‘Hausbackene Combinationen’

Abstract

The success of Mayer’s lunar tables depended to a large extent on his artful adjustment of their underlying coefficients to observations. In his own view, expressed in the introduction of Theoria Lunae, the theory was incapable of producing all coefficients accurately, hence fitting was a necessity. The size of such a task must not be underestimated: Mayer fitted all 14 longitude equations plus a few provisional ones plus the epochs and mean motions to over a hundred lunar observations. With least-squares algorithms now omnipresent on today’s computers, such a fit costs hardly more time than what is needed for the data entry. But the panorama looked completely different in the 1750s. Computers were workers of flesh and blood operating with pencil and paper, the method of least squares had not yet been invented, and even statistical reasoning about model fitting was in its infancy. One of the pioneers in this area was Tobias Mayer. He held a particular appetite for large data sets and their application to the modelling of reality: be it with regard to the position of the moon, a geographical map of Germany, or temperature distribution on the earth.