would occurin the year.

In astronomical almanacs referring to this study,six solar eclipses1 are recorded for three stages, i.e.,Chukui, Fuyuan and Shishen together with the eclipsemagnitude (Emag). Each stage is the first and lastexternal contacts of the penumbra (P1 and P4), andgreatest eclipse (GE�), respectively, in modern termi-nology (Lee 2017). On the other hand, twelve lunareclipses2 are recorded in five stages, i.e., Chukui, Shigi,

1Actually, eight solar eclipses, including two eclipses (unobservableat Xinjing) in 1933 and 1937.2Actually, 14 lunar eclipses, including two eclipses (unobservableat Xinjing) in 1939 and 1942.

Shengguang, Fuyuan and Shishen including the umbralmagnitude (Umag). In modern terminology, each stageis the first external and internal contacts of the umbra(U1 and U2), the last internal and external contacts ofthe umbra (U3 and U4), and greatest eclipse (GE�),respectively. We utilized the algorithms used in theworks of Lee (2008) and Lee et al. (2016) in the moderncalculations for solar and lunar eclipses, respectively.

In Table 3, we present the solar eclipse times recordedin the almanacs and obtained from modern calcula-tions at Xinjing but in units of minutes, for clarity ofthe table. Including the solar eclipse of 1941 Septem-ber 21 observed in Korea by Yumi, a Japanese scholar,all eclipses were recorded on the Korean astronomicalalmanacs at corresponding times, i.e., visible in Koreaas well. According to our calculations, the MAD value


Figure 6. Diagram of the solar eclipse that occurred in 1936June 19. The asterisk and cross symbols indicate the point ofgreatest eclipse and the location of Xinjing, respectively.

for the times of the three stages is 0.29 min and thesolar eclipse that occurred in 1936 June 19 had thelargest magnitude, 0.82, among six eclipses, In addi-tion, it seems that the solar eclipse magnitude of 0.81occurred in 1943 February 5 is a typographic error of0.71 considering the MAD value of 0.021 in magnitude.In Figure 6, we present a diagram showing the eclipsemagnitude with respect to longitude and latitude for theeclipse of 1936 using a �T value of 23.73 s. In the

figure, red asterisk and black cross symbols representthe geographical regions of greatest eclipse and of Xin-jing, respectively.

In Table 4, we present lunar eclipse times at Xinjingfrom the almanacs. The symbol ‘T’ in the 9th columnof the table indicates the total lunar eclipse as recordedon the almanac. Although we do not present the lunareclipse times obtained from modern calculations forclarity of the table, those times can also be found on theNASA eclipse website3 providing the times in units ofTT. Because the circumstances of a lunar eclipse eventis the same over all areas of the Earth if the Moon isvisible, the lunar eclipse times at Xinjing can easily beobtained by considering the standard meridians usedin Manchukuo (i.e., 120◦ or 135◦E). For reference, theaverage differences of the lunar eclipse times betweenthis study and those on the NASA website are less than10 s for all stages. According to our study, the MAD val-ues for all lunar eclipse times and umbral magnitudesare 0.49 min and 0.008 mag, respectively. In Figure 7,we present the lunar eclipse map showing the visibilityareas at five stages for the lunar eclipse that occurredin 1936 January 9, which was total. In the figure, theentire eclipse was observed in the unshaded area whilethere was no eclipse in the darkest area. In the remainingshaded areas, some phases of the eclipse were visibleduring progress. The axis of the shadow of the Earthand the geographical location of Xinjing are denotedby the red asterisk and black cross symbols, respec-tively.

