Between Theory and Observations: Tobias Mayer's Explorations of Lunar Motion, 1751-1755

This book presents a detailed and rigorous account of the work of Tobias Mayer, a mathematician and astronomer of the middle 18th century. Mayer's most famous contribution is his set of lunar tables, which were the best available in their time. The use of lunar tables was the most sophisticated method to calculate latitude. Because of their accuracy, Mayer's lunar tables became very popular and were used extensively in nautical navigation.

The book focuses on three of Mayer's major achievements:

-First, is Mayer's dynamical lunar theory based on Newton's principle of gravitation. His theory is compared to Euler's work in celestial mechanics of the same period. Evidence is presented that refutes the commonly held opinion that Mayer's lunar theory was just a variant of Euler's, although certain similarities between the theories do exist.

-Second, the special computational scheme that is embodied in Mayer's lunar tables is investigated. This scheme is shown to originate in Newton's lunar theory of 1702.

-Lastly, the book provides a detailed analysis of Mayer's process of adjusting the coefficients of his lunar tables to fit an extensive collection of observational data. This regression technique can be considered a precursor to the later formalized least squares method.

This book is the most complete and accurate account of Tobias Mayer's contributions to lunar theory.