Studies in the History of Natural Sciences NO.3 2011

Supplementary Research on the Gnomon Shadow Template from Taosi

HE Nu
（Archaeology Institute, CASS, 27 Wangfujing St., Beijing 100710, China）

Abstract  Based on the criterion of 1 Taosi chi equaling to 25 cm., the author  compares the precise calculations about the gnomon shadows of solstices and equinoxes at Taosi from 2,100 to 2,000 BC, to the color marks on the lacquer stick from royal tomb No. IIM22 at Taosi, from which the conclusion for the use of the stick as a gnomon shadow template is being affirmed. This conclusion is also supported by the archaeological contexts of jade Cong-cursor, Qi-shadow refiner, Qi-plumb bob, and archaeological evidence from early Taosi cemetery about using a vertical  pole for gnomon measurement.
Key words　 archaeo-astronomy, Taosi, gnomon shadow template

Chronology Issues of Astronomical Records in the Period of Tai’an to
Huangxing of the Northern Wei Dynasty

LIU Ciyuan
(National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China)

Abstract　 The astronomical records in “Weishu” are analyzed in this paper. It is discovered that 59 of the 62 continuous records were dated mistakenly ahead of time by one year in 457 to 469AD, the reign Tai’an to Huangxing. One possible reason is that a wrong conversion was used when those records were copied from another dynastic History “Songshu”. Another explanation is the historians of the Wei made wrong chronology of their own dynasty.
Key words　 history of astronomy, Astronomical record, Weishu, chronology

The Measurement Proof of Su Song’s Astronomical Clock Tower
WANG Dechang 
(Purple Mountain Observatory, CAS, Nanjing 210008,China)

Abstract  This paper demonstrates the scale value of six historical astronomical relics ranging from the Eastern Han Dynasty to the Ming Dynasty: 1 “Chi” (ancient Chinese “尺”)=24.5cm, the standard measurement in manufacture of astronomical instruments and eight “chi” high gnomon surveying shadow in Chinese history, which remained unchanged for 1500 years from the Eastern Han dynasty to the late Ming dynasty, thereby, the height (35.65—36 “chi”) and width (21 “chi”) of Su Song’s astronomical clock-tower in the Northern Song Dynasty has been set to the height (873—882 cm) and width (514.5 cm) correspondingly as well as the other parts which were determined by the criteria. This is a major revision and correction of the standard measurement for height (11—12 meters) and width (7 meters) of the astronomical clock tower restored by Wang Zhenduo in 1957 and later by many researchers and manufacturers at home and abroad.
Key words　 Su Song, astronomical clock tower, measurement

The Eclipse Calculation Accuracy of the Huihui Calendar

LI Liang,  LU Lingfeng,  SHI Yunli
(Dept. of History of Science, University of Science and Technology of China, Hefei 230026，China)

Abstract  Based on the original book Huihui calendar (回回历法Huihuilifa) used in Ming China (1368—1644), the eclipse accuracy of this calendar is analyzed with the method through the computer software developed by the authors. And then the result is compared with the eclipse calculation of Datongli used as the other official method in Ming China. From the above calculation and some original documents in Veritable Rcords of the Ming Dynasty (明实录Mingshilu), we concluded that the accuracy of Huihuilifa is not better than Datongli as to the middle of eclipse, but as to the calculation of the magnitude of eclipse, the Datongli couldn't hold its advantage over Huihuilifa. The reason for these features is related to the accuracy of the moon location with Huihui calculation.
Key words　 Huihui calendar,  Datongli,  eclipse

Exploration on Yanduan
——And on the Evolution of Algebraic Algorithm Mode in East Asia
XU Zelin
(School of Art, Donghua University, Shanghai 201620)
WEI Xia
(School of Mathematics ,Tianjin Normal University, Tianjin 300387)

