The simplified discussion for infinitely small oscillations in a vacuum is as follows: If T_{1} and T_{2} are the times of swing about the knife edges, and if h_{1} and h_{2} are distances of the knife edges from the center of gravity, and if k is the radius of gyration about an axis through the center of gravity, then from the equation of motion of a rigid body oscillating about a fixed axis under gravity (T_{1})^{2} = [pi]^{2}(k^{2} + (h_{1})^{2})/gh_{1}, (T_{2})^{2} = [pi]^{2}(k^{2} + (h_{2})^{2})/gh_{2}. Then (h_{1}(T_{1})^{2} - h_{2}(T_{2})^{2})/(h_{1} - h_{2}) = ([pi]^{2}/g)(h_{1} + h_{2}) = [tau]^{2}. [tau] is then the time of swing of a simple pendulum of length h_{1} + h_{2}. If the difference T_{1} - T_{2} is sufficiently small, [tau] = (h_{1}T_{1} - h_{2}T_{2})/(h_{1} - h_{2}). Prior to its publication by Bessel in 1828, the formula for the time of swing of a simple pendulum of length h_{1} + h_{2} in terms of T_{1}, T_{2} had been given by C. F. Gauss in a letter to H. C. Schumacher dated November 28, 1824.[43] The symmetrical compound pendulum with interchangeable knives, for which Bessel gave a posthumously published design and specifications,[44] has been called a reversible pendulum; it may thereby be distinguished from Kater's unsymmetrical convertible pendulum. In 1861, the Swiss Geodetic Commission was formed, and in one of its first sessions in 1862 it was decided to add determinations of gravity to the operations connected with the measurement--at different points in Switzerland--of the arc of the meridian traversing central Europe.[45] It was decided further to employ a reversible pendulum of Bessel's design and to have it constructed by the firm of A. Repsold and Sons, Hamburg. It was also decided to make the first observations with the pendulum in Geneva; accordingly, the Repsold-Bessel pendulum (fig. 16) was sent to Prof. E. Plantamour, director of the observatory at Geneva, in the autumn of 1864.[46]