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corrected a typo
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ytliu0 committed May 11, 2024
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Expand Up @@ -252,7 +252,7 @@ <h2 id="references">Footnotes and References</h2>

<li id="vondrak11"><p>[<span class="ref">Vondr&#225;k</span>] J. Vondr&#225;k, N. Capitaine, P. Wallace, <a href="https://ui.adsabs.harvard.edu/abs/2011A%26A...534A..22V/abstract" target="_blank">"New precession expressions, valid for long time intervals"</a>, Astron. Astrophys., 534, A22 (2011).</p></li>

<li id="xiaoan"><p>[<span class="ref">Xiaoan</span>] Many scholars at that time objected using dingqi for calendar calculation and intercalation. Two of the famous scholars were W&#225;ng X&#299;ch&#462;n (王錫闡) and M&#233;i W&#233;nd&#464;ng (梅文鼎). W&#225;ng not only criticized using dingqi for intercalation, but only pointed out a sneaky thing the Imperial Astronomical Bureau did in order to avoid being ridiculed. He pointed out that there was a leap month after month 7 in <span class="nowrap">N<sub>1661</sub></span>, but then two major solar terms Z11 (Winter Solstice) and Z12 (Great Cold) appeared in month 11. The subsequent major solar term Z1 (Rain Water) was originally placed on the last day of month 12, but then the first month of <span class="nowrap">N<sub>1662</sub></span> would not contain any major solar term. The Astronomical Bureau decided to move the New Year Day a day ealier so that it would contain Z1, thus moving the month without major solar term to the last month of <span class="nowrap">N<sub>1661</sub></span>. Looking at the imperial planetary almanac for <span class="nowrap">N<sub>1662</sub></span> on the <a href="https://qingarchives.npm.edu.tw/index.php" target="_blank">Digital Library of Qing Archives</a> managed by the National Palace Museum in Taiwan, I see that the month 1 conjunction was listed on a y&#464; h&#224;i day (18 February, 1662). However, from the positions of the Sun and Moon given by the almanac, it's clear that the conjunction should have been on the following day (19 February). This cofirms W&#225;ng's claim. Such a sneaky operation was only done once. There were seven more cases in the Qing calendars where two months without a major solar term appearing within several months. One such case occurred in the first month of <span class="nowrap">N<sub>1833</sub></span>. The situation was exactly the same as that of <span class="nowrap">N<sub>1662</sub></span> originally planned: the major solar term Z1 appeared on the last day of month 12 in <span class="nowrap">N<sub>1832</sub></span> and there was no major solar term in the first month of <span class="nowrap">N<sub>1833</sub></span>. The conjunction date was not altered in this case. After the fall of the Qing dynasty, the first month of <span class="nowrap">N<sub>1985</sub></span> also did not contain a major solar term. The first month of <span class="nowrap">N<sub>2034</sub></span> won't contain a major solar term either.</p>
<li id="xiaoan"><p>[<span class="ref">Xiaoan</span>] Many scholars at that time objected using dingqi for calendar calculation and intercalation. Two of the famous scholars were W&#225;ng X&#299;ch&#462;n (王錫闡) and M&#233;i W&#233;nd&#464;ng (梅文鼎). W&#225;ng not only criticized using dingqi for intercalation, but only pointed out a sneaky thing the Imperial Astronomical Bureau did in order to avoid being ridiculed. He pointed out that there was a leap month after month 7 in <span class="nowrap">N<sub>1661</sub></span>, but then two major solar terms Z11 (Winter Solstice) and Z12 (Great Cold) appeared in month 11. The subsequent major solar term Z1 (Rain Water) was originally placed on the last day of month 12, but then the first month of <span class="nowrap">N<sub>1662</sub></span> would not contain any major solar term. The Astronomical Bureau decided to move the New Year Day a day earlier so that it would contain Z1, thus moving the month without major solar term to the last month of <span class="nowrap">N<sub>1661</sub></span>. Looking at the imperial planetary almanac for <span class="nowrap">N<sub>1662</sub></span> on the <a href="https://qingarchives.npm.edu.tw/index.php" target="_blank">Digital Library of Qing Archives</a> managed by the National Palace Museum in Taiwan, I see that the month 1 conjunction was listed on a y&#464; h&#224;i day (18 February, 1662). However, from the positions of the Sun and Moon given by the almanac, it's clear that the conjunction should have been on the following day (19 February). This cofirms W&#225;ng's claim. Such a sneaky operation was only done once. There were seven more cases in the Qing calendars where two months without a major solar term appearing within several months. One such case occurred in the first month of <span class="nowrap">N<sub>1833</sub></span>. The situation was exactly the same as that of <span class="nowrap">N<sub>1662</sub></span> originally planned: the major solar term Z1 appeared on the last day of month 12 in <span class="nowrap">N<sub>1832</sub></span> and there was no major solar term in the first month of <span class="nowrap">N<sub>1833</sub></span>. The conjunction date was not altered in this case. After the fall of the Qing dynasty, the first month of <span class="nowrap">N<sub>1985</sub></span> also did not contain a major solar term. The first month of <span class="nowrap">N<sub>2034</sub></span> won't contain a major solar term either.</p>
<p>The history of the controversies on using dingqi in calendar calculation was similar to the situation of using dingshuo (true lunar conjunction) in calendar calculation. Before the 7th century, lunar conjunctions in a calendar were calculated based on Moon's mean motion, which were called the pingshuo (mean conjunctions). In the fifth century, astronomer H&#233; Ch&#233;ngti&#257;n (何承天) advocated using dingshuo in calendar calculation. However, the frequent appearances of three consecutive long months and two consecutive short months were strongly opposed by other people and dingshuo was not implemented. In 619, the <i>Wuyinyuan</i> astronomical canon (戊寅元曆) broke the tradition and used dingshuo in calendar calculation, but dingshuo was abandoned after the appearance of four consecutive long months in 645. About 20 years later, the <i>Linde</i> astronomical canon (麟德曆) reintroduced dingshuo, but a new <i>jinshuo</i> rule (進朔法) was introduced to reduce the frequency of several consecutive long and short months. This rule was also adopted by the subsequent astronomical canons until 1281 when the <i>Shòushí</i> canon (授時曆) abolished the rule. At that time, no one cared about four consecutive long months or three consecutive short months. Today, some people don't even know that sometimes four consecutive long months appear in the Chinese calendar. Even though dingqi has been used in calendar calculation for almost 400 years, some people still criticize it to this day and advocate the restoration of pingqi. However, these people don't advocate the restoration of pingshuo.</p>
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