[Illustration: Figure 1.--A STUDY OF THE FIGURE OF THE EARTH WAS one of
the earliest projects of the French Academy of Sciences. In order to
test the effect of the earth's rotation on its gravitational force, the
Academy in 1672 sent Jean Richer to the equatorial island of Cayenne to
compare the rate of a clock which was known to have kept accurate time
in Paris. Richer found that the clock lost 2 minutes and 28 seconds at
Cayenne, indicating a substantial decrease in the force of gravity on
the pendulum. Subsequent pendulum experiments revealed that the period
of a pendulum varied not only with the latitude but also regionally,
under the influence of topographical features such as mountains. It
became clear that the measurement of gravity should be made a part of
the work of the geodetic surveyor.]
_The history of gravity pendulums dates back to the time of
Galileo. After the discovery of the variation of the force of
gravity over the surface of the earth, gravity measurement
became a major concern of physics and geodesy. This article
traces the history of the development of instruments for this
purpose._
THE AUTHORS: _Victor F. Lenzen is Professor of Physics,
Emeritus, at the University of California at Berkeley and Robert
P. Multhauf is Chairman of the Department of Science and
Technology in the Smithsonian Institution's Museum of History
and Technology._
The intensity of gravity, or the acceleration of a freely falling body,
is an important physical quantity for the several physical sciences. The
intensity of gravity determines the weight of a standard pound or
kilogram as a standard or unit of force. In physical experiments, the
force on a body may be measured by determining the weight of a known
mass which serves to establish equilibrium against it. Thus, in the
absolute determination of the ampere with a current balance, the force
between two coils carrying current is balanced by the earth's
gravitational force upon a body of determinable mass. The intensity of
gravity enters into determinations of the size of the earth from the
angular velocity of the moon, its distance from the earth, and Newton's
inverse square law of gravitation and the laws of motion. Prediction
of the motion of an artificial satellite requires an accurate knowledge
of gravity for this astronomical problem.
The gravity field of the earth also provides data for a determination of
the figure of the earth, or geoid, but for this problem of geodesy
relative values of gravity are sufficient. If g is the intensity of
gravity at some reference station, and [Delta]g is the difference
between intensities at two stations, the values of gravity in geodetic
calculations enter as ratios ([Delta]g)/g over the surface of the earth.
Gravimetric investigations in conjunction with other forms of
geophysical investigation, such as seismology, furnish data to test
hypotheses concerning the internal structure of the earth.
Whether the intensity of gravity is sought in absolute or relative
measure, the most widely used instrument for its determination since the
creation of classical mechanics has been the pendulum. In recent
decades, there have been invented gravity meters based upon the
principle of the spring, and these instruments have made possible the
rapid determination of relative values of gravity to a high degree of
accuracy. The gravity meter, however, must be calibrated at stations
where the absolute value of gravity has been determined by other means
if absolute values are sought. For absolute determinations of gravity,
the pendulum historically has been the principal instrument employed.
Although alternative methods of determining absolute values of gravity
are now in use, the pendulum retains its value for absolute
determinations, and even retains it for relative determinations, as is
exemplified by the Cambridge Pendulum Apparatus and that of the Dominion
Observatory at Ottawa, Ontario.
The pendulums employed for absolute or relative determinations of
gravity have been of two basic types. The first form of pendulum used as
a physical instrument consisted of a weight suspended by a fiber, cord,
or fine wire, the upper end of which was attached to a fixed support.
Such a pendulum may be called a "simple" pendulum; the enclosure of the
word simple by quotation marks is to indicate that such a pendulum is an
approximation to a simple, or mathematical pendulum, a conceptual object
which consists of a mass-point suspended by a weightless inextensible
cord. If l is the length of the simple pendulum, the time of swing
(half-period in the sense of physics) for vibrations of infinitely small
amplitude, as derived from Newton's laws of motion and the hypothesis
that weight is proportional to mass, is T = [pi][sqrt](l/g).
The second form of pendulum is the compound, or physical, pendulum. It
consists of an extended solid body which vibrates about a fixed axis
under the action of the weight of the body. A compound pendulum may be
constituted to oscillate about one axis only, in which case it is
nonreversible and applicable only for relative measurements. Or a
compound pendulum may be constituted to oscillate about two axes, in
which case it is reversible (or "convertible") and may be used to
determine absolute values of gravity. Capt. Henry Kater, F.R.S., during
the years 1817-1818 was the first to design, construct, and use a
compound pendulum for the absolute determination of gravity. He
constructed a convertible pendulum with two knife edges and with it
determined the absolute value of gravity at the house of Henry Browne,
F.R.S., in Portland Place, London. He then constructed a similar
compound pendulum with only one knife edge, and swung it to determine
relative values of gravity at a number of stations in the British Isles.
The 19th century witnessed the development of the theory and practice of
observations with pendulums for the determination of absolute and
relative values of gravity.