Analysis of Time Data in Japanese Astronomical Almanacs for 1885 – 1943
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Ki-Won Lee , G. E. Choi , and Y. S. Ahn

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Catholic University of Daegu, 13-13 Hayang-ro, Hayang-eup, Gyeongsan 712-702, S. Korea
Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 305-348,
S. KoreaE-mail: leekw@cu.ac.kr

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Abstract: In this study, we analysed Japanese astronomical almanacs for the period from 1885 to 1943.
During this period, two astronomical almanacs were published each year in Japan: the Honreki (a formal
almanac) and its simplified version, the Ryakuhonreki, which are the focus elements of this study. Japan
introduced the solar calendar in 1873, adopted the standard meridian of 135° E in 1883, and adopted thelocation of the Tokyo Astronomical Observatory as the reference point for observations in 1891. In thispaper, we verified facts regarding the introduction years of both the solar calendar and the standard
meridian of 135° E. In addition, we investigated the accuracy of time data such as new moon time,sunrise time, and twenty-four seasonal subdivision times by comparing data from the astronomical
almanacs with results based on modern calculations. We think that this study will contribute to a better
understanding of Japanese astronomical almanacs.
Keywords: Historical Astronomy, Astronomical
Taiyōryakureki , Reki ), Astronomical Calendar

Almanac(Honreki,

Ryakuhonreki,

Taiyōreki,

1 INTRODUCTION
Many changes were made to the Korean astronomical almanac [曆書] during the period of 1864 – 1945
(Choi 2010). In particular, Korean astronomical almanacs after 1913 were calculated and published by
Japanese scholars (Ahn et al. 2010), because Japan had occupied Korea (beginning in 1910). During
this period, Japan also underwent many changes such as the introduction of the solar calendar in 1873
(1896 in Korea), adoption of the standard meridian of 135° E in 1888 (1912 in Korea), use of the Tokyo
Astronomical Observatory [東京天文臺] (now the National Astronomical Observatory of Japan; hereafter
NAOJ) as the reference point for observations after 1893 (Incheon Meteorological Observatory after
1912 in Korea; for details regarding the Observatory, refer to Lee et al.2011), and so forth.
During preliminary research on the Japanese astronomical almanac, we verified the introduction years of
the solar calendar and the standard meridian of 135° E. In addition, we investigated the accuracy of thetime data such as the new moon [朔] time, and sunrise and sunset times, using the astronomical
almanacs from 1885 to 1943.
This rest of paper is organized as follows. In section 2, we briefly introduce Japanese astronomical
almanacs and list the almanacs used in this study. We describe our data reduction in section 3, present
our results in section 4, and offer a summary in section 5.
2 REVIEW OF JAPANESE ASTRONOMICAL ALMANACS
According to the 337th official report [官報] of the Dajōkan (太政官), announced 9 November 1872, Japan
would adopt the solar calendar starting in the year 1873 (refer to Appendix A). Based on the timing of thisannouncement, it was likely too late to prepare the almanac for the year 1873. However, we found an
astronomical almanac based on the solar calendar, entitled Taiyōreki (太陽曆), in the library of the NAOJ
together with that based on a luni-solar calendar, entitled Hanreki (頒曆) (see Figure 1). As mentioned in
the Dajōkan report, the former almanac was published in early 1873. A similar situation was seen for the
astronomical almanac of 1667 published by the Joseon (朝鮮) dynasty in Korea. The Joseon court
urgently published a single-page almanac because the court had recently learned that the Ching (淸)dynasty of China would re-introduce the Datong (大統) calendar for the almanac of 1667 (Lee et al 2010).
In addition, the term “solar calendar” in the report seems to refer to the Julian calendar based on a clause
explaining the method of inserting one leap day at four-year intervals. However, we found that there were1

28 days in February in the almanac for the year 1900. Therefore, we know that the solar calendar refers
to the Gregorian calendar, not the Julian calendar. Meanwhile, two types of astronomical almanacs were
published in the Joseon dynasty in around 1900, Myeongsiryeok (明時曆), based on a luni-solar calendar,
and Ryeok (曆), based on a solar calendar. There are 29 days in February in the former almanac,
although this error was corrected in the almanac published in the following year (Lee et al. 2011).

Figure 1. Astronomical almanacs for 1873, published in Japan: Hanreki (left) and Taiyōreki (right).

