Mayer earned the lunar-table prize

Siegfried Bodenmann’s article “The 18th-Century Battle over Lunar Motion” (Physics Today, January 2010, page 27 ) leaves the reader with the erroneous impression that Tobias Mayer simply utilized Leonhard Euler’s lunar theory to produce the lunar tables that earned the £3000 reward paid to his widow by the British Parliament. The article states, “A look at [Mayer’s] correspondence and works reveals that his tables are based on the lunar theory of none other than Euler.”

According to Eric Forbes and Curtis Wilson, the lunar tables that Mayer submitted to the Admiralty in 1754 were a revision of his 1753 tables, which in turn were based on his own theory, not Euler’s. ¹ From the Forbes and Curtis article it seems clear that Mayer benefitted from Euler’s advice but pursued a somewhat different strategy. One important difference between the two is that Mayer allowed his theory to be guided by observations in evaluating the coefficients rather than trying to obtain precise values analytically through lengthy calculations. His theory was therefore semi-empirical, not purely analytic. Forbes and Wilson comment that Euler, the “supposed author of the theory on which Mayer’s tables were based” [italics mine], was “surprised” by his own £300 award. They imply that Mayer’s widow might have received as much as £5000 but for a letter of Alexis Clairaut’s published in an English magazine. In the letter Clairaut claimed that his and Euler’s theories were more rigorous than Mayer’s and that Mayer’s tables were accurate mainly because of his skillful discussion of observational data. Clairaut may well have been correct on both points. However, for reasons that should be obvious, one would expect the Admiralty to have been more concerned with accuracy than mathematical rigor.