(ProQuest: ... denotes formulae omitted.)4. Discussions and ResultsThe relatively accurate observational data obtained by the early Islamic astronomers resulted in the good values for the length of the seasons and for the time intervals between successive mid-seasons that were achieved (Tables 1 and 2) and, consequently, as we shall see presently, the reasonable values for the solar eccentricity that were obtained in the Middle East during the medieval period. Since the accuracy of the observational data has already been discussed by Said and Stephenson,95 we turn our main attention to making comparisons between the methods and the corresponding recorded historical values.96 In order to reach the main goals defined at the beginning of the paper, it should be mentioned that, concerning the varying historical values for the solar orbital elements, we are confronted with a three-fold problem consisting of the following factors:(1) the sensitivity of methods and observational data;(2) the methods and theoretical errors due to the mismatch of the two models, eccentric and elliptical; and(3) the secular decrease in the eccentricity of the Earth.(1) As explained in Section 2, the three methods are all sensitive in varying degrees to the input data, but the essential observational data for them are substantially different. This makes, hypothetically, the Three-Point Method more grounded and the Seasons Method less trustworthy.It can be seen from Tables 1 and 2 that the immense observational activities in the Middle East between A.D. 800 and 1000 brought clearly into focus the sensitivity of the Seasons and Mid-Sign Methods to the observational data, by leading to different values for the solar eccentricity in a relatively short period (as remarked by BirunT himself; see below). The sensitivity in the case of the Seasons Method led, for instance, to an eleventh-century astronomer's obtaining Battanl's value for e (cf. Table 1, no. 7), and (cf. Table 1, no. 8) to a twelve-century astronomer's producing that ofYahya.Basically, the possible sources of the observational errors in measuring the time interval between an equinox and its subsequent solstice or between two successive mid-seasons may be due to (a) the skill of the observers, (b) the probable deficiencies and systematic errors in the instruments applied, and (c) the inevitable difficulties and possible errors in exact determinations of the instants of the equinoxes, midseasons, and solstices.It should be noticed that it is difficult to distinguish between the errors caused by factors (a) and (b). Said and Stephenson have analysed the measurements of the solar meridian altitude related to equinoxes, solstices, and mid-seasons by a group of early Islamic astronomers (al-Marwarudhl, the Banu Musa, Ibn 'Ismat, al-Suft, Abu Mahmud al-Khujandi, and BirunTin both Ghazni and Juijaniyya), and confirmed that the results achieved are of a high precision. The smallest error was observed in the case of al-Marwarudhl (±0.01°), while none of the errors exceeded ±0.02°, which falls within the maximum resolution power of the unaided eye (around one arc-minute).97 Besides high observational accuracy, as Maeyama notices,98 two other factors were effective in achieving these results: the neglect of the Ptolemaic solar parallax (except in the case of Ibn 'Ismat),99 and the fact that the observations were made in localities (in the Middle East) with a low geographical latitude, which caused the meridian solar observations not to be affected too much by refraction.100Now, in view of this remarkable accuracy, the problem of distinguishing factors (a) and (b) appears to be of less significance. However, the recorded observational data may inspire the idea that the instruments applied involved mistakes and deficiencies; for example, Said and Stephenson found that BlrQnT's observation in Ghazni was exposed to a systematic error of around -0. …