How to Calculate Specific Gravity


There are two principal methods of determining specific gravity.

The Direct Weighing Method

From the definition: specific gravity is equal to the weight of a stone divided by the weight of an equal volume of water. The weight of a stone can be found readily by weighing on an accurate balance. The weight of an equal volume of water can be found by the simple principle discovered by Archimedes, which states that "if a body is totally immersed in water, it loses an amount of weight equal to the weight of the water it displaces. Hence the weight of an equal volume of water is equal to the weight lost by the stone when immersed. Thus:

S.G. = (Weight in Air ) / (Weight in Air - Weight in Water)

In other words, the specific gravity of a stone is the number obtained by dividing its weight in air by its loss of weight when weighed in water. This gives a simple method of finding the S.G. of a cut stone.

In further explanation:

  1. Weigh the stone in air; assume this is 4.2 carats.
  2. Weigh the stone in water; assume this is 3.0 carats.
  3. The difference in the two weighs gives the loss of weight in water: loss of weight: 4.2 - 3.0 = 1.2 carats.
  4. S.G. of stone = weight in air divided by loss of weight in water: S.G. = 4.2/1. 2 => 3.5
    (Note that the S.G. is a number that represents a RATIO I not a weight.)

For making S.G. determinations by the direct-weighing methods, a delicate balance, such as a good diamond balance is needed. Weighing the stone in air is simple, but to obtain an accurate weight in water is a slightly more complicated undertaking. The problem is how to weigh the stone in water with a minimum of time and equipment. The balance must be adapted so that the stone can be weighed accurately in air and in water. This is accomplished by using a few simple attachments consisting of two thin wires, a glass beaker and a suitable support. These accessories can be constructed easily or purchased by those who have a diamond balance and who wish to add the necessary equipment.

The small metal support is bridged over one balance pan, so that it does not interfere with the free swing of the balance. The beaker of water is then placed on this stand and one of the thin wires is bent to form a basket at one end to hold the stone. This is suspended from one arm of the balance and immersed in the liquid. The other wire is suspended from the opposite arm of the balance and then clipped or filed off until it balances exactly the wire suspended in the water.

The surface tension of the water acting on the wire at the point where it enters the water causes a damping effect(drag) on the free swing of the balance. This considerably reduces the accuracy normally obtained from the balance. However, a detergent such as "Dreft", "Vel" or "Tide" effectively reduces the surface tension of water, and the pinch or two necessary docs not alter the density of the water sufficiently to require a correction factor. The proper temperature for the distilled water used in the direct weighing method is, as previously mentioned, 4°C, or about 40°F, However, using water at ordinary room temperature of about 70°F, will not materially affect the calculation.

The following example will make the method clear. Given a yellow stone to test:

  1. Weight of the stone in air = 12.89 carats.
  2. Place the stone in the wire cage, remove all bubbles, and see that it is completely immersed. New weigh the stone carefully in water. It weighs 9.67 carats.
  3. Loss of weight in water = 12.89 - 9.67 carats.
  4. S.G. = 12.89/3.22 = 4.00
  5. Looking up this value in the accompanying table, we see that the stone is probably yellow sapphire (corundum), either natural or synthetic.

It will be noted in the table that normal S.G. values as well as the most generally encountered variations are listed. However, no tolerance is considered for mechanical errors in making S.G. determinations. There is a definite lower limit in the weight of the stone being tested to which diamond-balance determinations can be given any accuracy.

A colored mineral usually varies in specific gravity from one specimen to another, due particularly to slight variations in chemical composition. Therefore, several similar minerals may have the same S.G. because their values overlap, as seen in the table. The values for specific gravity in all mineralogy texts and in some gemology texts are for all varieties of a given mineral species. Such tables may add unnecessarily to the confusion of the gemologist who is using them and who needs to consider only gem qualities of the various species. The figures in the table are for gem materials, and show specific gravity to be one of the more important tests.

To illustrate the effects of errors in weighing, refer again to the example given above. The weight of the stone in air is 12.89 carats and its weight in liquid is 9.67 carats. Suppose a mistake of one point had been made in weighing the stone in liquid. If the weight had been 9.66 instead of the correct 9.67 figure, the difference between 9.66 and 12.89 is 3.23 carats. By dividing 3.23 into 12.89, a specific-gravity determination of 3.99 is made. Therefore, an error of only. 0 1 occurs because of a mistake of one hundredth of a carat in the weight.

A stone that weigh's 1.20 carats in air and 90 points in water would have an S.G. of 4.00. If, however, a mistake is made in the weighing and the weight in water is determined as .89 carats instead of .90, the error will be greater. Dividing 1.20 by .31 gives a resulting S.G. of 3.87; therefore, the error is 0.13. Carrying this example one step further, if a stone weighs .40 carats in air and. 30 carats in water, it has a specific gravity of 4.00. An error in this case of one point, giving a water weight of .29, would result in the determination being 3.63 to 3.64. In other words, an error of more than 0.35 in S.G. would result.

From the above discussion, it can be seen that specific-gravity determinations by the diamond-balance method for stones of less than one-half carat are not accurate unless very careful weightings are made. No such limitation exists when heavy liquids are used instead of the diamond balance.



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