Studies in the History of Natural Sciences  NO.3 2009 

On the Gnomon Shadow Template Function of the Lacquer Stick from the Royal Tomb IIM22 at Taosi Walled-town of Middle Period

HE Nu

（Institute of Archaeology, Chinese Academy of Social Sciences, Beijing 100710, China）

Abstract　In 2002, the lacquered wooden stick unearthed from the top part of the chamber of the royal Tomb IIM22 of Middle Period at Taosi Walled-town, where is traditionally considered as “the Capital for King Yao in Pingyang”. Standing against the southeastern wall of the chamber, remaining 171.8 cm. in length, with a damaged section of 8.2cm, it could be reconstructed as long as 180 cm. Tagged as IIM22∶43, the stick is painted with lacquer in dark and green sections alternately, bounded with pink belts, implying its special function. What is very striking is that the Section 10 in green is abnormally interrupted by a pink belt, the Secition 11. The length from Section 1 to 11 is 39.9 cm. According to the research for the length unit of Taosi Culture, 1 chi is equivalent to 25 cm, so that 39.9 cm is 1.596 chi, parallel to the length of solar shadow right in the noon of summer solstice——1.6 chi, based on the records in historical document entitled as Zhou Bi Suan Jing. From Section 1 to 33, the stick might have measured the solar shadow of spring equinox and autumn equinox, which is 141.6 cm long, parallel to 5.664 chi.If one moves the stick forward, and puts the top of the stick right on the end signal of previous stick could reach to the length totally 337.4 cm, 13.496 chi, indicating the winter solstice at Taosi over four millenaries ago. Given this, we estimated that the Lacquer Stick IIM22∶43 might have served as gnomon shadow template which could be dated at Middle Taosi period, ranging from 2100 to 2000 BC.

Key words　Taosi's royal tomb IIM22, lacquer stick, gnomon shadow template

Exploration in Alchemy of Western Han Dynasty

HAN Jishao

（Institute of Religion, Science and Social Studies, School of Literature & Journalism, Shandong University, Jinan 250100, China）

Abstract　There are two kinds of documents on the practices of early Chinese alchemy. The first kind shows that fangshi（方士） of the Western Han dynasty used cinnabar and mercury to make fake gold, which was called huangbai（黄白） or huangye（黄冶） at that time. Influenced by re-vermilion （huandan） theory which emerged in the mid of the two Han dynasties, the second kind takes fangshi's practices of Western Han for true alchemy. Those practices, however, revealed the idea of becoming immortal by eating gold, and promoted fangshi's discovering the secret of re-vermilion. There was an important theoretical revolution in the early history of Chinese alchemy.

Key words　Western Han dynasty, Chinese alchemy, yellow and white （huangbai）, golden elixir, eating and drinking for immortality （immortal diet）

Further Discussion on the Reduction of Fractions to a Common Denominator in Nine Chapters on the Mathematical Art

ZHU Yiwen

（Institute for the History of Natural Science, CAS, Beijing 100010,China）

Abstract　As regards the history of Chinese mathematics, our predecessors have a common understanding about the reduction of fractions to a common denominator in Nine Chapters on the Mathematical Art, which is actually the same as the rule of today. This article argues that the rule in Nine Chapters on the Mathematical Art is different from the rule of today, which uses a whole number to multiply a fraction so as to get an integer. Moreover, because of misapprehension, there is a misunderstanding between “finding a common denominator to reduce fractions” in Jingfen rule（经分术） of Nine Chapters on the Mathematical Art and “reducing fractions to find a common denominator” in Shaoguang rule（少广术），and there is dispute on collation of the precise rule of annular field problem. Based on new understanding of the reduction of fractions to a common denominator, the article reviews the problems above and reaches the conclusions as follows:“finding a common denominator to reduce fractions” and “reducing fractions to find a common denominator” are different in arithmetic procedure, and the main purpose of the precise radio rule of annular field problem is to introduce the concept of“tongfen neizi”（通分内子）。Suanshushu（算数书） and the main body of Nine Chapters on the Mathematical Art are both accomplished in the pre-Qin period. It is hard to decide which is earlier and which is later. However，there must be some common rules. Actually, on the reduction of fractions to a common denominator, the two books are the same. And the result enhances the article's argument. The article argues further that the basic reason is that ancient rule and today's rule are equivalent in mathematical principle, and the main cause for misapprehension not only roots in overlooking the unification of the ancient mathematical terms and mathematical rules, but also roots in overlooking the economical and applied demands for using counting rods, and also roots in largely using nowadays knowledge to explain ancient knowledge. In fact, there is no present mathematics rule corresponding to the rule in Nine Chapters on the Mathematical Art. The misapprehension of the past obliterates the history of the reduction of fractions to a common denominator. From the disagreement between the main Shaoguang rule（少广术） and its secondary rules, a historical trace of Suanshushu in pre-Qin period to Nine Chapters on the Mathematical Art composed in the Western Han Dynasty can be found.

