Figure 20.—Support for the Peirce pendulum, 1889. Much of the work of C. S. Peirce was concerned with the determination of the error introduced into observations made with the portable apparatus by the vibration of the stand with the pendulum. He showed that the popular Bessel-Repsold apparatus was subject to such an error. His own pendulums were swung from a simple but rugged wooden frame to which a hardened steel bearing was fixed.
Another novel characteristic of the Peirce pendulums was the mainly cylindrical form. Prof. George Gabriel Stokes, in a paper “On the Effect of the Internal Friction of Fluids on the Motion of Pendulums”[77] that was read to the Cambridge Philosophical Society on December 9, 1850, had solved the hydrodynamical equations to obtain the resistance to the motions of a sphere and a cylinder in a viscous fluid. Peirce had studied the effect of viscous resistance on the motion of his Repsold-Bessel pendulum, which was symmetrical in form but not cylindrical. The mainly cylindrical form of his pendulums (fig. [19]) permitted Peirce to predict from Stokes’ theory the effect of viscosity and to compare the results with experiment. His report of November 20, 1889, in which he presented the comparison of experimental results with the theory of Stokes, was not published.[78]
Peirce used his pendulums in 1883 to establish a station at the Smithsonian Institution that was to serve as the base station for the Coast and Geodetic Survey for some years. Pendulum Peirce no. 1 was swung at Washington in 1881 and was then taken by the party of Lieutenant Greely, U.S.A., on an expedition to Lady Franklin Bay where it was swung in 1882 at Fort Conger, Grinnell Land, Canada. Peirce nos. 2 and 3 were swung by Peirce in 1882 at Washington, D.C.; Hoboken, New Jersey; Montreal, Canada; and Albany, New York. Assistant Preston took Peirce no. 3 on a U.S. eclipse expedition to the Caroline Islands in 1883. Peirce in 1885 swung pendulums nos. 2 and 3 at Ann Arbor, Michigan; Madison, Wisconsin; and Ithaca, New York. Assistant Preston in 1887 swung Peirce nos. 3 and 4 at stations in the Hawaiian Islands, and in 1890 he swung Peirce nos. 3 and 4 at stations on the west coast of Africa.[79]
The new pattern of pendulum designed by Peirce was also adopted in France, after some years of experience with a Repsold-Bessel pendulum. Peirce in 1875 had swung his Repsold-Bessel pendulum at the observatory in Paris, where Borda and Cassini, and Biot, had made historic observations and where Sabine also had determined gravity by comparison with Kater’s value at London. During the spring of 1880, Peirce made studies of the supports for the pendulums of these earlier determinations and calculated corrections to those results for hydrodynamic effects, viscosity, and flexure. On June 14, 1880, Peirce addressed the Academy of Sciences, Paris, on the value of gravity at Paris, and compared his results with the corrected results of Borda and Biot and with the transferred value of Kater.[80]
In the same year the French Geographic Service of the Army acquired a Repsold-Bessel reversible pendulum of the smaller type, and Defforges conducted experiments with it.[81] He introduced the method of measuring flexure from the movement of interference fringes during motion of the pendulum. He found an appreciable difference between dynamical and statical coefficients of flexure and concluded that the “correction formula of Peirce and Cellérier is suited perfectly to practice and represents exactly the variation of period caused by swaying of the support, on the condition that one uses the statical coefficient.” Defforges developed a theory for the employment of two similar pendulums of the same weight, but of different length, and hung by the same knives. This theory eliminated the flexure of the support and the curvature of the knives from the reduction of observations.
Pendulums of 1-meter and of 1/2-meter distance between the knife edges were constructed from Defforges’ design by Brunner Brothers in Paris (fig. [21]). These Defforges pendulums were cylindrical in form with hemispherical ends like the Peirce pendulums, and were hung on knives that projected from the sides of the pendulum, as in some unfinished Gautier pendulums designed by Peirce in 1883 in Paris.
Figure 21.—Reversible pendulum apparatus of Defforges, as constructed by Brunner, Paris, about 1887. The clock and telescope used to observe coincidences are not shown. The telescope shown is part of an interferometer used to measure flexure of the support. One mirror of the interferometer is attached to the pendulum support; the other to the separate masonry pillar at the left.