Kater’s pendulum Little g Local variation Commentary

Christiaan Huygens, Gaspard de Prony, Henry Kater kinematics

Kater’s pendulum

• Calculating the precise length of a pendulum
• is difficult because
• a pendulum is constructed of multiple materials
• and the masses of its parts
• are not uniform.
• But Christaan Huygens proved
• that a pendulum’s center of oscillation
• is interchangeable with its pivot point;
• that is, if you interchange their positions,
• the pendulum will have the same period.
• Huygens also gave the formula
• that relates the length and period of a pendulum
• to the force of gravity, so Gaspard de Prony realized
• you could use this formula and the length of a pendulum
• to calculate the local force of gravity.
• Independently, Henry Kater had the same realization
• but also built and refined the reversable pendulum
• with reversable pivot blades
• and showed how to use it to calculate
• the local force of gravity.

Little g

• It turns out that local gravity is affected
• by the bulging of the globe at the equator,
• by centrifugal force of Earth’s rotation,
• by the gravitational pull of the sun and moon,
• by the atmospheric pressure and your altitude,
• and by the thickness and density of the earth beneath you,
• not necessarily in that order.
• Gravitational anomalies beacon the tourist
• to watch water flow uphill or otherwise indulge
• in fantasies related to visual illusions.
• Very small differences are imperceptable
• except to the skeptical and refined.

Local variation

• After your first drink, you feel lighter;
• after your last drink, heavier.
• Individual gravitas may differ.
• In free-fall, you feel no gravity at all.
• Between individuals, differences
• are greater than between groups.
• Trying harder may harden the effect.