JACOB HERMANN (1678–1733)

Born in Basel, he entered the University to study Philosophy in which he took a master's degree in 1696, after which he continued with the study of Theology, qualifying Licencié in 1701. But long before this, he had fallen under the influence of Jacob Bernoulli, who, recognising his ability, directed his study of Mathematics. In 1700 appeared his first mathematical publication, Responsio ad Clarissimi Viri Bernhardt Nieuwentijt considerationes secundas circa calculi differentialis principia editas (Basel, 1700)—a response to the Dutch physician Nieuwentijt, who had tried to attack the Calculus of Leibniz. It was through Jacob Bernoulli that Hermann made the acquaintance of Leibniz and on the death of Bernoulli in 1705 it was Hermann that Leibniz chose to write an obituary notice for the Acta Eruditorum.

It was through the influence of Leibniz that Hermann was appointed Professor of Mathematics in Padova (1707) and later in Frankfurt an der Oder (1713). In Italy he compiled his largest work, Phoronomia, sive de viribus et motibus corporum solidorum et fluidorum libri duo, published in Amsterdam (1716). It consists of a treatise on Mechanics in which we find for the first time the presentation of Newton's Law of Motion (the "Second Law") in the form we now recognise—formulated in terms of differential calculus. This work received the highest praise in a review by Leibniz in the Acta Eruditorum, but has been largely neglected in later years.

All these years Hermann was hoping for a suitable appointment in Basel, which did not materialize. In 1724 he accepted the invitation to the Academy in St. Petersburg from Emperor Peter the Great: and it was a dissertation by Hermann that launched the new Journal of the Academy—Commentarii Academiae Petropolitanae, Vol. 1, 1726 (1728) [CP I].

In 1727 he was appointed to the Chair of Ethics and Natural Law in Basel: as it was not his choice position he nominated a substitute to deliver the lectures pending his return.

In the years 1728 to 1730 there was published in St. Petersburg a series of volumes under the general title Abrégé des Mathématiques. Hermann wrote both Vol. 1 (Arithmetic and Geometry) and Vol. 3 (Military Fortifications) in this series. Finally in 1731 he returned to Basel to take up his duties as Professor of Ethics: unfortunately he had but two years to live. Like his master he died at the height of his powers—in 1733. His steady, gentle temperament earned him the regard and affection of both Leibniz and Bernoulli and of many others of the learned of his time.

In his work he was mainly concerned with two areas:

1. Mechanics; besides his basic work, Phoronomia, he concentrated particularly on questions relating to both the compound pendulum and elasticity—the motivation being a consuming desire to understand the physics underlying the rhythm and tone of string vibration in musical instruments.

2. Optics; in this area he was driven by the close connection between the design of optical instruments and the accuracy possible in Astronomical measurements.

Hermann was the first to study what, to-day, we call the direct Kepler problem: namely, given the central force inverse square law, determine the orbit. In spite of the pioneering excellence of this analysis, including the proof that in such a force-field all orbits are conic sections, it was immediately superseded by the more comprehensive treatment of Johann I Bernoulli. Although Hermann had priority in tackling the problem, he had not obtained the complete solution.

His work and writings require more detailed examination. Due to the excellence of his work and the close connection between it and that of Jacob Bernoulli he is included in the project.

Ó Mathúna, 1999