# Hydrostatic Balance

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The hydrostatic balance is used to determine the specific gravity of a gemstone. Although it is a fairly simple apparatus to operate it can be time consuming and one would need to put the results in a calculation, something not all gemmologists enjoy doing.

## Basic

Specific gravity (SG) is a constant ratio of an object's weight compared to an equal volume of water. When an object in totally immersed in water it will experience an upward trust that is equal to the volume of water which is displaced by the object. This will make the object appear lighter in water.
The first to observe this was Archimedes while investigating a possible fraud with a crown for King Hiero of Syracuse (present day Sicili).

### Archimedes and Archimedes' Principle

When King Hiero commisioned a new gold crown a certain volume of gold was provided to a goldsmith, who manufactured the crown to the liking of the king. Soon after rumours started that the goldsmith may have been frauduleus and added silver to the gold, making a nice profit for himself on the side.
King Hiero asked Archimedes to investigate and one day while taking a bath, Archimedes noticed that his body mass caused the water in the bath to overflow. In his excitement over finding a possible answer to the problem he ran home naked, shouting "eureka" (I've found it out).

He immersed equal weights of gold and silver in water and by observing the amount of water that was displaced, he noticed that the mass of gold displaced less water than the silver. He then immersed the crown and through a series of calculations he was able to determine how much gold and silver was used to create the crown. The fraud was detected and this was the first time in history SG was used.

Archimedes' Principle (or the Law of Buoyancy) states that: the upward force on an immersed object is equal to the weight of the displaced fluid.

### Types of hydrostatic balances

In gemmology 4 different types of hydrostatic balances are used.

• The two-pan scales
• The one-pan scales
• Spring balances

#### Two-pan scales

The two-pan scales are the most time consuming scales to use. Some jewelry stores still use them but little of them are used for determining SG of stones. Mostly because the counterweights in general are not small enough to be of any help and they really need to be calibrated every few years.

The principle of the two-pan scale is very useful for explaining the hydrostatic balance though.

A gemstone is placed on the left pan of the balance and on the right pan weights are placed so that the balance "zeros out". When the balance is equal, the total of the weights on the right pan is read and that will be the weight of the stone in air.

Then a freestanding stage with a beaker filled with water is introduced. After that a thin coil wire basket is hung on the left side of the balance with the basket totally immersed in the water. At this time the balance should be in complete balance by adding a small weight (equal to the weight of the basket).
The stone is placed in the thin coil wire basket and then immersed in the water. Again counterweights are placed on the right pan as before and the result of added weights will be the weight of the gemstone in water.
The wire basket should be of a material that is not water absorbant to avoid false readings. One should also take care that airbubbles around the basket and stone will not influence the readings (air bubbles tend to rise upwards and could add to the upward trust).
To avoid surface tension a small droplet of detergent is added to the water.

After taking both the weight in air as in water the following calculation should be carried out.

$SG = \frac{weight\ of\ stone\ in\ air}{weight\ of\ stone\ in\ air\ -\ weight\ of\ stone\ in\ water}$

#### Single-pan scales

Most gemmological scales are of this type and they can be either analogue or digital. They come in various sizes and in every price range. For our purposes it is best to get a carat scale opposed to a gram scale, although the latter could serve very well when it has a high precision (for instance 0.01 grams, which is equivalent to 0.05 carat). These digital scales are very economical (under USD 100,00).

Various hydrostatic setups can be used for them. One could use a bridge on which the glass beaker is placed, with a coil wire that is placed directly on the scale (see video below). Or the beaker is placed directly on the scale with the stone hanging from a wire that is attached to a stage (as illustrated on the right).

##### Video presentation

In the following video (2:28 minutes) the use of a single-pan electronic scale is given. The hydrostatic addition uses a beaker in a bridge and the wire directly on the scale.

 Specific Gravity Video Video showing the method of determining hydrostatic specific gravity - WMV/video format - 7.96MB

#### Spring balances

This type of hydrostatic weighing can come in handy when handling large pieces of rough that are heavier than your usual balance can handle.
Spring balances are relatively inexpensive and come in a large variety of accuracy. As usual, the stone is first weighed in air and then it is weighed in water (one should ofcourse also weigh the part of the balance that is immersed into the water).
The larger the rough and the higher the accuracy of the balance, the more precise your measurements will be.

A spring balance is usually used in the field just like a recreational fisherman would use it to weigh a fish.