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.

Kater’s pendulum was so commonly used to measure the strength of the gravitational field that instead of expressing the value in units of acceleration, distance per second squared, scientists expressed the value as the length of the seconds pendulum.

Jean Richer was the first to discover, in 1671, that gravity did not have the same magnitude over the surface of the earth. This was 244 years before Einstein’s general theory of relativity.

See also in

The book of science:Pendulum clock—Christiaan HuygensGravimetry—Jean RicherPrincipia Mathematica—Isaac NewtonGeneral relativity—Albert EinsteinReadings on wikipedia: