Desert Gold Diggers

Specific Gravity Test

Introduction

Club member Vince Simkins asked "How is a specific gravity test done with a nugget containing quartz?". That is, how to determine the amount of gold in a specimen containing gold and quartz. I sent him a link to another site but in looking closely at that site and other sites, I was either confused about their discussion or their formulas. Thus I have written the following notes which give the formula in general terms for any two known minerals, using two different methods, with examples, followed by a complete derivation of the formulas for those who want to know how the results were obtained. I have also added an online calculator to simplify the calculations. Thanks to Vince for bringing this omission to my attention.

These tests will only give a general idea since it is extremely unlikely that the specimen only contains two pure minerals. However it will at least give a ballpark estimation. If possible, for best results try to obtain a sample of each mineral from the same area that appears to only contain that mineral and measure the specific gravity of each for the values in the following formulas. One can look up the average specific gravity of gold for many areas since gold is almost never found in a pure state. Many minerals have a range of values for specific gravity as shown in the list of minerals on the Gold Facts page. For more information about sources of error see the discussion below. This discussion assumes gold in a matrix of another mineral such as gold in quartz. However this test can also be used to determine the amount of gold in a nugget that also contains silver or copper.

Specific Gravity Measurements

For both methods discussed below, the weight of the sample should be first measured dry and noted. Call this Wsa Weight of the sample in air.

For both methods, you need a container of water large enough that the sample can be completely submerged without water going over the top. Figure 2 below is adapted from a graphic at Gem Identification.

Method 1

Weight of displaced 
		water
Figure 1: Weight of the displaced water.

For the first method, place the container with water on a scale and note the weight or zero the scale for a direct measurement. Suspend the sample in the container of water by a very thin thread or thin fishing line or similar line so that the volume of the line is negligible compared to the volume of the sample. You can hold the string or tie it to a brace such as a simple banana holder. The sample must be completely submerged but not touch the bottom or sides of the container. Then note the weight of the container with the sample suspended in the water. The increased weight of the water should be noted. Call this Ww Weight of the displaced water. (See Figure 1) The advantage of this method is that a variety of scales can be used such as the triple beam balance that is shown.


Method 2

Weight of 
		sample in water
Figure 2: Weight of the sample in water.

The second method requires a balance or similar type scale as the weight of the sample itself must be measured while it is completely suspended in water. Again the sample must be completely submerged but not touch the bottom or sides of the container. Note the weight, which we will call Wsw Weight of the sample in water. (See Figure 2)


Specific Gravity Formulas

Two formulas for the weight of gold (or first mineral) are given below corresponding to the two methods above. All the weight measurements must be in the same units, i.e. all in grams or all in ounces or all in some other unit.

  1. Wg = (Wsa * A) - (Ww * A * B)
    where A = Sg / (Sg - So)
    and B = So
    with Wg being the weight of gold in the sample,
    Sg is the specific gravity of the gold (or the first mineral) and
    So is the specific gravity of the second mineral
  2. Wg = Wsa * A * (1 - B) + (Wsw * A * B).
    with A and B as defined above.

Both formulas above are related by the fact that the weight of the sample in air is equal to the weight of the sample in water plus the weight of the displaced water, Wsa = Wsw + Ww. The specific gravity of a single mineral is Wsa / Ww which is the same as Wsa / (Wsa - Wsw) as shown at Gem Identification.

For the specific gravities of several common minerals, see our Gold Facts page.

Specific Gravity Calculations (Online calculator)

To use this calculator, enter the proper values in the Common Variables form, then enter the first value in either the Method 1 or Method 2 form and click the Calculate button. The computed values will appear below the Calculate button.

The default values below are for gold, using an average specific gravity of 18.6, and quartz, using a specific gravity of 2.65. These values assume a specimen of gold in a matrix such as quartz. However for a gold nugget, containing another mineral such as silver, use the specific gravity of pure gold, 19.3, and pure silver, 10.5.

Common Variables
(Enter these values first and then proceed to either Method 1 or Method 2 below)
VariableValue
Specific gravity of the gold or the first mineral (Sg)
Specific gravity of the second mineral (So)
Dry Weight of the sample (Wsa)
Significant decimal digits in answer, default 1

The number of significant decimal digits should be set to the least number of digits after the decimal point in the input values. For instance, the value of 18.6 has only 1 number after the decimal point. Thus the number of significant decimal digits should be set to one. Calculations are set to use one more digit than this entry.

The Common Variables above must be completed before proceeding. For either method below, fill in the first value and then press the Calculate button. The bottom 2 values are then computed.

