The Determination Of The Weight Of A Set Stone By Hydrostatic Weighing

2007: I tried it; it works.

(via The Australian Gemmologist, Vol.18, No.5, February 1993) R K Mitchell writes:

Another gemological tip arising from our earlier discussion of hydrostatic weighing is the fact that it is by no means a waste of time to do a hydrostatic on a stone in a mount. How often are we called upon to estimate the weight of set stone for insurance purposes or with a view to buying it in over the counter? Various methods have been advocated from plain guesswork, to gauges of greater or lesser efficiency, to comparison with stones of a known weight, to weighing another mount to get somewhere near the weight of the one in question, or even to measuring the stone in all its dimensions and working out a weight using complicated mathematical formulae to obtain an approximation. Some of these might work, but there is a risk of getting hopelessly wrong answers to what should be simple enough question even when we cannot get permission to unset and weigh the stone separately.

In the past I have been offered a peridot ring with the remark that it ‘must weigh over 12 carats’ and have found myself in possession of a nice stone of over 26 carats. A star sapphire offered at ‘about 15 carats’ estimated weight, turned out to be around 35 carats when I took it out of its setting. Such inexact guesses are quite unnecessary and are very dangerous to the jeweler if he is valuing the stone. The answer lies in doing an ordinary hydrostatic weighing, a matter of a few minutes only.

Simply weigh the whole item in air and then weigh it again in water. Subtract the second weight from the first to find the total loss of weight.

Then, if we already know what the stone is (from its RI) and the nature and quality of the metal (hallmark), it is very easy to arrive at a weight for either the stone or for the mount by simple calculation. First assume that the whole ring is composed of stone and multiply the stone’s SG by the loss of weight. Deduct this figure from the total weight of the piece and that will give us the extra weight due to the greater density of the metal used. Divide this figure by the known SG of the metal less the SG of the stone.

Specific gravity of precious metals

Yellow gold
9 ct=11.2
14 ct= 14.1
18 ct= 15.5

White gold
9 ct= 12.0
14 ct= 12.9
18 ct = 16.1

Platinum = 21.4
Silver = 10.3

Victorian gold mounts with silver settings are usually 15 ct gold, so an SG figure of 12 would be a fair approximation, but the method is a little less accurate with such mounts.

This gives us the loss of weight due to the mount alone. Subtract this from the total loss of weight to find the loss due to the stone only, and multiply the result by the SG of the stone. This sounds complicated, but it is nothing of the kind. Try it and see. The longest part is the weighing and even that should not take more than a few minutes.

To give you an actual example:
An aquamarine (SG=2.70) and 18ct gold (SG=15.5) ring weighs 35.32 cts.
In water it weighs 28.75 carats
Loss of weight = 6.57 carats
If all aquamarine then weight would be 6.57 x 2.70 = 17.74
Extra weight due to gold = 35.52 – 17.74 = 17.58.
So loss of weight of mount is 17.58 divided by 15.5 – 2.7 = 1.37.
So loss of weight due to the stone is 6.57 – 1.37 = 5.20.
Weight of the stone is then 5.20 x 2.70 = 14.04 carats.

There are very minor differences in the SG of a gem species from stone to stone, and rather greater differences in the SG of gold of a given caratage (bullion dealers for this reason usually quote only to one place of decimals). But this method can usually be relied upon to give an answer well within 10% of the true weight of a stone. Where there are a few small diamonds included in the design one obviously needs to take these into account at the end of the main calculation by deducting say half a carat from the estimated weight of the main stone. Most jewelers are expert at estimating the weight of small diamonds by sight and should have little difficulty in making a reasonable correction for this situation. The method only really comes to grief when a mass of large stones of mixed species are found in one mount, and even then some guidance can be obtained from the exercise if it is used intelligently.