Since the creation of classical mechanics in the 17th century, the
pendulum has been a basic instrument for the determination of the
intensity of gravity, which is expressed as the acceleration of a freely
falling body. Basis of theory is the simple pendulum, whose time of
swing under gravity is proportional to the square root of the length
divided by the acceleration due to gravity. Since the length of a simple
pendulum divided by the square of its time of swing is equal to the
length of a pendulum that beats seconds, the intensity of gravity also
has been expressed in terms of the length of the seconds pendulum. The
reversible compound pendulum has served for the absolute determination
of gravity by means of a theory developed by Huygens. Invariable
compound pendulums with single axes also have been used to determine
relative values of gravity by comparative times of swing.
The history of gravity pendulums begins with the ball or "simple"
pendulum of Galileo as an approximation to the ideal simple pendulum.
Determinations of the length of the seconds pendulum by French
scientists culminated in a historic determination at Paris by Borda and
Cassini, from the corrected observations with a long ball pendulum. In
the 19th century, Bessel found the length of the seconds pendulum at
Koenigsberg and Berlin by observations with a ball pendulum and by
original theoretical considerations. During the century, however, the
compound pendulum came to be preferred for absolute and relative
determinations.
Capt. Henry Kater, at London, constructed the first convertible compound
for an absolute determination of gravity, and then he designed an
invariable compound pendulum, examples of which were used for relative
determinations at various stations in Europe and elsewhere. Bessel
demonstrated theoretically the advantages of a reversible compound
pendulum which is symmetrical in form and is hung by interchangeable
knives. The firm of A. Repsold and Sons in Hamburg constructed pendulums
from the specifications of Bessel for European gravity surveys.
Charles S. Peirce in 1875 received delivery in Hamburg of a
Repsold-Bessel pendulum for the U.S. Coast Survey and observed with it
in Geneva, Paris, Berlin, and London. Upon an initial stimulation from
Baeyer, founder of _Die Europaeische Gradmessung_, Peirce demonstrated by
experiment and theory that results previously obtained with the Repsold
apparatus required correction, because of the flexure of the stand under
oscillations of the pendulum. At the Stuttgart conference of the
geodetic association in 1877, Herve Faye proposed to solve the problem
of flexure by swinging two similar pendulums from the same support with
equal amplitudes and in opposite phases. Peirce, in 1879, demonstrated
theoretically the soundness of the method and presented a design for its
application, but the "double pendulum" was rejected at that time. Peirce
also designed and had constructed four examples of a new type of
invariable, reversible pendulum of cylindrical form which made possible
the experimental study of Stokes' theory of the resistance to motion of
a pendulum in a viscous fluid. Commandant Defforges, of France, also
designed and used cylindrical reversible pendulums, but of different
length so that the effect of flexure was eliminated in the reduction of
observations. Maj. Robert von Sterneck, of Austria-Hungary, initiated a
new era in gravity research by the invention of an apparatus with a
short pendulum for relative determinations of gravity. Stands were then
constructed in Europe on which two or four pendulums were hung at the
same time. Finally, early in the present century, Vening Meinesz found
that the Faye-Peirce method of swinging pendulums hung on a Stueckrath
four-pendulum stand solved the problem of instability due to the
mobility of the soil in Holland.
The 20th century has witnessed increasing activity in the determination
of absolute and relative values of gravity. Gravimeters have been
perfected and have been widely used for rapid relative determinations,
but the compound pendulums remain as indispensable instruments.
Mendenhall's replacement of knives by planes attached to nonreversible
pendulums has been used also for reversible ones. The Geodetic Institute
at Potsdam is presently applying the Faye-Peirce method to the
reversible pendulum.[115] Pendulums have been constructed of new
materials, such as invar, fused silica, and fused quartz. Minimum
pendulums for precise relative determinations have been constructed and
used. Reversible pendulums have been made with "I" cross sections for
better stiffness. With all these modifications, however, the foundations
of the present designs of compound pendulum apparatus were created in
the 19th century.
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