The development of the reversible pendulum in the 19th century
culminated in the absolute determination of the intensity of gravity at
Potsdam by Kuehnen and Furtwaengler of the Royal Prussian Geodetic
Institute, which then became the world base for gravity surveys.[96]
We have previously seen that in 1869 the Geodetic Institute--founded by
Lt. Gen. Baeyer--had acquired a Repsold-Bessel reversible pendulum which
was swung by Dr. Albrecht under the direction of Dr. Bruhns.
Dissatisfaction with this instrument was expressed by Baeyer in 1875 to
Charles S. Peirce, who then, by experiment and mathematical analysis of
the flexure of the stand under oscillations of the pendulum, determined
that previously reported results with the Repsold apparatus required
correction. Dr. F. R. Helmert, who in 1887 succeeded Baeyer as director
of the Institute, secured construction of a building for the Institute
in Potsdam, and under his direction the scientific study of the
intensity of gravity was pursued with vigor. In 1894, it was discovered
in Potsdam that a pendulum constructed of very flexible material yielded
results which differed markedly from those obtained with pendulums of
greater stiffness. Dr. Kuehnen of the Institute discovered that the
departure from expectations was the result of the flexure of the
pendulum staff itself during oscillations.[97]
Peirce, in 1883, had discovered that the recesses cut in his pendulums
for the insertion of tongues that carried the knives had resulted in the
flexure of the pendulum staff.[98] By experiment, he also found an even
greater flexure for the Repsold pendulum. In order to eliminate this
source of error, Peirce designed a pendulum with knives that extended
from each side of the cylindrical staff, and he received authorization
from the superintendent of the Coast and Geodetic Survey to arrange for
the construction of such pendulums by Gautier in Paris. Peirce, who had
made his plans in consultation with Gautier, was called home before the
pendulums were completed, and these new instruments remained
undelivered.
In a memoir titled "Effect of the flexure of a pendulum upon its period
of oscillation,"[99] Peirce determined analytically the effect on the
period of a pendulum with a single elastic connection between two rigid
parts of the staff. Thus, Peirce discovered experimentally the flexure
of the staff and derived for a simplified case the effect on the period.
It is not known if he ever found the integrated effect of the continuum
of elastic connections in the pendulum. Lorenzoni, in 1896, offered a
solution to the problem, and Almansi, in 1899, gave an extended
analysis. After the independent discovery of the problem at the Geodetic
Institute, Dr. Helmert took up the problem and criticized the theories
of Peirce and Lorenzoni. He then presented his own theory of flexure in
a comprehensive memoir.[100] In view of the previous neglect of the
flexure of the pendulum staff in the reduction of observations, Helmert
directed that the Geodetic Institute make a new absolute determination
of the intensity of gravity at Potsdam. For this purpose, Kuehnen and
Furtwaengler used the following reversible pendulums which had been
constructed by the firm of A. Repsold and Sons in Hamburg:
1. The seconds pendulum of the Geodetic Institute procured in
1869.