A hydrometer measures the relative density of different liquids. When an object floats in a liquid—when it is neutrally buoyant—the upward force of the liquid perfectly balances the downward force of gravity on the object, better known as its weight.
According to the Archimedes’ principle, this force is equal to the weight of the fluid that the object displaces. This means the volume of the fluid that used to be in the space that the floating object now occupies weighs the same as the floating object.
The force required to keep your hydrometer buoyant is dependent on the hydrometer's shape, mass, and volume. When it is placed in fluid, it will sink until it displaces enough fluid to balance this force. The amount displaced will be a fixed mass of fluid, regardless of the fluid. Therefore, the volume of fluid displaced depends on the fluid’s density.
You may have noticed that your hydrometer floated higher in the salt-water solution. This is because adding salt to water makes the solution more dense.
If a fluid is less dense, the hydrometer will need to displace more fluid to reach the balancing point between upward and downward force, so it sinks deeper into the fluid. If the fluid is more dense, such as the salt-water solution, the volume the hydrometer needs to displace will be less, so it floats higher.
By using water as your zero-reference point, you can calibrate your hydrometer to show the relative density of liquids compared to water. Try testing different concentrations of salt water or even other liquids, such as corn syrup, oil, or alcohol.