Hop

Month number „ Column A entry Calc. line segment 1 Calc. line segment 2_Calc. line segment 3

Figure 7.7. A plot of the Column A entries (solar velocity in days/month) in Babylon Tablet No. 120 against month number, demonstrating the characteristic zigzag function of System B.

Tablet 5 Column F, which contains the lunar velocity, under the assumption of constant solar velocity (corrections in other columns were applied to get the "final" prediction). Column F found in Tablet 120 is also a zigzag function and represents a calculation of the lunar velocity. The Tablet 5 zigzag function is plotted in Figure 7.8a. The analysis results are shown in Table 7.13. The lunar velocity is high, especially that from Tablet 5, 13?5. Similarly large values are found from Column F on other System A tablets (Neugebauer 1955/1983, I, p. 58).

A final example of the zigzag function usage is in Column ® of Tablet 5 (Figure 7.9). The analysis results for all of the selected columns are shown in Table 7.13. Notice the difference between the period of the ® function and that of Column F of Tablet 5, but the similarity of the period with that of Column F in Tablet 120. Thus, we find that System A is scarcely cruder than System B, despite a simpler initial assumption about the Sun's motion.

The determinations of the rate of motion might have been obtained as follows: First, the Moon's longitude is directly measured by noting its position relative to that of reference stars near the full moon, month after month. The result is a tabulation of lunar longitude, as in Column B of Tablet 120. A table of the monthly differences in position from month to month is then drawn up (Column A), and the maximum, minimum, mean values, and period found. Once the function representing the run of values of the difference table is characterized by these variables, future positions of the Sun or Moon are obtained. The result is evocative of the modern mathematical process of integration. The relationship of Column A to that of Column B is revealed in rows 4 and 5 of Table 7.13, where the determined parameters of the zigzag function from Column A and the differences in Column B are essentially identical. Now, we discuss the treatment of the planets in the Mesopotamian tables.

7.1.4.4. Planetary Tables

Other texts deal with planetary positions. Neugebauer (1955/1983, Vol. II, p. 279) lists 11 ephemerides for Mercury, 9 for Venus, 8 for Mars, 41 for Jupiter, and 12 for Saturn; the procedural texts are also heavily weighted in favor of Jupiter. Nevertheless, taking all five planets together, there are fewer than half the number of lunar texts, indicating that the planets had distinctly less importance for Mesopotamia at that time. Neugebauer (1955/1983, Vol. II, pp. 279-281) notes how little the theory behind the planetary tables reflects observations. Moreover, although the data are sparse, they seem complete enough for scholars to conclude

Figure 7.7. A plot of the Column A entries (solar velocity in days/month) in Babylon Tablet No. 120 against month number, demonstrating the characteristic zigzag function of System B.

Table 7.12. Parameters for intersecting lines.

Tablet (Column)/parameters

ai

b1

a2

b2

a3

b3

0 0

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