Johann Bernoulli (1742)

Abstract

Throughout the era that we are studying, Johann Bernoulli held presence as the great teacher and as a central figure in the scientific community. (His correspondence includes more than 2000 letters exchanged with more than 100 scholars¹). Thus, if we look for a contemporary but comprehending reaction to the work of Euler and Daniel Bernoulli on vibrating systems, we could not be more fortunate than to have Johann Bernoulli’s own reaction. This he provides. Indeed, his collected works, published in 1742, contain a volume of previously unpublished notes which include a study of vibrating systems.² It seems that he made this study around the year 1740.³One can presume that he had heard of Euler’s and Daniel Bernoulli’s results from before; but he probably first read their great works on the hanging chain at this time.⁴ The vibrating systems in question include a number with a single degree of freedom that we will mention briefly, as well as the dangling rod which we will discuss in section 15.2 and the linked pendulum with two treatments which we will discuss in section 15.3 and section 15.4 respectively. His two treatments of the linked pendulum could represent his ideas on the subject from before and after his reading of Euler’s and Daniel Bernoulli’s works.