Figure 19.—Three pendulums used in early work at the U.S. Coast and Geodetic Survey. Shown on the left is the Peirce invariable; center, the Peirce reversible; and, right, the Repsold reversible. Peirce designed the cylindrical pendulum in 1881-1882 to study the effect of air resistance according to the theory of G. G. Stokes on the motion of a pendulum in a viscous field. Three examples of the Peirce pendulums are in the U.S. National Museum.
The conference received a memoir by Cellérier[68] on the theory of the double pendulum and a report by Plantamour and Cellérier.[69] Cellérier’s mathematical analysis began with the equations of Peirce and used the latter’s notation as far as possible. His general discussion included the results of Peirce, but he stated that the difficulties to be overcome did not justify the employment of the “double pendulum.” He presented an alternative method of correcting for flexure based upon a theory by which the flexure caused by the oscillation of a given reversible pendulum could be determined from the behavior of an auxiliary pendulum of the same length but of different weight. This method of correcting for flexure was recommended to the General Conference by Plantamour and Cellérier in their joint report. At the fourth session of the conference on September 16, 1880, the problem of the pendulum was discussed and, in consequence, a commission consisting of Faye, Helmholtz, Plantamour (replaced in 1882 by Hirsch), and Von Oppolzer was appointed to study apparatus suitable for relative determinations of gravity.
The Permanent Commission met September 11-15, 1882, at The Hague,[70] and at its last session appointed Prof. von Oppolzer to report to the Seventh General Conference on different forms of apparatus for the determination of gravity. The Seventh Conference met October 15-24, 1883, in Rome,[71] and, at its eighth session, on October 22, received a comprehensive, critical review from Prof. von Oppolzer entitled “Über die Bestimmung der Schwere mit Hilfe verschiedener Apparate.”[72] Von Oppolzer especially expounded the advantages of the Bessel reversible pendulum, which compensated for air effects by symmetry of form if the times of swing for both positions were maintained between the same amplitudes, and compensated for irregular knife edges by making them interchangeable. Prof. von Oppolzer reviewed the problem of flexure of the Repsold stand and stated that a solution in the right direction was the proposal—made by Faye and theoretically pursued by Peirce—to swing two pendulums from the same stand with equal amplitudes and in opposite phases, but that the proposal was not practicable. He concluded that for absolute determinations of gravity, the Bessel reversible pendulum was highly appropriate if one swung two exemplars of different weight from the same stand for the elimination of flexure. Prof. von Oppolzer’s important report recognized that absolute determinations were less accurate than relative ones, and should be conducted only at special places.
The discussions initiated by Peirce’s demonstration of the flexure of the Repsold stand resulted, finally, in the abandonment of the plan to make absolute determinations of gravity at all stations with the reversible pendulum.
Peirce and Defforges Invariable, Reversible Pendulums
The Repsold-Bessel reversible pendulum was designed and initially used to make absolute determinations of gravity not only at initial stations such as Kew, the observatory in Paris, and the Smithsonian Institution in Washington, D.C., but also at stations in the field. An invariable pendulum with a single knife edge, however, is adequate for relative determinations. As we have seen, such invariable pendulums had been used by Bouguer and Kater, and after the experiences with the Repsold apparatus had been recommended again by Baeyer for relative determinations. But an invariable pendulum is subject to uncontrollable changes of length. Peirce proposed to detect such changes in an invariable pendulum in the field by combining the invariable and reversible principles. He explained his proposal to Faye in a letter dated July 23, 1880, and he presented it on September 16, 1880, at the fourth session of the sixth General Conference of Die Europäische Gradmessung, in Munich.[73]
As recorded in the Proceedings of the Conference, Peirce wrote: