Galileo, Huygens, and Newton
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.
Glossary of Gravity Terminology
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.