Studies in the History of Natural Sciences 　NO.4 2003

Hermann Weyl's Generalization About Riemann Geometry……HAO Liuxiang

【Abstract】 Based on first-hand materials, this article mainly focuses on Hermann Weyl's systematical elucidation and significant generalization about Riemann geometry during the year 1917—1923, including the intrinsic definition of affine connection, the foundation of purely infinitesimal geometry, the introduction of projective and conformal structure, and group analysis of the nature of metric space. Partly because Weyl's generalization did not enter into modern nomenclature of differential geometry, Weyl's contribution has almost been buried in oblivion. But the author argues that Weyl's work in this field is not only an important historical linkage from Riemann geometry to fiber bundle but also a main incentive for his research diversion from analysis to Lie group.

From Scientific Propaganda to Scientific Research:A Change in the Strategy of Saving the Nation of the Science Society of China……ZHANG Jian

【Abstract】 Saving the nation by science”became a trend of the times after the revolution of 1911.As founding an organization to rally comrades was one of the significant measures for developing science,the Science Society of China was established in the U S A.In view of the fact that the failure of preceding scientific propaganda,the undeveloped science of China and the limited capability of its own members,the Science Society of China initially chose to propagate scientific knowledge as a plan of saving the nation. However,merely persisting in doing propaganda meant indulging in empty talk after all.Hence,the Science Society of China advocated scientific research while its members engaged themselves in concrete practice.The Society set up the Biological Laboratory,which later became a model of scientific research organization in modern China.As the most outstanding “voice of science”in the May 4th Movement,scientific research exerted a far-reaching influence on modern Chinese science.

The Ratios of Several Kinds of Rice in Ancient China——A New Research Based on the Suanshu Shu and Qin Bamboo Strips……ZOU Dahai

【Abstract】 The records of several kinds of rice from the Nine Chapters on Mathematical Procedures and the Shuowen Jiezi have some differences, which have been collated by several scholars referring to the Qin bamboo strips unearthed from Shuih udi of Yunmeng county in Hubei province and the bamboo book Suanshu Shu unearthed from Zhangjia Shan of Jianglin county in Hubei province. This paper provides new collations, and argues that both the Nine Chapters and the Shuowen have fewer mistakes than what they were thought of. The mistakes in the Nine Chapters are only the ratios of the Zuomi and Zuofan, and the rate of Baimi in the Shuowen is not of the early times. The kinds of rice husked from millet and paddy belong to two series, which cannot be confused. The authors of the Shuowen and Nine Chapters did not directly accept the influences of Suanshu Shu.

Quantification and Reduction About Records of Sunspots in Annals……WANG Yumin

【Abstract】 The records of “big as X” of sunspots in annals were estimation and measurement about the area of sunspots. One can quantify and reduce them with the celestial sphere model of observing astronomical phenomena with the naked eyes. The author uses the principle of seeing physiology and statistical method and the model of the plane vault of heaven to reduce to the area the scale of 17 comparative objects that come from 95 records of “big as X” of sunspots in annals.

Algorithm for the Transformation of Coordinates Between Equator and Lunar Orbit in the Shoushi Li……QU Anjing

【Abstract】 A main aim of the lunar motion theory in ancient China is to calculate the longitude of the Moon at the lunar orbit at any given time. One could obtain this parameter from the longitude or right ascension of the Moon if one knew the transformation of coordinates between the ecliptic or the equator and the lunar orbit. It is well known that the jiu dao shu, an algorithm for determining the nine paths of the Moon, is the core algorithm in a traditional Chinese calendar-making system before the Shoushi Li (AD 1280). It is an algorithm designed for the transformation of coordinates between the ecliptic and the lunar orbit. Unfortunately, according to the study of Yabuuti Kiyoshi (1906-2000), the precision of the jiu dao shu is not good. In their calendar- making system of the Shoushi Li, Guo Shoujing (1231—1316) and Wang Xun (1233—1281) replaced the jiu dao shu with a new method, which is an algorithm designed for the transformation of coordinates between the equator and the lunar orbit. The new model of the lunar motion theory in the Shoushi Li is reasonable and effective. It deserves to be served as a successful reformation in the history of mathematical astronomy in ancient China.

