**Tobias Mayer** was a German scientist who developed the method of determining longitude by lunar observations.

- A comparison of Mayer's book with those others indicates that he was dependent upon Wolff for his knowledge of mathematical techniques and upon Sturm for providing the model on which he based his own presentation.
- The method which is given by the former for determining the area of an irregular polygon (or irregularly-shaped field) was illustrated by Mayer in his next major work, the 'Mathematischer Atlas' Ⓣ(Mathematical Atlas) (Augsburg, 1745).
- In 1749, while working for the Homann Company, Mayer produced a map of the moon measuring seven and a half inches in diameter.
- Mayer measured the positions of 24 craters, which he included in the map, using a micrometer to obtain an accuracy of 1' in latitude and longitude.
- Mayer's map was published by Homann in 1751.
- Mayer showed his outstanding abilities by introducing many improvements in cartography, but he also discovered the libration of the Moon which he published in Kosmographische Nachrichten Ⓣ(Cosmographic News) (Nürnberg, 1750).
- Being a map maker, it was natural for Mayer to make a map illustrating his journey from Nürnberg to Göttingen.
- From the time he took up his position in Göttingen, Mayer corresponded with Leonard Euler.
- Mayer invented a clever improvement to the reflecting circle in 1752.
- The celebrate Tobias Mayer contrived, however, a method to determine, at one reading, instead of the simple angle observed, a multiple of the same angle; and, by this means, the instrument became, in practice, capable of any degree of accuracy, as far as regards the above mentioned errors.
- Tobias Mayer's improvements to the reflecting circle were further developed by Jean Charle de Borda and used in the measurements of the arc of the meridian by Jean Baptiste Delambre and Pierre Méchain in their efforts to define the metre.
- In 1754 Mayer was made Director of the Göttingen Observatory where he continued to work until his death.
- On 1 March 1755, Mayer addressed the Göttingen Academy of Sciences.
- Mayer began calculating lunar and solar tables in 1753 and in 1755 he sent them to the British government.
- Mayer's method of determining longitude by lunar distances and a formula for correcting errors in longitude due to atmospheric refraction were published in 1770 after his death.
- The Board of Longitude sent Mayer's widow £3000 as an award for the tables.
- Beginning in 1779, seventeen years after Mayer's death, William Herschel began searching for double stars.
- However, when he was given the memoir of Tobias Mayer, published after his death, he found that Mayer had discovered 31 double stars that he had overlooked.
- There are other achievements by Mayer which we should mention such as his theories of earthquakes, atmospheric refraction, magnetism, vision, and colour.
- Finally, let us look briefly at Mayer's theory of colour.
- Mayer's colour triangle was unpublished at his death but Johann Heinrich Lambert made use of the triangle and suggested that it be published, which took place in 1775.
- Lambert also made use of Mayer's stellar data in 1761 when he used Mayer's catalogue of stars with proper motions in his theory of the universe given in his Cosmological Letters.

Born 17 February 1723, Marbach, Württemberg, Germany. Died 20 February 1762, Göttingen, Germany.

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Astronomy, Geography, Origin Germany, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive