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Knowing that the Shenshai year consists of a vague year of 365 days: |
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| Western Date | Shenshai | Julian Day | Difference | | 1996 Aug 22 | 1 Far 1366 | 2,450,318 |  |
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0 |
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| | 1995 Aug 23 | 1 Far 1365 | 2,449,953 | |
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365 |
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| | 1992 Aug 23 | 1 Far 1362 | 2,448,858 | 1,460 (4365) | | 1938 Sep 6 | 1 Far 1308 | 2,429,148 | 21,170 ( 58365) |
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Now, use 100-year multiples of 365 days to count backwards in both calendars: |
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| Western Date | Shenshai | Julian Day | | Difference | | 1896 Sep 15 | 1 Far 1266 | 2,413,818 | | 36,500 (100365) | | 1796 Oct 9 | 1 Far 1166 | 2,377,318 | | 73,000 (200365) | | 1696 Nov 2 | 1 Far 1066 | 2,340,818 | | 109,500 (300365) | | 1596 Nov 27 | 1 Far 966 | 2,304,318 | | 146,000 (400365) | | 1496 Dec 12 | 1 Far 866 | 2,267,818 | | 182,500 (500365) | | 1397 Jan 6 | 1 Far 766 | 2,231,318 | | 219,000 (600365) | | 1297 Jan 31 | 1 Far 666 | 2,194,818 | | 255,500 (700365) | | 1197 Feb 25 | 1 Far 566 | 2,158,318 | | 292,000 (800365) |
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At this point, observe that the intercalations of 120 years were last carried out in A.D. 1131, so the 365-day year in backward calculations may continue to be used for another 1,197 1,131 = 66 years. Hence: |
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| 1131 Mar 14 | 1 Far 500 | 2,134,228 | 316,090 (866365) # |
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This result makes sense, since it is close to the vernal equinox and is a year evenly divisible by 100 in the Shenshai calendar. At this point, begin counting backward by 120-year increments, noting that if a whole 30-day month were intercalated every 120 years, then 120 years consist of 11936 + 365 + 30 = 43,830 days. |
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| 1011 Mar 14 | 1 Far 380 | 2,090,398 | 359,920 (# + 43830) $ |
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At this point, also take note of the information that in 375 A.Y., given in texts as A.D. 1006, the position of the five gatha days was shifted from the end of the eighth month to the end of the 12th month. Thus, from this point in the table down, the internal structure of each year is different, with the gatha days being intercalary, not epagomenal. The length of the year is unaffected for these calculations, however. |
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| 1006 Mar 15 | 1 Far 375 | 2,088,573 | 361,745 ($ + 5365) |
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