ABSOLUTE GRAVITY: the value of the acceleration of gravity, also
expressed by the length of the seconds pendulum.
RELATIVE GRAVITY: the value of the acceleration of gravity relative to
the value at some standard point.
SIMPLE PENDULUM: see theoretical pendulum.
THEORETICAL PENDULUM: a heavy bob (point-mass) at the end of a
weightless rod.
SECONDS PENDULUM: a theoretical or simple pendulum of such length that
its time of swing (half-period) is one second. (This length is about one
meter.)
GRAVITY PENDULUM: a precisely made pendulum used for the measurement of
gravity.
COMPOUND PENDULUM: a pendulum in which the supporting rod is not
weightless; in other words, any actual pendulum.
CONVERTIBLE PENDULUM: a compound pendulum having knife edges at
different distances from the center of gravity. Huygens demonstrated
(1673) that if such a pendulum were to swing with equal periods from
either knife edge, the distance between those knife edges would be equal
to the length of a theoretical or simple pendulum of the same period.
REVERSIBLE PENDULUM: a convertible pendulum which is also symmetrical in
form.
INVARIABLE PENDULUM: a compound pendulum with only one knife edge, used
for relative measurement of gravity.
* * * * *
From Newton's laws of motion and the hypothesis that weight is
proportional to mass, the formula for the half-period of a simple
pendulum is given by T = [pi][sqrt](l/g). If a simple pendulum beats
seconds, 1 = [pi][sqrt]([lambda]/g), where [lambda] is the length of the
seconds pendulum. From T = [pi][sqrt](l/g) and 1 = [pi][sqrt]([lambda]/g),
it follows that [lambda] = l/T^{2}. Then g = [pi]^{2}[lambda]. Thus, the
intensity of gravity can be expressed in terms of the length of the
seconds pendulum, as well as by the acceleration of a freely falling
body. During the 19th century, gravity usually was expressed in terms of
the length of the seconds pendulum, but present practice is to express
gravity in terms of g, for which the unit is the gal, or one centimeter
per second per second.
[Illustration: Figure 2.--THIS DRAWING, FROM RICHER'S _Observations
astronomiques et physiques faites en l'isle de Caienne_ (Paris, 1679),
shows most of the astronomical instruments used by Richer, namely, one
of the two pendulum clocks made by Thuret, the 20-foot and the 5-foot
telescopes and the large quadrant. The figure may be intended as a
portrait of Richer. This drawing was done by Sebastian Le Clerc, a young
illustrator who made many illustrations of the early work of the Paris
Academy.]