In the preface of his first book Mayer acknowledged his debt to Christian von Wolff’s Anfangs-Gründe aller mathematischen Wissenschaften, through which he had taught himself mathematics, a subject not included in the curriculum of the Esslingen Latin school (now Georgii-Gymnasium Esslingen), which he attended.
College/University
Career
Gallery of Johann Mayer
Portrait of Tobias Mayer.
Achievements
Lunar crater T. Mayer (Southwest of crater Copernicus).
In the preface of his first book Mayer acknowledged his debt to Christian von Wolff’s Anfangs-Gründe aller mathematischen Wissenschaften, through which he had taught himself mathematics, a subject not included in the curriculum of the Esslingen Latin school (now Georgii-Gymnasium Esslingen), which he attended.
Johann Tobias Mayer was a German astronomer, cartographer, and educator. He is famous for his studies of the Moon. He was mostly known by his middle name as Tobias Mayer.
Background
Johann Tobias Mayer was born on February 17, 1723, in Marbach, am Neckar, Holy Roman Empire (now Marbach, Baden-Wurttemberg, Germany) to the family of a cartwright, also named Johann Tobias Mayer, and his second wife, Maria Catherina Finken. In 1723 the father left his trade and went to work as the foreman of a well-digging crew in the nearby town of Esslingen, where his family joined him the following year. After his father’s death in 1737 Mayer was taken into the local orphanage, while his mother found employment in St. Katharine’s Hospital, where she remained until her death in 1737. It was probably through her occupation that Mayer found the opportunity to make architectural drawings of the hospital, as he did when he was barely fourteen years old.
Education
Mayer was engaged in self-learning. There is some evidence to indicate that he was encouraged in his draftsmanship by Gottlieb David Kandler, a shoemaker who was subsequently responsible for the education of orphans in Esslingen.
In the preface of his first book, Mayer acknowledged his debt to Christian von Wolff’s Anfangs-Gründe aller mathematischen Wissenschaften, through which he had taught himself mathematics, a subject not included in the curriculum of the Esslingen Latin school (now Georgii-Gymnasium Esslingen), which he attended.
Mayer’s skill in architectural drawings also brought him to the attention of a certain Geiger, a noncommissioned officer in the Swabian district artillery, which was then garrisoned in Esslingen. Under Geiger’s instruction, Mayer, in early 1739, prepared a book of plans and drawings of military fortifications. Later in the same year, he drew a map of Esslingen and its surroundings (the oldest still extant), which was reproduced as a copper engraving by Gabriel Bodenehr of Augsburg in 1741.
Mayer’s first book, written on the occasion of his eighteenth birthday, was published at about this same time. It was devoted to the application of analytic methods to the solution of geometrical problems. The influence of Wolff’s compendium is again apparent in the arrangement and content of Mayer’s Mathematischer Atlas of 1745; the sixty plates of the latter work duplicate Wolff’s choice of subjects - arithmetic, geometry, trigonometry, and anal v sis, as applied to mechanics, optics, astronomy, geography, chronology, gnomonics, pyrotechnics, and military and civil architecture. This atlas, published in Augsburg by the firm of Johann Andreas Pfeffel for which Mayer worked during his brief stay there (from 1744 to 1746), provides a good index to the extent of his scientific and technical knowledge at that period. It was probably in Augsburg that he acquired much of his knowledge of French, Italian, and English. He also became acquainted with a local mechanic and optician, G. F. Brander.
Mayer left Augsburg to take up a post with the Homann Cartographic Bureau in Nuremberg. He spent five years there, which he devoted primarily to improving the state of cartography. To this end, he collated geographical and astronomical data from the numerous printed and manuscript records to which the Homann office permitted him access. He also made personal observations of lunar occultations and other astronomical eclipse phenomena, using a nine-foot-focus telescope and a glass micrometer of his own design. Of more than thirty maps that he drew, the “mappa critica” of Germany is generally considered to be the most significant, since it established a new standard for the rigorous handling of geographical source materials and for the application of accurate astronomical methods in finding terrestrial latitude and longitude.
In order to facilitate the lunar eclipse method of longitude determination, Mayer in 1747 and 1748 made a large number of micrometric measurements of the angular diameter of the moon and of the times of its meridian transits, In his determinations of the selenographic coordinates of eighty-nine prominent lunar markings, he took account of the irregularity of the orbital and libratory motions of the moon and of the effect of its variable parallax. In addition his analysis correctly - although fortuitously - reduced twenty-seven conditional equations to three “normal” ones, a procedure that had never before been attempted, and one for which theory had still be developed.
Mayer was the editor of the Kosmographische Nachrichten und Sammlungen auf das Jahr 1748, which was published in Nuremberg in 1750, under the auspices of the newly established Cosmographical Society. The work contains Mayer’s own description of his glass micrometer, his observations of the solar eclipse of 25 July 1748 and the occultations of a number of bright stars, his long treatise on the libration of the moon, and his argument as to why the moon cannot possess an atmosphere. The Cosmographical Society itself, founded by Johann Michael Franz, director of the Homann firm, was crucial in determining the nature, scope, and, to some degree, motivation of Mayer’s subsequent scientific research. The aims of the mathematical class of the society, to which Mayer belonged, as set out by Franz in the preface to the Homannisch-Haseschen Gesellschafts Atlas (Nuremberg, 1747), define much of Mayer’s later work.
