As the density of must decreases during fermentation due to the consumption of sugar, we want a proportional amount of tilt to be experienced by the floating hydrometer. In order for this to happen, principles of density, buoyancy, gravity, and stability, all must work in concert.
As the must’s gravity lowers, the hydrometer sinks lower into the liquid and the angle of the device approaches vertical. This is because volume of liquid that must be displaced increases as the density of that liquid decreases in order for the hydrometer to stay afloat. The center of mass being towards the bottom of the device means that the center of buoyancy is also located towards the bottom, and this concentration of forces towards one end causes the device to tilt.
This tilting is due to tiny incremental shifts that cause the center of buoyancy to reorient with respect to the center of mass. As this happens, the forces of gravity and buoyancy find equilibrium only after the device’s tilt angle shifts. Given that these two sole forces on device continually form a neutral equilibrium, and that the mass, center of mass, and density of the device are constant, we can deduce that the density of the liquid is the only factor that will cause the device’s angle to change. Combined with the temperature, we can then calculate the gravity.