Page:On Chronology and the Construction of the Calendar.pdf/35

 year T of the European (Christian) era from the Chinese cycles. According to equation (27), when y denotes the place of the year in the cth cycle of 60 years, we have: $$T = c \cdot 60 + y - 2697$$, hence in our case $$T= 75 \cdot 60 + 31 - 2697 = 1834 A.D.$$

The Chinese golden number of 1834 A.D. is the remainder of $1834⁄19$ or 10 and the European golden number g = 10 + 1 = 11; therefore, according to table (16) the epact = 20, that is: the first Newmoon in 1834 A.D. was 10 January and the second the 8th February. As the Chinese Newyear must happen always between the 21 January and the 20 February, the Newmoon about the 8th February must by [sic] the Chinese Newyear. By help of the table (33) below, we find, that the 8th February 1834 A.D. was the 3th day in the Chinese sexagesimal week and called Ping-Yin.

In order to get the exact time of this Newyear, we start from February 8, midnight and calculate from the fundamental tables, according to the simple rules, explained in these tables, the longitude of the sun and the moon. Thus we obtain by help of the old fundamental tables, calculated for the sun by the astronomer De Lambre and for the moon by the astronomer Mayer about 1780 A.D. and probably still used by the Chinese astronomers of the present day,

1834 February 8 12h Peking mean time, sun's longitude 319° 30,′0

8 12h , moon's longitude 319° 6,4

As, at 12h in the night the moon's longitude had not reached that of the sun, the conjunction or Newmoon happened in the morning of the next Calendar-day, February 9 (in the Chinese sexagesimal week the 4th day, called Ting-Mao). Further, as the sun's longitude hourly increases 2,′5 and that of the moon increases 32,′9, the moon moves quicker than the sun by 30,′4 in 1 hour, therefore the moon has reached the sun $$\frac{23{,}6}{30{,}4} = \frac{319^\circ 30{,}'0 - 319^\circ 6{,}'4}{30{,}4} = 0{,}^{h}78 = 47$$ minutes after midnight.

The required exact time of the Newmoon of the first month in the 31th year of the 15th cycle or the 14th year of the emperor Tao-Kuang, is the 4th day, Ting-Mao, of the Chinese sexagesimal week, 4,5 days after the tsie-khi Li Chun, in the morning 0 o'clock 47 minutes Peking mean time. The result of this calculation coincides exactly with that of the Chinese astronomers.

When for the year, in which the required Newmoon occurs, exist an ephemeris such as the Nautical Almanac, the exact Greenwich time of the Newmoon is already calculated in this work. We add only the longitude (if east from Greenwich positive and if west negative) to the Greenwich time and have the required local time of the place. For instance, as the longitude east of Peking from Greenwich is equal to 4h 45,m9, we have to add it to the data