Tobias, one of the greatest astronomers of the eighteenth century, was the son of a civil engineer, and was born at Marbach in Württemberg, on the 17th February 1723. The elements of mathematics he received from his father, but the rest of his knowledge in that science was self-acquired. At an early age he was left an orphan, and was forced to earn a livelihood by giving mathematical lessons. His first publications, A Treatise on Curves for the Construction of Geometrical Problems, and A Mathematical Atlas, appeared in 1745. In the following year he contributed to the establishment of the Cosmographical Society of Nuremberg. He was appointed director of the observatory of Göttingen in 1751; and there, in the midst of the turmoil of the Seven Years' War, and in the vicinity of powder magazines, he prosecuted his studies with untiring devotion. The Lunar Tables, the chief result of his labour, appeared in the "Acts of the Academy of Göttingen" in 1755. About this time also, Mayer discovered the principle of the Repeating Circle. His extreme application, however, had caused a disease which was gradually undermining his health. He died on the 26th February 1762, at the age of thirty-nine. Over his grave at Göttingen, a monument was erected in 1801. (For an account of Mayer's Lunar Tables, and his invention of the Repeating Circle, see Dissertation Fifth, § 2, pp. 749, 781.)

An edition of his works had been promised, but of these only one volume appeared under the care of Lichtenberg, his friend and associate. It contains, 1. A method for determining more exactly the variations of the thermometer, with a formula for calculating the mean degree of heat in every latitude, and the seasons of the year in which occur the greatest heat and the greatest cold. 2. A memoir on the observations which he made with his mural arc of six feet, and the observations to which he subjected that instrument. 3. An easy method for calculating eclipses of the sun, being at bottom the method of Kepler, which La Caille also reproduced in his Leçons d'Astronomie. 4. A memoir on the affinity of the colours, in which he recognised only three primary colours, all the rest being obtained by different combinations of these. 5. His new catalogue of the stars, the work of two years, during which he experienced several interruptions, especially when the old tower on which his observatory stood was converted by the French into a powder magazine. 6. A memoir, followed by a catalogue of eighty stars, to which he assigned a peculiar motion, independently of the general motion of precession. His eloge, pronounced at the academy by Kaestner (Göttingen, 1762, in 4to), is followed by a list of his works, which we shall here subjoin: 1. Description of a new Globe of the Moon; 2. Tables of Reductions; 3. Geographical Charts, including a Critical Chart of Germany; 4. Map of Switzerland; 4. Description of a new Micrometer; 5. Observations on the Eclipse of the Sun in 1748; 6. Conjunctions of the Moon and the Stars observed in 1747 and 1748; 7. Proofs that the Moon has no atmosphere; 8. Motion of the Earth explained by a change in the direction of gravity; 9. Latitude of Nuremberg, and other Astronomical Observations; 10. Memoir on the Parallax of the Moon and its distance from the Earth, deduced from the length of a pendulum beating seconds; 11. On the Transmutation of rectilinear into circular triangles; 12. Invention of a species of Painting of which the products may be multiplied; 13. Inclinations and Declinations of the Magnetic Needle, deduced from theory; 14. Inequalities of Jupiter.