In November 1750 Mayer was called to a professorship at the Georg-August Academy in Göttingen, a post that he took up after Faster of the Following year. Mayer’s academic title, professor of economy, was purely nominal since his actual duties were assigned, in his letter of appointment, as the teaching of practical (that is, applied) mathematics and research. His reputation as a cartographer and practical astronomer had preceded him and was indeed the basis for his selection as a professor.
In 1752 Mayer drew up new lunar and solar tables, in which he attained an accuracy of ±,’an achievement attributable to his skillful use of observational data, rather than to the originality of his theory or the superiority of his instruments, Mayer subsequently undertook an investigation of the celestial positions of the moon at conjunction and opposition; he compared the values that he obtained with those derivable from a systematic study of all lunar and solar eclipses reported since the invention of the astronomical telescope and the pendulum clock.
Mayer’s further astronomical researches consequently included the problem of the elimination of errors from a six-foot-radius mural quadrant made in 1755 by John Bird for installation in Mayer’s newly completed observatory in Göttingen; the invention of a simple and accurate method for computing solar eclipses; the compilation of a catalogue of zodiacal stars; and the investigation of stellar proper motions. He wrote treatises on each of these topics that were published posthumously in Georg Christoph Lichtenberg’s Opera inedita Tobiae Mayeri (Göttingen, 1775). This work also contains a treatise on the problem of accurately defining thermometric changes (an extension of Mayer’s research on astronomical refraction) and another on a mathematical theory of color mixing (a topic that Mayer may have taken up in response to the need of the Homann firm, part of which had been transferred to Göttingen in 1755, to train unskilled workers in the accurate reproduction of maps). Appended to Lichtenberg’s book, in accordance with one of Mayer’s last wishes, is a copper engraving of Mayer’s map of the moon; the original map and the forty detailed drawings from which it was constructed were also reproduced by photolithography more than a century later.
Others of Mayer’s treatises, lecture notes, and correspondence have been neglected since their deposit, shortly after his death, in the Göttingen observatory archives, although abstracts of some of his lectures to the Göttingen Scientific Society were printed in the Göttingische Anzeigen von gelehrten Sachen between 1752 and 1762. His researches during these years included his efforts to improve the art of land measurement, for which purpose he invented a new goniometer and explored the application of the repeating principle of angle measurement, developed a new projective method for finding the areas of irregularly shaped fields, and transformed the common astrolabe into a precision instrument. He further applied the repeating principle to an instrument of his own invention, the repeating circle, which proved to be of use not only for the sea navigation for which it had been designed but also for making standard trigonometrical land surveys. (The instrument used by Delambre and Méchain in their determination of the standard meter was a variant, designed by Borda, of the Mayer circle.)
Mayer also undertook to devise a method for finding geographical coordinates independently of astronomical observations. In so doing he arrived at a new theory of the magnet, based, like his lunar theory, on the principles of Newtonian mechanics. This theory represented a convincing demonstration of the validity of the inverse-square law of magnetic attraction and repulsion, and antedated Coulomb’s well-known verification of that law by some twenty five years. Mayer’s manuscripts on this theory and on its application to the calculation of the variation and dip of a magnetic needle are among those that went virtually unnoticed after his death.
In 1763 Mayer’s widow, acting upon another of his last requests, submitted to the British admiralty his Theoria lunae juxta systema Newtonianum, which contained the derivations of the equations upon which his lunar theory was based, and his Tabulae motuum solis et lunae novae et correctae, which were published in London in 1767 and 1770, respectively. The tables were edited by Maskelyne, and printed under his direct supervision; they were used to compute the lunar and solar ephemerides for the early editions of the Nautical Almanac. They were superseded a decade later by tables employing essentially the same principles, but based upon the newer and more accurate observational data that were gradually being assembled at the Royal Observatory at Greenwich.
Mayer is remembered also for his improvements in mapmaking and for the invention of the repeating circle, later used in measuring the arc of the meridian. In 1765 the British parliament authorized Maria Mayer to receive an award of £3,000, in recognition of her husband’s claim, lodged ten years before, for one of the prizes offered to “any Person or Persons as shall Discover the Longitude at Sea.” Lunar crater T. Mayer was named in his honor.
Mayer’s chief scientific concerns when he started his professorship in Nuremberg were the investigation of astronomical refraction and lunar theory. His results after conducting experiments led him to recognize that the discrepancies of up to ±5’ that he and his contemporaries had found were due largely to errors in the determination of star places and to the poor quality of their instruments.
Interests
Philosophers & Thinkers
Christian von Wolff, Charles-François Sturm
Connections
Tobias Mayer married Maria Victoria Gnüge. Of their eight children, two, Johann Tobias and Georg Moritz lived to maturity.
