An Integrated Approach: Tobias Mayer

  • John M. SteeleEmail author
Part of the Sources and Studies in the History of Mathematics and Physical Sciences book series (SHMP)


Three years after Dunthorne published the first detailed study of the moon’s secular acceleration, Tobias Mayer produced the first set of lunar tables which incorporated the secular acceleration directly into the calculation of the moon’s longitude. Dunthorne had provided a table that allowed a correction to be applied to lunar positions calculated from his lunar tables. Dunthorne’s correction, however, was applied after the moon’s position had been calculated. By contrast, Mayer integrated the secular acceleration within the initial calculation of the moon’s mean position. This meant that the effect of the secular acceleration was taken into account when determining the various equations of anomaly (which depend upon the elongation of the mean moon from the sun and the mean moon from the apogee). The difference between applying the correction for the secular acceleration before or after calculating the anomaly is small but not trivial, and Mayer’s method was the theoretically correct one. Mayer adopted a value for the size of the secular acceleration that was considerably smaller than that found by Dunthorne. Mayer did not explain how he had derived this value in the introduction to his published tables, but it is possible to reconstruct his general method from his preserved manuscript notes.


Solar Eclipse Secular Equation Lunar Eclipse Eclipse Observation Lunar Theory 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Egyptology and Ancient Western Asian StudiesBrown UniversityProvidenceUSA

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