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The Ancient World

months, showing that these sums were used for prediction at that interval. Brack-Bernsen has undertaken the comparison of SU + NA and ME + GE6 in goal-year texts of the third and second centuries B.C. and the early text known as Cambyses 400 from 523-22 B.C. with those computed from modern lunar theory. Although the quantity of surviving material available thus far is not large, the results have met expectations in showing that the observed quantities match the computed within reasonable limits of error of measurement. The author has also found, in part theoretically and in part using the goal-year texts and a procedure text known as TU 11 giving instructions for computation, how the lunar four may be computed individually from values one Saros earlier, and how the lunar four one Saros plus six months earlier was also used to compute the two remaining quantities of the lunar six, which are: NAN time from sunset to moonset the evening of first visibility KUR time from moonrise to sunrise the morning of last visibility. The rules are simple and ingenious. SU is computed by adding to and NA by subtracting from its value one Saros earlier one-third of SU + NA one Saros earlier, and ME is computed by adding to and GE6 by subtracting from its value one Saros earlier one-third of ME + GE6 one Saros earlier, all quantities found regularly in the goal-year texts at intervals of one Saros. NA^ and KUR are more complicated. TU 11 gives the rule for two Saroi, but at an interval of one Saros NAN is equal to its value one Saros earlier minus one third SU + NA one Saros plus six months earlier, and correspondingly KUR is equal to its value one Saros earlier plus one third ME + GE6 one Saros plus six months earlier. And these quantities too, at intervals of one Saros plus six months, are also found in the goal-year texts. May I say in conclusion that Dr. BrackBernsen has come closer to the very foundation of Babylonian lunar theory, both theoretically and empirically, than any research done prior to her own work. The results are extraordinary and entirely transform our understanding of Babylonian lunar theory and its empirical foundation. And what she has accomplished here will doubtless lead to more discoveries revealing still more of the first and most sophisticated science of antiquity.