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 Umagh: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 0.0081934 Jul 26 20:15 09:36 0.67 −0.15 0.33 0.0081935 Jan 19 21:53 23:04 23:47 24:31 25:41 T −0.82 0.00 −0.10 0.65 0.461936 Jan 09 00:28 01:58 02:10 02:21 03:51 T −0.25 −0.97 0.52 0.88 0.181936 Jul 05 00:27 01:25 02:24 0.27 0.11 0.10 0.73 0.0031937 Nov 18 17:19 18:01 0.15 −0.11 1.24 0.0051938 Nov 08 05:41 06:45 T −0.21 −0.571939 May 03 22:28 23:40 24:11 24:43 25:55 T 0.28 −0.04 −0.22 0.48 0.161941 Mar 13 19:55 20:55 21:56 0.33 −0.50 −0.28 0.67 0.0071941 Sep 06 02:19 02:47 03:15 0.06 −0.94 0.26 1.49 0.0091943 Aug 16 02:59 04:29 0.88 −0.10 0.75 0.0101945 Jun 25 22:37 24:14 25:51 0.87 −0.57 0.17 0.67 0.010


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 symbolsrepresent the geographical location of greatest eclipse and of Xinjing, respectively.

4. Summary

We investigated the astronomical almanacs of Manchu-kuo, a puppet Japanese state that lasted for 14 yearsfrom 1932 to 1945, in terms of the contents and theaccuracy of the time data. Considering that the annualalmanac for each year was published in the previousyear, the Manchuria almanacs were published for 13years from 1933 to 1945, which were used in this study.From the examination of the contents, we found thatthe name of the almanacs was Shixianshu, the name ofthe calendar used in the Qing dynasty of China. Thereference location of time data was Xinjing, nowadaysknown as Changchun, and the standard meridian waschanged from 120◦E to 135◦E, the standard meridianof Japan, starting from the almanac of 1937. In addi-tion, two kinds of the almanac were published in 1934,as the reign-style was changed from Datong to Kangde,and in 1945 written in both Chinese and Mongolian, asfar as we know. We classified the time data into fourgroups and the summary of our finding for each groupis as follows:

Rising and setting: The sunrise and sunset times arerecorded only on the days of the 24 solar terms at Xin-jing, while moonrise and moonset times are recordedon a daily basis, but for a dozen of cities. In addition,the atmospheric refraction was considered for calculat-ing the rising and setting times of the Sun and Mooncompared with the results of modern calculations. Inparticular, the moonrise and moonset times show rel-atively large differences with modern calculations for1941. The MAD values are 0.31 min for the sunrise andsunset times, and 0.43 and 0.46 min for the moonriseand moonset times, respectively.

Solar term: Solar terms are presented only in terms ofdays in the almanacs of 1933 and 1934, and both days

and hours in the almanacs afterwards. For the periodof 1933–1934, the days show good agreement withmodern calculations. On the other hand, the MADvalues are 0.41 min for the remaining period. Accordingto our study, there were no days of the 24 solar terms forwhich the day might be changed due to the uncertaintyin modern calculations such as the uncertainty in thevalue of �T .

Phases of the Moon: The MAD values for the times ofthe phases of the Moon show the minimum accuracyamong four groups: 0.27, 0.27, 0.28 and 0.25 min fornew, first quarter, full and last quarter moons, respec-tively.

Eclipses: Six solar and twelve lunar eclipses arerecorded in the almanacs together with the eclipse mag-nitude. All these were visible in Korea, hence theywere recorded on Korean almanacs at that time as well.Except for the almanacs of 1933 and 1934, the solareclipse times were recorded in seconds, different fromother time data such as the lunar eclipse times. The timesfor the three and five stages are recorded for solar andlunar eclipses, and the MAD values are 0.29 and 0.49min, respectively.

In conclusion, we think that our findings will con-tribute to the study of astronomical almanacs of Japanand Taiwan and to the comparison of the astronomicalalmanacs of East Asia that were published during thisperiod.

Acknowledgements

The second author was supported by the National Re-search Foundation of Korea (NRF) grant funded by theKorea government (MSIP) (No. 2016R1A2B4010887).


The third author was supported by the National ResearchFoundation of Korea (NRF) grant funded by the Koreagovernment (MSIT) (No. 2019R1F1A1057508).

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Analysis of Manchuria astronomical almanacs of 1933–1945