Key words　Suanshushu（A Book of Arithmetic）, Nine Chapters on the Mathematical Art, tongfenshu（The Reduction of Fractions to a Common Denominator）

The Refused Goethe: Contemporaries' Acceptance of and Responses to Goethe As a Researcher of Nature

MO Guanghua

（Sichuan International Studies University, Chongqing 400031,China）

Abstract　As a great figure of world literature, Goethe spent more than fifty years in studying nature. During his study, reams of writings on this subject were accomplished. As far as his study was concerned, his contemporaries responded quite differently. Though his science works Versuch die Metamorphose der Pflanzen zu erklren and Zur Farbenlehre were widely accepted, his outstanding achievement in optics and nature research met with the cold shoulder from many physical scientists and philosophers of the mainstream of that age. Only a few young scientists who were influenced by German Romanticism show him some understanding and encouragement. Goethe attaches much importance to intuition, belittles logic and reason, and excludes the experimental methods of maths and modern science, all of which, to a large extent, predisposes Goethe to the refusal he suffers from the history of modern natural science.

Key words　Goethe, study of nature, die Metamorphose, Zur Farbenlehre

The Calculus of Variations from Euler to Lagrange: As a Result of Formalized Improvement

JIA Xiaoyong,

（School of Mathematics and Statistics, Chongqing University of Arts and Sciences, Yongchuan 402160, China）

LI Yuewu

（Mathematics Department, Hezuo Minorities Teachers College, Hezuo 747000, China）

Abstract　The calculus of variations was established as a distinct branch of analysis with the publication in 1744 of Euler's Methodus inveniendi curvas lineas maximi minimive proprietate gaudentes sive solution problematis isoperimetrici latissimo sensu accepti. The invention in 1755 of the δ -algorithm of Lagrange ushered in a new epoch in the calculus of variations. From Euler to Lagrange the subject had gone through great innovations. Based on some original literature and the detailed comparison and analysis between methods of Euler and Lagrange, the background and genesis and influence of Lagrange's algorithm are considered and explored in this paper. Finally, the paper concludes that Lagrange's improvement in the calculus of variations is essentially the result of formalization, and that the success of the formal improvement produced great effects on the development of the 18th calculus, and to some extent reinforced the trust of mathematicians in mathematical symbol.

Key words　the calculus of variations, L. Euler, J. L. Lagrange, formalization

An Historical Perspective on the Study of Chinese Nomenclatures for Benzene and Aromatic Compounds: 1875—1945

