Density, and what a stone weighs

Weight is the first thing a hand notices and the property most often over-read. A tool that feels substantial gets called jade; a tool that feels light gets called fake. Both judgements are density judgements, and density is genuinely one of the most useful measurements available on these materials — once you know which comparisons it can make and how much precision each one needs.

The property

Density is mass per unit volume. Specific gravity is the ratio of a material’s density to that of water, so it is a bare number, and because water is close to 1 gram per cubic centimetre the two figures are numerically almost the same. Gemmology uses specific gravity, and every value below is one.

Laid out in order, the tool materials fall into a pattern with one wide gap and one bad pile-up:

  • Cast resin and plastic — close to 1, far below any stone
  • Obsidian, about 2.3 to 2.6, and manufactured glass, about 2.4 to 2.6
  • Serpentine, 2.4 to 2.8
  • Amazonite, 2.55 to 2.63
  • Chalcedony and agate, about 2.58 to 2.64
  • Quartz, about 2.65
  • Calcite, about 2.71
  • Nephrite, 2.90 to 3.03
  • Jadeite, 3.30 to 3.38
  • Austenitic stainless steel, about 7.9

Two things follow immediately. Jadeite is separated from everything else by a wide margin, and nephrite sits in its own band above the crowd. Everything from 2.4 to 2.71, however, is a single overlapping heap containing glass, serpentine, feldspar, both kinds of quartz and marble. A measured value in that range identifies nothing at all — it is consistent with half the possibilities, including the ones you were trying to rule out.

The method

Density needs a volume, and an irregularly shaped object has no volume you can calculate. The standard solution is over two thousand years old: measure it by displacement.

A submerged object is buoyed up by a force equal to the weight of the water it displaces, so it weighs less on a scale when submerged than in air, and the difference is the weight of that displaced water. Since a gram of water occupies about a cubic centimetre, the difference in grams is the volume in cubic centimetres.

So: weigh the object dry. Then weigh it suspended in water, hanging from a fine thread so that it touches nothing. Specific gravity is the dry weight divided by the difference between the two weights.

The arithmetic, and where it fails

Take a hypothetical tool. Dry weight 40.0 g. Suspended weight 27.0 g. The difference is 13.0 g, so the volume is about 13.0 cm³, and the specific gravity is 40.0 ÷ 13.0 ≈ 3.08. On the list above, that is nephrite’s top end or just above it, and clearly not jadeite.

Now attach error bars, because this is the part that decides whether the number means anything.

With a scale reading to 0.1 g, each weighing can be off by that much, and the difference of two weighings can be off by twice it. Worked at the extremes, 40.1 ÷ 13.2 and 39.9 ÷ 12.8 give a range of roughly 3.04 to 3.12. That is a usable measurement: it says nephrite rather than jadeite, and it says stone rather than glass.

With a kitchen scale reading to 1 g, the same object gives 41 ÷ 15 and 39 ÷ 11 — a range of about 2.73 to 3.55. That span contains serpentine, quartz, calcite, nephrite and jadeite. The physics is identical and the answer is worthless.

The reason is arithmetic rather than technique: the useful quantity is a small difference between two larger numbers, so the relative error in it is much bigger than the relative error in either weighing. On a light object it is bigger still. This is why the water test as usually described fails — not because it is the wrong idea, but because it is the right idea executed two decimal places short.

The other error sources

Air bubbles. Bubbles clinging to the surface add buoyancy, reduce the submerged weight, inflate the computed specific gravity, and are the single most common way this measurement goes wrong. Wetting the object thoroughly first and dislodging bubbles before reading is not optional.

The suspension. The thread is itself buoyed and itself wetted. Fine thread minimises it; ignoring it biases the result.

Contact. An object resting against the side or bottom of the container transfers part of its weight there, and the reading collapses.

Absorption. A porous stone takes water in, which changes its mass during the measurement in the wrong direction and unpredictably — so the technique is least reliable on exactly the materials whose connected pore structure makes them likely to be inexpensive substitutes.

Water temperature matters at the third decimal place and can be ignored at this level of precision.

What you can establish

WHAT YOU CAN TELL — from weight and displacement

  · Close to 1 → resin or plastic. Decisive
  · Below about 2.3 → not any of these stones
  · 2.4 to 2.71 → glass, serpentine, feldspar,
      quartz or marble. Identifies nothing
  · 2.90 to 3.03 → consistent with nephrite
  · 3.30 to 3.38 → consistent with jadeite;
      a genuinely strong finding
  · Which species inside an overlapping band
      → NOT DETERMINABLE from density at all

Why a rock’s density is not a species constant

One caution that applies to every value above. A mineral has a specific gravity; a rock has an average. Marble, serpentinite, quartzite and the dark rocks sold as bian stone are aggregates of more than one mineral in proportions that vary from block to block, so their densities are ranges, and a measurement lands inside a range rather than on a number.

Treatments shift it too, slightly. Wax, polymer filling and dye all add material of a different density to the stone’s pore space, and a heavily impregnated piece reads a little below the untreated mineral. The shift is small, and much smaller than the error bars discussed above, so density is not a treatment test.

The limit

Density is a constraint, not an identification. It excludes decisively at the extremes: nothing else explains a value near 1, and nothing common except jadeite explains a value above 3.3. In the middle it excludes nothing.

Used properly it is one of three home measurements worth making, alongside hardness and magnification, and the three together narrow the field considerably further than any one of them. Confirmation is a different order of thing — refractive index and spectroscopy, measured on instruments a gemmologist has and you do not. And a stone whose weight surprises you is telling you to measure it, not telling you what it is.