Regarding with the Gregorian almanacs from Japan, two types were published: Taiyōreki andTaiyōryakureki (太陽略曆), both published until 1880. Reki (曆; hereafter called the formal almanac) and
Ryakuhonreki (略本曆; a simplified version of the formal almanac, hence, hereafter called the simplified
almanac) were published after 1880. In Table 1, we list the astronomical almanacs used in this study
together with the ownership of the formal almanac (marked in columns 4 and 8). As can be seen in thetable, we mainly used the simplified almanac, which was collected by the author.
Table 1. Japanese astronomical almanacs used in this study.
Year
F. A1)S. A2)Note
Year
F. A1)S. A2)
Note
1885
O
1915
O
O
Author1886
O
BMSML3)
1916
O
O
Author
1887
O
1917
O
O
Author
1888
O
1918
O
BMSML
1889
O
1919
O
BMSML
1890
O
1920
O
1891
O
1921
O
NAOJ
1892
O
1922
O
BMSML
1893
O
1923
O
BMSML
1894
O
1924
O
BMSML
1895
O
1925
O
NLK4)
1896
O
1926
O
NLK
1897
O
1927
O
1898
O
BMSML
1928
O
1899
O
1929
O
1900
O
1930
O
O
NLK
1901
O
1931
O
1902
O
1932
O
1903
O
1933
O
1904
O
1934
O
1905
O
1935
O
NLK
1906
O
1936
O
1907
O
1937
O
O
NLK
1908
O
1938
O
1909
O
NAOJ
1939
O
O
NLK
1910
O
1940
O
NAOJ
1911
O
1941
O
1912
O
1942
O
1913
O
1943
O
O
NLK
1914
O
O
Author
Total
8
59
1)
Formal Almanac, 2)Simplified Almanac. 3)The Busan Metropolitan Simin Municipal Library,4)
National Library of Korea

23 DATA REDUCTION
3.1. Astronomical almanac data
We compiled the 11 types of time data from the Japanese astronomical almanacs from 1885 to 1943;
seven related to the moon (i.e., new moon, first quarter moon, last quarter moon, full moon, moonrise,
moonset, and lunar eclipse times) and four related to the Sun (sunrise, sunset, solar eclipse, and 24
seasonal subdivision [節氣] times). In those almanacs, sunrise/set and moonrise/set data are given inunits of 1min; twenty-four seasonal subdivision times are in units of 0.1min up until 1886 and in units of
1min thereafter. Strangely, the simplified almanac provides only twelve seasonal subdivisions in its “date”
data from 1923 onwards. In contrast, the formal almanac provides dates and hours for only four seasonal
subdivisions (i.e., summer and winter solstices, and vernal and autumnal equinoxes). In the case of theeclipses, the data are given in units of 1min. In particular, the solar eclipse of the year 1933 was not
visible in Japan; hence, the almanac contains observable time data at Seoul, Korea.
3.2 Modern calculations
In modern time data calculations, we use the algorithms of Meeus (1998), the astronomical ephemerisof Standish et al. (1997), and the ΔT (i.e., difference between terrestrial and dynamical times) values
from the Nautical Almanac Office (2009). To calculate the solar eclipse time in a given circumstance, weused Besselian elements (see Lee 2008 for details). Regarding the lunar eclipse, we used time datacompiled by the NASA (which can be found at http://eclipse.gsfc.nasa.gov/lunar.html).
Regarding the identification of dates used in the Japanese astronomical almanac, we do not need toconvert a luni-solar calendar date into a Gregorian calendar date because Japan adopted the Gregoriancalendar in 1873, as mentioned above. Instead, we must know the reference point for observations andthe standard meridian of a time to compare the times in the astronomical almanacs with those derived
from modern calculations. Regarding the reference point, we refer to the Japanese Astronomical
Almanac [曆象年表] of 2010 (NAOJ 2009); Tenshudai (天守臺; main tower, 09h 19m 01s in latitude and35° 41’ 06” in longitude) up to 1890 and the Tokyo Astronomical Observatory (09h 18m 58s in latitude
and 35° 39’ 15” in longitude) thereafter. In contrast, Japan adopted the standard meridian of 135° E in1888 (see Appendix B). Therefore, we assume that Japan started using the standard meridian as thereference point for observations some time before 1888.
We also have to know the definition of time data to compare the times listed in the astronomical
almanacs with results from modern calculations. For example, nowadays, the sunrise or sunset times aredefined as the moments when the upper part of the sun reaches the horizon, i.e., the zenith angulardistance of the sun is 90° 50’ considering the sun’s angular radius of 16’ and a mean atmosphericrefraction of 34’. Details pertaining to the definitions of the time data, including the changes of thereference point for observations in Japan, will be further discussed elsewhere.
4 RESULTS
In Figure 1, we present the results for the new moon and full moon times, which are independent of thereference point for observations. In this figure, the horizontal and vertical lines represent a year and thedifference (in minutes) between the times presented in the astronomical almanacs (TA) and thoseobtained from modern calculations (TC), TA – TC. In modern calculations, we use the standard meridian of
135° E for all years, for verifying whether the standard meridian of 135° E was actually used in thealmanac for the year 1888. As a result, we found that the time differences show a large change in 1888,
which verifies the Dajōkan report on the use of the standard meridian of 135° E.
In Table 2, we summarize the results for all time data. Column 1 presents the different types of time data,and columns 2, 3, and 4 present TA – TC data in units of seconds (according to the period). We divide theperiod into three classes based on the reference positions of the observation and the standard meridians:
periods I, II, and III. For the reference positions of the observation, we used the locations of the main
tower in periods I and II, and the Tokyo Astronomical Observatory in period III. However, the first quarter,
last quarter, twenty-four seasonal subdivision, and lunar eclipse data do not depend upon the reference
position of the observation, as the cases of the new and full moon time data do. On the other hand, we
assumed the main tower was used in period I, and 135° E was used in periods II and III as the standard
meridian of time. As a result, we found that the accuracy is better than ~1min on average.
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Figure 2. Time differences between astronomical almanacs and modern calculations in new moon (left) and full moon (right) data.
Table 2. Summary of results for time differences between astronomical almanacs and modern calculations.

