A set of descriptions of apparent solar motion on the celestial sphere round the year appears in a couple of ancient Chinese materials, such as the Yüeh-ling(Monthly Ordinances) section of Li-chi(Record of Rites), Lü-shih Ch'un-ch'iu(Master Lü's Spring and Autumn Annals), and Huai-nan-tzu. It consists of the solar R.A.'s, twilight culminations and dawn culminations for twelve solar months. Each of the 36 articles is described with the name of one of the 28 Hsiu's. This set of data is the result of the first systematic application of the Hsiu system as an astronomical coordinate, and also the best preserved remnants of an observational method which had constituted the main part of the ancient Chinese astronomy. Many astronomers and historians, East and West, has been attracted to the Study of this material by its potential value as a definite clue to the chronology of the ancient history of China. They have held the general belief that, by the proper application of the precession of the equinoxes, they could reach the exact period in which the observations for this material took place. Certain as it may seem in principle, this goal was not so easy to achieve in practice. The main difficulty lay in the disharmony among the articles: while each of the articles, applied with the precession, points to a certain range of period, all the ranges that respond to the 36 articles do not seem to include a common range to satisfy all the articles. In a sense, the variances among interpretations on this material may be reduced to variances in the methods to overcome such disharmony. After reviewing the failure of existing studies to establish a convincing method, I have set up following principles to surmount this problem. i) Interpretations on the material will be, as far as possible, based on the astronomical function of the culmination observation. ii) A fraction of the material will he excluded from the final interpretation lest the result should be unduly affected by accidental mistakes. iii) Margins will be defined for various errors in such a way that will reflect the technical aspects of the observations. Keeping to these principles, I have come to the conclusion that the observations in question were made most probably during the first half of the fourth century B.C. During the procedure, I could also ascertain the astronomical function of the twilight and dawn culminations by examining analogous factors in later calendrical systems.