is also expressed as a fraction, as will be explained below. Both the tropical year and synodic month were determined by observations, but they could be expressed as fractions in various ways that were consistent with observations within measurement errors. Use the chosen values of <span class="nowrap">P<sub>L</sub></span>, <span class="nowrap">P<sub>s</sub></span> and other observation data to set up a system of three congruence equations for N, the number of years between the superior epoch and a particul