The even tzie-khi, corresponding to the European signs of the zodiac, are called by the Chinese chung-k'hi.
The time, in which the sun passes over two tsie-khi is on an average throughout the year 30,44 days, whilst the interval between one New-moon and the next is only 29,53 mean solar days. For that reason, there must be one lunation, during which the sun does not enter into an even tsie-khi i.e. into one of the twelve signs of the zodiac. This month is the intercalary month and called djun yüő, not having its own number, but that of the previous month.
This intercalary month happens about the time when the sun is far_ therot from the earth, or near the aphelium, between April and September (between the Chinese 3th and 8th month), because, when near the aphelium, the sun's motion is slow and it passes over two tsie-Khi or 30 degrees of longitude in 31,5 mean solar days, whilst when near the perihelium, in January (the Chinese 12th month ) the sun makes 30 degrees in 29,4 days. In consequence of this arrangement the entrance of the sun in the four cardinal-points of the ecliptic, the Vernal equinox, the Summer solstice, the Autumnal equinox and the Wintersolstice must always occur respectively within the second, the 5th,the 8th and the 11th Chinese month.
In the chapter on the Lunar cycle it is stated, that 19 tropical solar years are equal to 235 synodical months (Lunation) and that 235 = 12.12 + 7.13. Therefore the lunar year of the Chinese can be rectified . and brought into accordance with the solaryear, when in the course of 19 solar years, 12 years consist of 12 Lunations and 7 years of 13 Lunations, or, if in the course of 19 years, there are 12 common and I leap years.
The Chinese leap years are, since some hundred years ago always the third, the 6th, the 8th, the 11th, the 14th, the 14th and the 19th year of the Chinese lunar cycle, which is one behind the European, not being the remainder of year A.D. + 119, as the European, but the remainder of year A.D19. Hence the Chinese leapyears are the 4th,7th, 9th, 12th,15th,18th and 1th year of the European Lunar cycle, or, which is the same thing, the Chinese golden numbers of the leap years are 3, 6, 8, 11, 14, 17, 19 and the European golden numbers 4, 7, 9, 12, 15, 18, 1. There have been only two exceptions to this rule viz. in the years 1795 A.D. and 1814 A.D., which were leap years with the Chinese golden number 9 instead 8.
For instance the year 1879 A.D., if divided by 19, gives the remainder 17, therefore the Chinese year, corresponding to 1879 A.D., i.e. commencing about Jan.-Fbr. 1879 A.D., is a leap year of 13 Lunations; the next Chinese year, about 1880 A.D., is a common year of 12 Lunations and the following Chinese year, about
