Aurora borealis systems in the German-Russian world in the first half of the eighteenth century: the cases of Friedrich Christoph Mayer and Leonhard Euler

We are interested in the case of Friedrich Christoph Mayer, who in the 1720s, while at the Imperial Academy of Sciences in St. Petersburg (in Latin Academiae scientiarum imperialis Petropolitanae), developed a system of the aurora borealis, as well as a mathematical method for calculating the height of the aurora from the geometrical characteristics of the auroral arc. Mayer, encountering a major contradiction in his system which placed the aurora at the height of the clouds, whereas his mathematical method led to an altitude a hundred times higher, never applied his method to concrete cases to deduce the height of the aurora, and quickly lost interest in their detailed description, a task that was nevertheless assigned to him at the St. Petersburg Observatory. Jean-Jacques Dortous de Mairan suggests that Mayer's abandonment was due to his lack of confidence in observations. We set Mayer's case against that of Leonhard Euler who, working with Mayer and being aware of the great height of the aurora, later developed a system of the aurora borealis that was compatible with the observational fact. We put forward possible hypotheses to explain Mayer's disinterest in observing the aurora and in the mathematical method he himself had developed.