between the 5th and 3rd century b.c. when the quarter-remainder calendar was in use, the winter solstice point was set at the entrance to the lunar mansion qianniu or the region approaching giedi(β capricorni). the zhuanxu calendar of 221 b.c. did the same, and this may be accepted as chinas earliest such datum obtained through actual observations. as it was isible to ascertain the suns relative ition by direct observation, the ancient astronomers resorted to indirect means. they identified the day of the winter solstice, ascertained its midnight by using the cleydra and found out the distance of the star at the zenith to the nearest lunar-mansion determinative star. they could thus tell the location of the sun, which stood directly opite that star. the data obtained were inevitably inaccurate because the cleydra was hardly a satisfactory chronometer. the chinese astronomers were ignorant of the precession until the 3rd century. before that they thought the sun made an exact round trip along its orbit in the celestial sphere between winter solstices. that was why they fixed the tropical year at 365.25 days and divided the natural celestial sphere into as many degrees. as far as they knew the winter solstice point was fixed, and the notion that the point was in the region approaching giedi remained. makers of the taichu calendar of 104 b.c. virtually based themselves on the same data. in a.d. 7 liu yin noted, if vaguely, the wavering of the winter solstice point.
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