ZHANG Hao

（Center for General Education，I-Shou University）

Abstract　This paper mainly inquires into the history of Chinese translations for such chemical compounds as benzene, toluene, xylene, mesitylene, naphthalene, anthracene and phenanthrene during 1875—1945. In Chinese, the terms used for these aromatic compounds consist of a syllable-imitation character and a 艹 grass radical, making them different from both （1）, the acyclic hydrocarbons, which were translated using a 火 fire radical after their combined chemical property of carbon; and （2）, aldehydes, ketones, and ethers, all of which were translated by the General Committee on Scientific Terminology （1921） using existing characters combined with a 酉 bottle radical. In the nineteenth century, the Chinese terms for benzene compounds were transliterated as pianxini 徧西尼 and piansuli 徧苏里. However, after the publication of Yu Heqin's Draft for Chinese Terms of Organic Chemistry in 1908, most chemical compounds were translated based on their chemical structures, and thus benzene compounds, for example, were translated as lunzhi 轮质, kun 困, lun 菕, lunti 轮体, and huantanqing 环炭化轻. Later, in 1931, Tu Xunli developed a principle using a syllable-imitation character, combined with a grass radical, for all aromatic compounds except benzene: thus nai 艿 for naphthalene, an 荌 for anthracene, and wen 芠 for phenanthrene. In 1932 Tu's principle for aromatic compounds was accepted in the Chemical Forum held in Nanjing. One year later, these and other compounds were listed in the Principles for Chemical Nomenclature and became standard organic terms in the Chinese language, including ben 苯 （benzene）, jiaben 甲苯 （toluene）, erjiaben 二甲苯 （xylene）, 1,3,5 sanjiaben 1,3,5-三甲苯（mesitylene）, nai 萘（naphthalene）, cong葱（anthracene）, and fei 菲 （phenanthrene）.

Key words　benzene, chemical nomenclature, aromatic compounds

The Rise of Special Scientific Society in China in 1930s: A Case Study on Chinese Chemical Society

YUAN Zhendong

（School of Chemistry and Environmental Science, Henan Normal University, Xinxiang 453007, China）

Abstract　In 1930s, the mass of special scientific talents for each subject, relatively steady social environment and the energetic support to scientific undertakings by Nanjing Nationalist Government provided fitting conditions for the establishment of special scientific society. After the establishment of Chinese Chemical Society （CCS）, other special scientific societies established in succession. Consequently, a new era of the development of scientific societies in China was ushered in. In operating its buisness, each society not only used foreign experience for reference and but also took domestic practicality into account. For example, during the period of establishment, the CCS founded all kinds of leading organizations, established and emended its constitution, set up branches at home and abroad and expanded its members rapidly, provided its members chances to communicate with each other by holding annual meeting and publishing periodicals, Journal of the Chinese Chemical Society,Chemistry and The Chemical News Reagent, which gathered and fostered the Chinese chemist group and through which the world chemical communication recognized Chinese chemical researches. Meanwhile, members made concerted effort to pull together and overcome economic difficulties. In one word, the development of special scientific society in this period has a far-reaching influence on Chinese scientific undertakings.

Key words　special scientific society, Chinese Chemical Society, organizations, constitution, members, annual meeting, periodicals

Contextual Explanation on the Occurrence of Scientific Revolution and Its Realistic Significance

WEI Yidong， SU Yujuan

（Research Center for Philosophy of Science and Technology, Shanxi University, Taiyuan 030006, China）

Abstract　Scientific revolutions are important changes in the development of science. In history, quite a number of scholars have studied the scientific revolutions. Among them there is Cohen, who put forward four criterions for judging the occurrence of scientific revolutions. But these criterions can't explain that theoretical or minor revolutions ever happened, so that people are inclined to doubt whether the scientific revolutions actually took place. Through an overall analysis of the scientific revolutions in the history, the authors of this paper give a new definition of scientific revolution. Examining the indequacy of internalist and externalist explanation, they put forward a contextual explanation for the occurrence of scientific revolutions as well as their transformation model. The contextual explanation accounts for not only the theorical problem of the occurrence of scientific revolutions, but also the enhancement of the ability of science and technology in China.

Key words　scientific revolution, internalist and externalist explanation, Cohen's explanation, contextual explanation

On Bian Gang's Method of “Subtract Before Multiply” Being Derive from Yi Xing

WU Jiabi

（National Astronomical Observatory, CAS, Beijing 100012, China）

Abstract　The method of “subtract before multiply” summarized by Bian Gang of late Tang dynasty is an important one about ancient Chinese calendric calculation. Previously, nobody knew where it derived from. In fact, it was spread from the calculating formula for the difference of ecliptic longitude and right ascension in monk Yi Xing's Dayan Calendar. Being derived from traditional Chinese algorithm, it was similar to the simple proposition of isoperimetric problem that of all isoperimetric rectangles only the area of a square was maximum.

Key words　Bian Gang, calendar, solar equation, extremum, isoperimetric problem