Abstract　 Yanduan（演段）was the primary algebraic method in the Song and Yuan dynasties and commonly used in mathematics of the period. This method was accompanied by the transmission and reconstructing of Tianyuanshu（天元术） in Japan’s Edo（江户） period, and became the basic algebraic method in Wasan. However, the understanding of “Yanduan” was confused in China and Japan, and there is no exact interpretation as yet. This paper attempts to explore the meaning of “Yanduan” with a study on the course of its development in China and Japan, and concludes that “Yan（演）”denotes calculation and “Duan(段)” denotes the coefficient of polynomial ,so Yanduan is an algebraic method  of calculating the coefficient of polynomial with the polynomial as its center. The paper further discusses  the historical development of “Yanduan” in East Asia, and states that it originated from graphic interpretation used in equation in the Han and Tang dynasties, and gradually evolved as Tianyuanshu from Tiaoduanfa（条段法）in the Song and Yuan dynasties, ending with the decline of Yanduan along with the loss of TianyuanShu in the Ming dynasty. Nevertheless, the Hoshoho（旁书法）and elimination were evolved from TianyuanShu in Japan in the Edo period and enriched the concept of “YanDuan” with TianyuanShu、Hoshoho and elimination. In addition, Yanduan is an algebraic analysis method in East Asian traditional mathematics and contrasts finely with the Descartes’ methods in the West.
Key words  Yanduan , Tiaoduanfa , equation, elimination, algebraic analysis

Observation and Understanding of Crickets’ Behaviors by Chinese during Ancient Times to the Period of the Republic of China
CHEN Tianjia
（Center for Social Studies of Science, Peking University, Beijing 100871，China）
REN Dingcheng
（Center for Social Studies of Science, Peking University, Beijing 100871; College of Humanities & Social Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049，China）
Abstract  From the perspective of ethology on relevant Chinese documents about crickets  during ancient times to the period of the Republic of China, this paper finds that the Chinese people already recognized that crickets in different environments have different physical features, their behaviors display strong seasonal and day-night rhythm, it is possible to realize the trilateral relationship among cricket chirping, mating and aggressiveness to observe “female recognition” “female recollection” and “female indifference”, and they developed the technique to control temperature and humidity by using cricket pot． More importantly, the observations of cricket fighting by the Chinese show over ten detailed fighting patterns more than ones by modern ethologists．
Keywords　 China, history of zoology, ethology, cricket, games, behavior

T. S. Chang’s Contribution to the Quantization
of Constrained Hamiltonian Systems
YIN Xiaodong　
(Physics Department of Capital Normal University, Beijing 100048, China)
ZHU Zhongyuan
(Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China)

Abstract  This paper demonstrates an important contribution by T. S. Chang, a Chinese theoretical physicist, to the quantization of constrained Hamiltonian systems through textual research and analysis. It shows that in 1946 Chang pointed out that the previous studies about Hamiltonian canonical forms of constrained systems can not pass to quantum theory because these studies did not deal properly with one of the key issues, that is, undetermined multipliers. Meanwhile, he was the first to work out a feasible formulation of quantization which could solve this problem in many constrained systems.
Key words　 T. S. Chang, quantization of constrained system, contribution

A Case Study on China’s Self-made Major Technical Equipment: The Design and Manufacturing of Shanghai’s 120MN Forging Hydraulic Press
SUN Lie
(Institute for the History of Natural Sciences, CAS, Beijing 100190, China)

Abstract　As a successful self-made important machine, Shanghai’s 120MN forging hydraulic press has become a prominent landmark for the development of China’s industry, which has turned from copying to self-designing and self-manufacturing. Through technical analysis of the design and manufacturing of the body of the machine, especially its columns, beams and cylinders, this paper discusses technical difficulties, lines and measures in the process of the engineering led by Mr. Shen Hong. The case study indicates that the synthetic approach, which combines imitation with model, experiment and technical integration, was effective for manufacturing some major technical equipment independently in China.
Key words Shanghai’s 120MN forging hydraulic press, self-made, major technical equipment, Shen Hong, imitation, technical integration