The pendulum has been both an objective and an instrument of physical
investigation since the foundations of classical mechanics were
fashioned in the 17th century.[1] It is tradition that the youthful
Galileo discovered that the period of oscillation of a pendulum is
constant by observations of the swings of the great lamp suspended from
the ceiling in the cathedral of Pisa.[2] The lamp was only a rough
approximation to a simple pendulum, but Galileo later performed more
accurate experiments with a "simple" pendulum which consisted of a heavy
ball suspended by a cord. In an experiment designed to confirm his laws
of falling bodies, Galileo lifted the ball to the level of a given
altitude and released it. The ball ascended to the same level on the
other side of the vertical equilibrium position and thereby confirmed a
prediction from the laws. Galileo also discovered that the period of
vibration of a "simple" pendulum varies as the square root of its
length, a result which is expressed by the formula for the time of
swing of the ideal simple pendulum. He also used a pendulum to measure
lapse of time, and he designed a pendulum clock. Galileo's experimental
results are important historically, but have required correction in the
light of subsequent measurements of greater precision.
Mersenne in 1644 made the first determination of the length of the
seconds pendulum,[3] that is, the length of a simple pendulum that beats
seconds (half-period in the sense of physics). Subsequently, he proposed
the problem to determine the length of the simple pendulum equivalent in
period to a given compound pendulum. This problem was solved by Huygens,
who in his famous work _Horologium oscillatorium_ ... (1673) set forth
the theory of the compound pendulum.[4]
Huygens derived a theorem which has provided the basis for the
employment of the reversible compound pendulum for the absolute
determination of the intensity of gravity. The theorem is that a given
compound pendulum possesses conjugate points on opposite sides of the
center of gravity; about these points, the periods of oscillation are
the same. For each of these points as center of suspension the other
point is the center of oscillation, and the distance between them is the
length of the equivalent simple pendulum. Earlier, in 1657, Huygens
independently had invented and patented the pendulum clock, which
rapidly came into use for the measurement of time. Huygens also created
the theory of centripetal force which made it possible to calculate the
effect of the rotation of the earth upon the observed value of gravity.
The theory of the gravity field of the earth was founded upon the laws
of motion and the law of gravitation by Isaac Newton in his famous
_Principia_ (1687). It follows from the Newtonian theory of gravitation
that the acceleration of gravity as determined on the surface of the
earth is the resultant of two factors: the principal factor is the
gravitational attraction of the earth upon bodies, and the subsidiary
factor is the effect of the rotation of the earth. A body at rest on the
surface of the earth requires some of the gravitational attraction for
the centripetal acceleration of the body as it is carried in a circle
with constant speed by the rotation of the earth about its axis. If the
rotating earth is used as a frame of reference, the effect of the
rotation is expressed as a centrifugal force which acts to diminish the
observed intensity of gravity.
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