TA - TC (sec)Period II1)

Items
New moon

3.57±20.95

8.92±18.88

First quater moon

1.93±16.63

11.60±20.17

Full moon–5.41±13.93

8.17±19.92

Last quater moon

–5.28±18.20

7.80±19.57

24 Sea. Subdiv.

–21.02±15.36–7.43±26.38

Sunrise–14.10±18.56–15.07±17.37–5.50±17.94

Sunset11.64±19.68

10.73±18.69

4.58±16.86

Moonrise–14.12±17.03–11.40±1778–5.89±17.49

Moonset15.64±18.60

4.75±19.12

Solar eclipse–7.02)

14.99±1835
no data

Lunar eclipse

2.30±19.61

Period I1)

Period III1)

1.67±07.65–14.12±16.04≤ 1min on average

Total
1)

Refer to the text for the assumed reference position of the observations and the standard meridian.
2)
Only one data point is used for this calculation.

5 SUMMARY
In this paper, we analysed Japanese astronomical almanacs from 1885 to 1943, relying primarily on thesimplified almanacs. First, we found that the astronomical almanac used the solar calendar beginning in
1873, although the 337th official report of the Dajōkan, regulation on the use of the solar calendar, wasannounced too late to allow the preparation of the astronomical almanac of the calendar. In addition, we
pointed out that the solar calendar actually refers to the Gregorian calendar based on information in theastronomical almanac of 1900. Second, we verified that the standard meridian of 135° E was used in thealmanacs from the year 1888 onwards in Japan, based on the analysis of the new moon and full moontime data. Last, we estimated the accuracy of the time data presented in the Japanese astronomical
almanacs of 1885 – 1943, which were collected from various sources including a private owner. As aresult, we found that the time data are very accurate, that is, better than 1min. We think that this study
contributes to a better understanding of historical Japanese astronomical almanacs.

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6 ACKNOWLEDGEMENT
Ki-Won Lee would greatly like to thank Dr. Mitsuru Sôma of NAOJ for providing the opportunity to talk at
the third symposium on Historical Records and Modern Science and providing travel and accommodation
funds. The authors would like to thank the librarians at NAOJ, National Library of Korea, and the Busan
Metropolitan Simin Municipal Library for help in reading the Japanese astronomical almanacs.
7 REFERENCES
Ahn, S. H., Lee, K.-W., & Mihn, B. H., 2010, Modern Astronomy in Korea, Korea Astronomy and Space
Science InstituteChoi, G. E., 2010, A Study of Korean Astronomical Almanacs for 1864 – 1945, Msc Thesis, Chungbuk
National University
Lee, K.-W., 2008, A Study of Solar Eclipse Records during the Three Kingdoms Period in Korea, Journalof the Korean Earth Science Society, 29, 408
Lee, K.-W., Ahn, Y. S., Mihn, B.-H., & Lim, Y. R., 2010, Study on the Period of the Use of Datong-li in
Korea, Journal of Astronomy and Space Sciences, 27, 55
Lee, K.-W., Ahn, Y. S., Mihn, B. H., & Shin, J.-S., 2011, Database Construction and Textual Analysis of
Korean Astronomical Almanacs, Publications of the Korean Astronomical Society, 24, 1
Lee, K.-W., Ahn, Y. S., Mihn, B.-H., & Kim, B.-G., 2011, The Incheon Meteorological Observatory and Its
Astronomical Activities, in Proceedings of the Seventh International Conference on Oriental Astronomy,
eds T. Nakamura, W. Orchiston, M. Soma, & R. Storm, 238
National Astronomical Observatory of Japan, 2009, Japanese Astronomical Almanac [ 曆象年表] of theYear 2010, National Astronomical Observatory of Japan
Nautical Almanac Office, 2009, Astronomical Almanac for the Year 2010 and Its Companion,
Meeus, J., 1998, Astronomical Algorithms, Willmann-Bell Inc.
Standish, E. M., Newhall, X. X., Williams, J. G., & Folkner, W. F., 1997, JPL Planetary and Lunar
Ephemerides (CD-ROM), Willmann-Bell Inc.
APPENDIX A(source: http://kindai.da.ndl.go.jp/info:ndljp/pid/787952/172)

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APPENDIX B(source: http://kindai.da.ndl.go.jp/info:ndljp/pid/787968/362)

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