206 Shnizo Shin jo 



The clivonology of the Gli'^in-cli'iu ^^, and the date of the 

 compilation of the Tso-clman "J^^-, are two quetions veiy important 

 for the study of ancient history, which, though much discussed, have 

 not yet been solved. We find in the Ch'un-ch'iti ^^ records of 36 

 solar eclipses, of which 5 cases must be cancelled as mistakes, leaving 

 31 cases to be utilized for study, and also the mention of 389 dates, 

 given according to the sexagesimal system. Now comparing these 31 

 records of solar eclipses with the results of modern calculation ( e. g., 

 with Oppolzer's Canonen der Fimternisse), we should obtain 31 fixed 

 epochs during 242 years, and then studying the distribution among 

 these fixed spochs of the 389 dates in the sexagesimal system, we 

 should able to find out the proper arrangement of the intercalary 

 months, i.e., the arrangement practised at that time. 



As the result of a thorough study made in 1920, I have been 

 able to carry out this procedure, and have obtained the arrangement 

 of the intercalary months shown in the diagram (PI. XLVII.) If the 

 positions of the intercalary months be once found, then the real 

 chronology of all the date can be put forward at once. 



We observe that for the latter half of the Ch'un-ch'iu period 

 (722-481 B.C.), the insertion of the intercalary months is tolerably 

 regular, amounting to seven in nineteen years, and so the beginning 

 of the year is kept at a nearly constant seasoual epoch, the first 

 month being always adjusted so as to include the winter solstice. 

 During approximately the first third of the period, the beginning of 

 the year seems to have been about one month later in every case, the 

 interval following it and preceding the latter half of the period being 

 a time of transition, and hence showing a comparatively large varia- 

 tion in the beginning of the year. This clearly shows that an 

 important improvemcDt must have taken place a little before the 

 middle of the Ch'un-ch'iu period. 



It may be well to notice here that the procedure of inserting 

 seven intercalary months in 19 years, is just a mode of keeping the 

 mean length of the year equal to 365.25 days, at the same time that 

 the lunar calendar is used, with lunar months of a mean length of 

 29.53 days. In fact, we have the relation 



29.53085 X (19 xl2 + 7) = 6939.75 = 365.25x 19. 

 This is exactly the same as the calendar system, known in the 

 Occident by the name of Callipos, compiled in 334 B.C. The coupling 

 of the solar with the lunar calendar to form a kind of lunisolar 



