JACOB II (1759–1789)

He then spent some time as secretary to the Imperial Envoy in the latter's sojourn through Northern Italy. It was there he received the news of Euler's death in 1783, followed by another message inviting him to the Academy in St. Petersburg. He accepted the invitation and soon after his arrival there he married a grand-daughter of Euler.

In the following years there came from him treatises on Hydromechanics and Elasticity in which he accepted the challenge of the problems left unsolved by Euler. In his work he shows a certain affinity with his grand-uncle Jacob I—the pursuit of a single problem in Physics could be most instructive if only one obtained complete mastery of it; also in the unfailing courage with which he attacked the problems which his contemporaries considered the most difficult.

The most interesting of his treatises is devoted to the problem of vibrations of an elastic plate—a problem that Daniel Bernoulli avoided and that Euler seemed to back away from after one unsatisfactory sally. Moreover Lagrange had let it be known that he considered it a problem of extreme difficulty. As it transpired his attempt did not come out right—and he himself was the first to realize the inadequacy of the equation he derived. It is now recognized that only an unlucky stroke deprived him of the correct outcome. The basic assumption underlying his analysis, he did not apply until two steps from the end, which meant that a crucial term was missing from his proposed equation; had he applied his basic assumption at the outset of the analysis, he would have derived the correct form of the equation and the recognition of his achievement would be unquestioned.

The work appeared in Nova Acta Academiae Scientiarum Petropolitanae, Vol. 5, 1789, pp. 197–219, as un premier essai and since he recognized his resulting equation as unsatisfactory, it could be presumed he intended to return to the problem. Unfortunately that same year he drowned in a swimming accident when barely thirty years old. With a little luck, his analysis of that problem would have yielded the correct equation and his fame would be secure. As it is, his work, when mentioned, is generally dismissed without cognizance of how close to correct it had been. The formulation of the correct equation had to await almost a quarter of a century when Lagrange gave the corrected form of Germain's incorrect derivation (1812). Following the formulation of the general theory in the 1820s (by Cauchy, Navier and Poisson) the boundary value problem did not reach full formulation until the work of Kirchhoff (1850).

In view of how little came from Johann III in the last twenty years of his life, one must consider the death of Jacob II in 1789 as bringing the Bernoulli mathematical dynasty to a close.

Ó Mathúna, 1999