24.
1881 A.D., is again a leap year, because the Chinese golden number is 19.
The Chinese were already acquainted with the Lunar cycle many centuries before the Christian era, and had determined its help the day of the New moon. However, as this method of fixing the first day of the month is not exact and can cause an error of some days, they abandoned about 160 years ago this method and substituted in all parts of their Calendar astronomical tables and exact principles .
The bases of all astronomical calculations are the tables, from which can be deduced at any time the position of the sun, moon and planets, and besides this the catalogues of the fixed stars, which have no proper motion or an insignificant one.
As the fundamental tables exhibit only the elements for calculating the position of the heavenly bodies, and as their position change very much with time, these calculations are long and tiresome. For this reason, in our time, in order to facilitate the application of astronomy to practical purposes as well as the advancement of the science itself, every important governement prepares an astronomical Almanac for every year, giving for every day or hour of the year the position of the most important heavenly bodies, called ephemerides. One of the best of these works is the Nautical Almanac, edited by the Government of Great Britain and printed in London.
The Chinese astronomers of the present day calculate and print ephemerides for the sun, the moon and the greater planets for every day, such as the Nautical Almanac gives, by means of the fundamental tables, constructed in the 18th century by De Lambre and Mayer, giving the time of the Newmoon and the beginning and end of the eclipses correct within a quarter of one hour.
The method of calculating the time of the Newmoon is as follows: First find an approximative value for the time of the New moon by help of the golden number and epact [Table (16)]; then calculate by the fundamental tables the longitude of the sun and moon for this approximate time. If the calculated longitude of the moon exactly coincides with that of the sun, the supposed approximate time will be the exact moment of the Newmoon; if not, the moment of the exact equality of the longitude of the sun and moon can be found by a simple proportion, and is the exact moment of the desired Newmoon.
For example: Required the exact time of the Chinese Newyear in the 31th year of the 75th cycle (14th year of Tao-Kuang).
In the next chapter, in dealing with the comparison of Chinese and European chronological dates, a method is given to find the