Method 1
VariableValue
Weight of the displaced water (Ww)
Calculate the weights of both minerals
Weight of the gold or the first mineral (Wg)
Weight of the second mineral (W2)

Method 2
VariableValue
Weight of the sample in water (Wsw)
Calculate the weights of both minerals
Weight of the gold or the first mineral (Wg)
Weight of the second mineral (W2)

To convert the above values to another unit of measurement, see the list of conversions at the top of the Gold Facts page. There are also many conversion charts and calculators on the internet.

Specific Gravity Examples

I thought that modern U.S. coins might make good examples but most are composed of Ni and Cu which have almost the same specific gravity or are composed of 3 elements. If anyone knows of objects with a known composition of 2 substances with each substance having a known specific gravity, please let me know. I am looking for a good test of the above methods with known quantities.

Two examples are shown and compared to results from other web sites. All weight measurements must be in the same units and the resulting weight of gold will be in the same units.

The value of 19.3 used below for the specific gravity of gold is too high for placer gold. This was only used for comparison to other web sites.

  1. Assuming that the specific gravity of gold is 19.3 and the specific gravity of quartz is 2.65, we have:
    A = 19.3 / (19.3 - 2.65) = 1.16
    B = 2.65
    A * B = 3.07
    which for the first method results in
    Wg = Wsa * 1.16 - Ww * 3.07
    Thus the weight of gold would be 1.16 times the weight of the sample in air minus 3.07 times the weight of the displaced water. This method doesn't seem to be used on other web sites even though it is mentioned.
  2. Wg = Wsa * A * (1 - B) + (Wsw * A * B).
    With A and B as defined above
    A * (1 - B) = -1.91
    A * B = 3.07
    Thus the weight of gold would be 3.07 times the weight of the sample in water minus 1.91 times the weight of the sample in air. This is the same result as shown on specific gravity test for gold nuggets. Any differences in final results of weights between this page and the cited page are due to rounding differences. The numbers, on the web site cited above, use 1 significant decimal digit in the calculations but show 2 in the final answer. This page uses uses a default of 2 significant decimal digits in the calculations but show only 1 in the final numbers.

Specific Gravity Definition

According to the "Dictionary of Geological Terms" the definition of specific gravity is as follows. "The ratio of the weight of a given volume of a substance to the weight of an equal volume of water." More accurately, "Specific Gravity is the ratio of the weight of a substance and the weight of an equal volume of pure water at 4 degrees C."

Limitations and Sources of Error

For best accuracy on our measurements the above definition has restrictions on water purity and temperature. There are charts if one wants to correct for temperature. However neither of these compare to the inaccuracy due to the unknown composition of the sample as we are just making guesses about composition and specific gravities. One source of error can be caused by air bubbles clinging to the sample. It is best to use distilled water. If air bubbles form, a slight movement of the sample in the water will help to remove them.

Scales

There are special scales for calculating specific gravity but these are not needed for the tests on this page. Ore samples found in the field have too many unknowns for any exact calculations. This section will mainly discuss the types of scales that can be used for the specific gravity tests on this page and for weighing your gold.

Equal Arm Balance
An Equal Arm Balance/Trip Balance scale can be used for either of the methods discussed above. This consists of two pans, each equidistant from the center or fulcrum. The material to be weighed is placed on one pan and standard weights are placed on the other pan until the scale is balanced. Any Balance scale measures mass, not weight. The scale shown is from Scales & Balances at Schoolmasters Science. The scale is only $42.50 but weights, total weight of 100 grams with a resolution of 1 gram, cost another $16.25. Most of these types of scales are fairly inexpensive but are designed for high school projects. They have minimum range and low resolution. Analytical Balances are highly accurate but also much more expensive.

Dillon's 'Eliminator' Scale Gun reloading Grain balance beam scales are great for weighing small pieces of gold. These usually have a 0.1 grain (0.0065 gram) accuracy but are limited in maximum capacity, usually around 500 grains (33 grams) and cost around $45 to $50. They can usually be found at a local gun shop or online. Bob Boor has one that he bought many years ago from a local gun shop, manufactured by Dillon Precision Products, that has a maximum capacity of 511 grains and is accurate to 0.1 grain. The present model, shown here, is Dillon's 'Eliminator' Scale with a price of $50. There is also an electronic version with a 900 grain capacity and accurate to 0.1 grain but it costs $140. In general, these have too small a capacity to be used for the specific gravity tests but are great for weighing small amounts of gold.

