 The torsion balance is a device used to measure very weak forces between two objects. You might be familiar with its use to measure the force of electricity or the force of gravity. The torsion balance's first big break came in 1777 when Coulomb used it to determine the electrostatic constant. But it was used famously again 21 years later by Cavendish to measure the force of gravity between two masses in an experiment that would lead to the determination of the universal gravitational constant. In this video, I'm going to show you how each of these torsion balances worked. The basic design of each torsion balance is the same. A bar is suspended from a fine wire or string. On the bar is a sphere which is placed near to another fixed sphere, a distance r away. r is the center to center separation between the two spheres. The word torsion means twisting and if the spheres are attracted or appell from each other, the wire will twist. The angle through which the wire twists can be directly related back to the force between the two spheres using some pretty heavy physics which I won't get into here. In Cavendish's design, the rod was made of wood and was just under two meters long. Two lead balls with a mass of about three quarters of a kilogram were placed at each end of the rod and the hanging spheres were placed initially about 23 centimeters from a large 30 centimeter and 156 kilogram lead ball. All of this mass was needed to produce the force of gravity between the spheres, something big enough to be measurable. Even still, the movement of the hanging spheres was tiny, only about 4 millimeters. The entire apparatus was placed in a shed in Cavendish's yard to remove the effect of air currents and it took measurements through a telescope fitted to the wall of the shed. Coulomb's torsion balance was an earlier and smaller design. The rod was a small needle and a small metal sphere was fixed on the end. A similar small sphere with an electric charge is introduced into the system. The charged sphere touches the neutral sphere and both have the same nature of charge, either positive or negative, and the spheres begin to repel each other. The torsion in the thread and the center-to-center separation between the spheres is again measured. The whole apparatus fits on a tabletop and is enclosed in a glass cylinder to reduce outside air currents. So what are the results of these experiments? Both Cavendish and Coulomb graphed the force measured as a function of the separation of the objects and found a very interesting relationship. As the separation between the objects increased, the force between the objects decreased. But it wasn't a linear decrease, meaning if the spheres were three times further apart, the force was not three times smaller. The relationship was an inverse square one. When the spheres were three times further apart, the force between them was three squared or nine times smaller. In Cavendish's data, the universal gravitational constant found in Newton's law of universal gravitation was derived. And in a similar fashion, Coulomb's data allowed for the determination of the electrostatic constant in Coulomb's law. The similarity between these two formula and the likeness of the experiments is one of my favorite examples of the beauty of the natural world as modeled by physics.