The Standard Scheme of the Moon and Its Mean Quantities

Abstract

The Papyrus Rylands 27, of the John Rylands Library, Manchester, is a portion of a Greek treatise or tract of the third century A.D., providing rules for the longitude and node of the Moon. Apart from the illuminating analysis provided by Hunt, it has been the subject of a number of profound studies by Neugebauer, van der Waerden and Jones.1 These have culminated in the presentation by Jones of what he calls the Standard Scheme of lunar motion, illustrated by its application in various parts of the Oxyrhynchus Papyri, and elsewhere.2 It is clear from all this that we have here a scheme for the computation of the true longitude and node of the Moon based on a Babylonian type of 'zigzag' model. Jones has provided all that one needs for the practical derivation of the lunar coordinates, including lengthy tables to facilitate the computation of the summation of values from the zigzag functions that determine the coordinates. That much completes the subject as a self-contained model within the context of 'arithmetical' schemes, but leaves untouched the question of the relation between the Standard Scheme and the trigonometrical models, that is, those based on the use of one or more epicycles, etc. The purpose of this article is to develop this relation, one that situates the model in the interface between Babylonian and Greek astronomy.