ProScale XX 500g x 0.1g
For weighing samples of gold in quartz, meteorites, or large nuggets (lucky you), a larger capacity may be needed. There are digital and analog pocket scales ranging from a 50 gram capacity with 0.01 gram accuracy to 500 grams with 0.1 gram accuracy; though some go up to 2000 grams with 0.1 gram accuracy. Shown here is a ProScale XX 500g x 0.1g digital scale. Most of these are less than $50. Depending on the scale capacity and sample size, these scales could be used with Method 1 above.


MyWeigh Triple Beam Balance
For very large items, Triple Beam Balance Scales have capacities of up to 2610 grams (2.6 kilograms or 5.75 pounds) with an accuracy of 0.1 grams. A MyWeigh brand balance can be purchased for around $75. These scales can definitely be used with Method 1 above for the specific gravity test.

Club member Vince Simkins mentioned that www.saveonscales.com has quality stuff and fair prices. Some of the above prices came from this web site.

Both Bob and Vince have scales made by a variety of manufacturers and both would be a good source of information about purchasing a scale. You can buy a calibrated weight to check your scale occasionally or even use a new coin. Coins have a known weight when minted and this weight is usually easy to find in coin books or on the Web. For instance, from the U.S. Mint web site, the dime weighs 2.268g, the nickel 5.000g and the cent 2.500g. Of course these weights only apply to newly minted coins.

Specific Gravity Formula Derivations

The above formulas are derived from first principles.

The volume of the sample is the sum of the volume of gold and the volume of the other mineral.
Vs = Vg + Vo or
Vo = Vs - Vg, where
Vs = Volume of the sample
Vg = Volume of gold (or the first mineral)
Vo = Volume of the second mineral

The weight of the sample is the sum of the weight of gold and the weight of the other mineral.
Wsa = Wg + Wo where
Wsa = Weight of sample in air
Wg = Weight of gold (or the first mineral)
Wo = Weight of the second mineral

Rearranging the equation to solve for the weight of gold
Wg = Wsa - Wo
Since Weight = Density * Volume * gravity (D * V * G)
Wo = Do * Vo * G
where Do = the density of the second mineral and
G = the force of gravity, we have
Wg = Wsa - (Do * Vo * G)

Noting that Vs = Vg + Vo or Vo = Vs - Vg, we have
Wg = Wsa - (Do * (Vs - Vg) * G)
Wg = Wsa - Do * Vs * G + Do * Vg * G

Since the volume of the sample is the volume of the water displaced (Vw),
Vs = Vw = Ww / (G * Dw) where Dw is the density of the water
Substituting for Vs we get
Wg = Wsa - Do * (Ww / (G * Dw)) * G + Do * Vg * G
Wg = Wsa - Do * (Ww / Dw) + Do * Vg * G
Wg = Wsa - Ww * (Do / Dw) + G * Do * Vg

Since Wg = G * Dg * Vg or Vg = Wg / (G * Dg)
Wg = Wsa - Ww * (Do / Dw) + G * Do * (Wg / (G * Dg))
Wg = Wsa - Ww * (Do / Dw) + (Do * Wg) / Dg
Wg = Wsa - Ww * (Do / Dw) + Wg * (Do * / Dg)
Wg - Wg * (Do * / Dg) = Wsa - Ww * (Do / Dw)
Wg * (1 - (Do / Dg)) = Wsa - Ww * (Do / Dw)
Wg * ((Dg - Do) / Dg) = Wsa - Ww * (Do / Dw)
Wg = Wsa * (Dg / (Dg - Do)) - Ww * (Do / Dw) * (Dg / (Dg - Do))

To simplify, let
A = (Dg / (Dg - Do)) and
B = (Do / Dw) giving
Wg = Wsa * A - Ww * A * B
However, since A is a ratio of densities, we can substitute the corresponding specific gravities. The B term is the specific gravity of the second mineral. Substituting the specific gravities results in
A = Sg / (Sg - So) and
B = So
which produces the first formula discussed at the top.

The weight of the displaced water (Ww) is equal to the weight of the sample in air (Wsa) minus the weight of the sample in water(Wsw) or
Ww = Wsa - Wsw
Substituting this into the first formula.
Wg = Wsa * A - Ww * A * B
gives
Wg = Wsa * A - (Wsa - Wsw) * A * B
Wg = Wsa * A - (Wsa * A * B + Wsw * A * B)
Wg = Wsa * A * (1 - B) + Wsw * A * B
which is the second formula discussed at the top.

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This page was last updated on 9 Feb 2008.