Here he introduced many improvements in mapmaking, and gained a scientific reputation which led (in 1751) to his election to the chair of economy and mathematics at the University of Göttingen.

An improved set was later published in London (1770), as also the theory (Theoria lunae juxta systema Newtonianum, 1767) upon which the tables are based.

[1] Mayer left behind him a considerable quantity of manuscript material, part of which was collected by G. C. Lichtenberg and published in one volume (Opera inedita, Göttingen, 1775).

The remaining manuscripts included papers on atmospheric refraction from 1755, on the motion of Mars as affected by the perturbations of Jupiter and the Earth (1756), and on terrestrial magnetism (1760 and 1762).

His star catalogue was re-edited by Francis Baily in 1830 (Memoirs of the Royal Astronomical Society IV, 391) and by Arthur Auwers in 1894.