Bessel’s experiments were significant in view of the care with which he determined the corrections. He corrected for the stiffness of the wire and for the lack of rigidity of connection between the bob and wire. The necessity for the latter correction had been pointed out by Laplace, who showed that through the circumstance that the pull of the wire is now on one side and now on the other side of the center of gravity, the bob acquires angular momentum about its center of gravity, which cannot be accounted for if the line of the wire, and therefore the force that it exerts, always passed through the center. In addition to a correction for buoyancy of the air considered by his predecessors, Bessel also took account of the inertia of the air set in motion by the pendulum.
Figure 8.—Mode of suspension of Bessel’s pendulum is shown here. The iron wire is supported by the thumbscrew and clamp at the left, but passes over a pin at the center, which is actually the upper terminal of the pendulum. Bessel found this “cylinder of unrolling” superior to the clamps and knife edges of earlier pendulums. The counterweight at the right is part of a system for supporting the scale in such a way that it is not elongated by its own weight.
With this apparatus, Bessel determined the ratio of the lengths of the two pendulums and their times of vibration. From this the length of the seconds pendulum was calculated. His method eliminated the need to take into account such sources of inaccuracy as flexure of the pendulum wire and imperfections in the shape of the bob. (Portion of plate 7, Mémoires publiés par la Société française de Physique, vol. 4.)
Figure 9.—Friedrich Wilhelm Bessel (1784-1846), German mathematician and astronomer. He became the first superintendent of the Prussian observatory established at Königsberg in 1810, and remained there during the remainder of his life. So important were his many contributions to precise measurement and calculation in astronomy that he is often considered the founder of the “modern” age in that science. This characteristic also shows in his venture into geodesy, 1826-1830, one product of which was the pendulum experiment reported in this article.
The latter effect had been discovered by Du Buat in 1786,[23] but his work was unknown to Bessel. The length of the seconds pendulum at Königsberg, reduced to sea level, was found by Bessel to be 440.8179 lines. In 1835, Bessel determined the intensity of gravity at a site in Berlin where observations later were conducted in the Imperial Office of Weights and Measures by Charles S. Peirce of the U.S. Coast Survey.