from overflowing, which is especially problematic for small samples. For this reason it is desirable to use a water container with as small a mouth as possible. For each substance, the density, ρ, is given by When these densities are divided, references to the spring constant, gravity and cross-sectional area simply cancel, leaving Hydrostatic weighing Relative density is more easily and perhaps more accurately measured without measuring volume. Using a spring scale, the sample is weighed first in air and then in water. Relative density (with respect to water) can then be calculated using the following formula: where Wair is the weight of the sample in air (measured in newtons, pounds-force or some other unit of force) Wwater is the weight of the sample in water (measured in the same units). This technique cannot easily be used to measure relative densities less than one, because the sample will then float. Wwater becomes a negative quantity, representing the force needed to keep the sample underwater. Another practical method uses three measurements. The sample is weighed dry. Then a container filled to the brim with water is weighed, and weighed again with the sample immersed, after the displaced water has overflowed and been removed. Subtracting the last reading from the sum of the first two readings gives the weight of the displaced water. The relative density result is the dry sample weight divided by that of the displaced water. This method allows the use of scales which cannot handle a suspended sample. A sample less dense than water can also be handled, but it has to be held down, and the error introduced by the fixing material must be considered. Hydrometer The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cross-sectional area, as shown in the adjacent diagram. First the hydrometer is floated in the reference liquid (shown in light blue), and the displacement (the level of the liquid on the stalk) is marked (blue line). The reference could be any liquid, but in practice it is usually water. The hydrometer is then floated in a liquid of unknown density (shown in green). The change in displacement, Δx, is noted. In the example depicted, the hydrometer has dropped slightly in the green liquid; hence its density is lower than that of the reference liquid. It is necessary that