Since by the letter of Hammurabi it is indisputably established that the intercalation took place not in years previously determined but at the command of the king, those who in spite of this would maintain the existence of an intercalary cycle hold to the assertion that the 27-year intercalary period was not a strictly fixed but a free cycle. In other words the intercalation rule only runs:--“Within a period of 27 years 10 intercalary months are to be inserted, but the choice of the leap-years is left open to the astronomer”[933]. But this is nothing less than an abandonment of the intercalary cycle. The purpose of such a cycle is to render it possible to compute the calendar beforehand for any number of years to come, and this purpose is frustrated by a regulation of this kind. It only says that in _x_ years _y_ intercalary months occur: this is not a rule for intercalation but an empirical observation, which readily results from a proper treatment of the empirical intercalation. Such observations must have been made by the Babylonians. In a tablet published by Kugler it is said of Saturn and of the fixed star _kak-si-di_, respectively, “ ... the period of the visibility of Sirius amounts to 27 years. Turn back and consider day after day,” according to Weidner, p. 73; according to Kugler I, 47 the inscription runs, “Day by day ... shalt thou see (the same phenomena as 59, or 27, years before).” Both Kugler and Weidner find here a 27-year intercalary cycle regulated by the star; the former places it before 533 B. C., the latter at a considerably earlier period. But in accordance with what has here been said about the empirical regulation of the intercalation by phases of the stars it follows that there is no intercalation at all, but only the empirical verification of the fact that the new moon and Sirius come back after 27 years into the same mutual relationship: this will actually be the result with an accurate treatment of the intercalation based on the observation of this constellation.