Kuiri houxing jiyao 揆日候星紀要

Kuiri houxing jiyao 揆日候星紀要 is a collection of essays on astronomy written by Mei Wending 梅文鼎 (1633-1721), who also compiled the collection Lisuan quanshu 曆算全書.

The book of 1 juan consists of five independent chapters: Qiuri yingfa 求日影法, Lun hengxing 論恒星, Jixing kao 極星考, Wangliang gedao kao 王良閣道考, and Sanshi zaxing kao 三十雜星考. The dates of compilation of these essays stretch over long years, but Sanshi zaxing kao, the latest essay, was finished in 1692. The collection is included in the series Mei Wu'an Xiansheng lisuan quanshu 梅勿庵先生曆算全書.

The essay Qiuri yingfa 求日影法 method for measuring the sun's shadow is one of Mei's summaries of observational techniques. Setting up a gnomon to measure shadows was a traditional Chinese practice. However, by the early Qing period 清 (1644-1911), with the introduction of Western observational techniques, this method gradually began to fade. Mei placed great importance on this old technique and studied it alongside modern mathematical calculations in an effort to revitalise it. He established latitude tables (Weidu biao 緯度表) and a table of polar elevations (Beiji chudi du biao 北極出地度表), which explain the gougu 勾股 method (the Pythagorean theorem) and urged consultation of the "Eight Trigonometric Lines" (cha baxian fa 查八綫法), which detail the necessary mathematical calculations. In addition to the gnomon, the author also addresses the issue of magnetic declination (cipian jiao 磁偏角), demonstrating remarkable foresight.

The chapter "On fixed stars" (Lun hengxing 論恒星) is an important summary of Mei Wending's research on stars. He emphasizes the significance of the central stars (zhongxing 中星) of constellations. He employs tables to adjust the equatorial coordinates of various stars, as well as the equatorial and ecliptic coordinates of stars in the twenty-eight lunar mansions (ershiba xiu 二十八宿) and the degrees and minutes of stars entering various asterisms in the year 1688. All these star tables were derived from the celestial catalog in Ferdinand Verbiest's (Chinese name Nan Huairen 南懷仁; 1623-1688) Lingtai yixiang zhi 靈臺儀象志 (completed in 1672). Mei describes Western star maps with their constellations that differ from Chinese tradition. The 1,022 stars are categorised according to their magnitude. Subsequent sections analyse various historical and contemporary star catalogs. The final sections discuss transient celestial phenomena. These records, included in the chapter Lifa xichuan 曆法西傳 "Western transmission of calendrical methods" (which is part of the Xinfa lishu 新法曆書; see Chongzhen lishu 崇禎曆書), reference the works of Tycho Brahe (1546-1601).

The essay Jixing kao 極星考 "Investigation of the Pole Star" presents Mei's insights into the study of the celestial pole. It recounts historical observations, including the mentioning of the deviation of the Pole Star from the Immovable Point (budong chu 不動處) by three degrees during the Song period 宋 (960-1279). Mei also corrects wrong historical data. This study highlights the gradual shift of the celestial pole due to the precession of the earth's axis.

The essay Wangliang gedao kao 王良閣道考 is a study that verifies the historical records of the two Chinese constellations Wangliang 王良 (determinative star β Cas) and Gedao (ι Cas; both part of the constellation Kui 奎). The research confirms that the two constellations together comprise six stars, as documented in ancient Chinese astronomical texts.

The final essay "Examination of thirty miscellaneous stars" (Sanshi zaxing kao 三十雜星考), presents Mei Wending's research on the Islamic astronomical star catalogue, analysing a set of thirty miscellaneous stars from Islamic astronomy. Prior scholars, Yuan Shilong 袁士龍 (courtesy name Huizi 惠子) and Xue Fengzuo 薛鳳祚 (1600-1680), studied these stars but left gaps in their research. Mei Wending undertook a comprehensive examination and discovered that Islamic astronomy included astrological interpretations for the thirty miscellaneous stars, yet their Chinese equivalents had not been translated. By calculating their positions using precession, he successfully identified more than twenty of them and matched them with the corresponding Chinese star names. When compared with the results of Yuan and Xue, 70 to 80 per cent of their conclusions were in agreement, demonstrating the reliability of their independent studies.