Shuǐ Èr Jú

局 means an arrangement, and the water bureau is the result of one small calculation. Find the stem of the 命宮 from the birth year by the rule that assigns a stem to 寅 and counts on. If that stem and branch fall on a water name in the 納音 song, which lists 澗下水, 泉中水, 長流水, 天河水, 大溪水 and 大海水, the chart is 水二局. A 甲 or 己 year with the 命宮 at 子 gives 丙子, 澗下水, for example.

The number two is the divisor that places 紫微. The calculator divides the lunar birth day by the bureau number, first adding the smallest amount that makes it divide evenly, then counts the quotient from 寅. An odd addition is stepped back that far and an even one stepped forward. For water the verse in 卷二 says day one is at 丑, day two at 寅, then one palace every two days, and the calculator's formula matches all of its table.

The same two is the age when the first ten-year period opens, in both the default chart and the book setting, though the book's rule for where that period sits differs, and no passage states the age as a rule. Only the 岁 in this verse supports it. The 長生 stages begin at 申 for this bureau, on which the book and the calculator agree, while they part over the direction those stages run.