Mei Wending's Theory About Left-handed Rotation of the Sun,Moon and Five Planets Around the Earth and Its Drawbacks……YANG Xiaoming

【Abstract】 In the debate about the left-handed or right-handed rotation of the Sun, Moon and Five Planets (namely, Mercury, Venus, Mars, Jupiter and Saturn) around the Earth, the left-handed rotation theory was almost in silence during the period from Ming Dynasty to Qing Dynasty. In early Qing Dynasty, however, influenced by Western astronomy especially its multi-heaven theory, Mei Wending proposed a new kind of left-handed rotation theory, that is, since the heaven is composed of many layers or circles and as a whole body, every layer of heaven which loads the Sun, Moon, Five Planets or even fixed stars has to rotate leftward dragged by outer layer of motive heaven. Meanwhile according to Mei's viewpoint, the rotation axis of motive heaven is the north pole of heaven, whereas the one of other layers of heaven the ecliptic pole, thus the questions are illuminated, such as the motions in view of the Sun, Moon and Five Planets from north to south as well as from east to west, and in view of their differences of velocity . Furthermore, this paper compares Mei's theory with the right-rotation theories especially the right-rotation theory of his contemporary Huang Baijia, and concludes that Mei's theory has more drawbacks, mainly in reasoning, actual measures and application. In the end, the paper analyses the origin and influence of Mei's theory.

Euler's Achievements in Combinatorics……LIU Jianjun,LIU Qinying

【Abstract】 Euler's foundational work on four basic questions, partition, derangement, Euler's square and Catalan numbers, is presented in this paper. The skills and methods that Euler gave in solving those questions have become the basal ones in combinatorics. Additionally, the paper offers supplement to the research on Euler's mathematical work.

The Scientific Significance for Discovering the Phase and the Date of Calendar on the Wu Lai Tripod Cauldron……CHEN Jiujin

【Abstract】 Someone had confirmed the Wu Lai tripod cauldron,which has on it king-year,phase and Chinese era records,as a kind of instrument in King Xuan's era according to a compositive consideration about the cached Western Zhou instrument group which was unearthed early this year from the Yang-family village in Mei county.But according to A Chronicled List for Twelve Dukes in Records of the Historian, the phase and Chinese era records of the 42nd and 43rd year,which is calculated from the numbering of years of King Xuan,do not agree.Besides it was approved by the king-year,phase and Chinese era records on the unearthed bronze instruments,so the numbered years of King Xuan are explicit and shouldn't be altered casually.If the years were still numbered based on King Li during the years of Gong He after King Li had gone to Zhi(NE5E9) for shelter in the 37th year of King Li's reign,the phase and Chinese era would coincide exactly.So this article confirms that the 42nd and 43rd year on the Lai tripod cauldron are the 42nd and 43rd year of King Li.The words “if the king said”in the table of Lai tripod cauldron refer that the ministerial dukes reigned in the name of King Li.Lai tripod cauldron and the table of Lai plate are not enough to ascertain the sequence of them.

On the New Translation of Kuhn's The Structure of Scientific Revolution……SUN Xiaochun

【Abstract】 This essay reviews the new translation by Jin Wulun and Hu Xinhe of Thomas Kuhn's The Structure of Scientific Revolution, published by Beijing University Press (2003). Two previous Chinese translations of the book exist: one is translated by Li Baoheng and Ji Shuli, published in Shanghai in 1980; the other is by Cheng Shude et al, published in Taibei in 1989. The new translation is problematic. It is no better than the former one, which is itself not recommendable, and is not a match to the latter. The examination of a sample of 22 short paragraphs discussing the nature of a paradigm, reveals an alarmingly high rate of occurrence of mistakes. Also, it reveals that the second translator, translating the second half of the book, used the Taibei translation as his major reference, but did not mention it. As a result, the second half of the translation is very similar to the Taibei one; but at the same time it has some improvements made by the new translator. Finally, the author laments on the general low quality of translation works in current academic world of China.