Holweck-lejay pendulum

Written by: Ahmed Magdy Beshr

Firstly, Fernand Holweck was a French physicist and the director of the laboratory

of the Radium institute in Paris. And Pierre Lejay was a French geophysicist and the

director of the astronomical observatory in China.

In 1930, they developed this pendulum as a gravimeter used to measure the

gravitational force. It depended on the principle of inverted or reverse pendulum. This

pendulum developed in 1932, the new model was said to be ten time more precise than

the original one. A third model developed later in the same year, was about two

hundred times as sensitive to gravity changes comparing by the ordinary free swinging

pendulums. The apparatus used for the first time in gravity

survey in France and China.

It consists of a short, flat, and vertical spring of elastic

metal, one end of the spring fixed to the horizontal, and the

other end carrying the mass, so that the period of oscillation

depends on the elasticity of the spring as well as on the mass,

and the inertia moment of the pendulum.

When the mass pulled away from the vertical position of

equilibrium the elasticity of the spring resulting in restoring

force restore the pendulum to the equilibrium position. The restoring force exceed the

gravity force. The result is small change in gravity causes a large relative change in the

restoring force and a great change in oscillating time, this mean that the apparatus has

high sensitivity to the gravity changes.

It was fast and sensitive and accurate gravimeter can be very useful in ore

prospecting, but the disadvantage of this pendulum that it need long time for reading.

The period oscillation and the oscillating time of the pendulum can be used to measure

gravitational acceleration, so it can be used in prospecting for natural resources.

Different types of underground resources have different densities, increasing or

decreasing gravitational attraction that can be detected by this pendulum.

The equation of the pendulum is: 𝑇 = 𝜋(𝐼

𝐾𝑀𝑔𝐿)

1

2

where: K is constant expressing the elasticity of the spring.

M is the mas.

L is the length of the pendulum.

I is the inertia moment of the pendulum.

g is the gravity acceleration.