Every stone article in this knowledge base opens with a small card of figures. They are not decoration: together they are how a gemmologist decides what a stone is, because two stones of the same colour almost never share all four.
Hardness
The Mohs scale ranks minerals from 1 (talc) to 10 (diamond) by what scratches what. It is a ranking, not a measurement: the step from 9 to 10 is far larger than the step from 1 to 2. In practice the test is done the other way round, with a set of hardness points pressed against an unseen part of the stone, and only when nothing else will do, because it leaves a mark. For what hardness means for wearing a stone, see which stones can be worn every day.
Specific gravity
Specific gravity is how much heavier a stone is than the same volume of water. Diamond is 3.52, quartz 2.65, hematite over 5. It explains why a cubic zirconia of the same size as a diamond feels heavier in the hand, and why a large opal is so light. A gemmologist measures it by weighing the stone in air and again in water, or by dropping it into liquids of known density to see whether it floats or sinks. The card gives a range, because most minerals vary a little with their composition.
Refractive index
Light slows down when it enters a stone, and the refractive index is the ratio: in diamond light travels at about 124,000 kilometres a second instead of 300,000, an index of 2.417. The higher the index, the more a well-cut stone sparkles, because more light is bent back towards the eye. It is measured on a refractometer, a small instrument on which the stone lies on a glass with a drop of contact fluid; the reading is exact and takes a minute. The instrument stops at about 1.81, so diamond, zircon and moissanite go off its scale and are identified by other means. Most stones show two readings, one for each of the rays the crystal splits light into; the difference is the birefringence, and the doubled facet edges in zircon and moissanite are it made visible.
Dispersion, or fire
White light entering a stone is split into its colours, and how far apart the colours come out is the dispersion. Diamond's 0.044 is what gives it its flashes of colour; sapphire's 0.018 is why a sapphire is bright but rarely fiery. Zircon (0.039) comes close to diamond, cubic zirconia (0.065) and moissanite (0.104) go well beyond it, which is one way to spot them. The card shows the figure where it is known; for opaque stones and glasses it means little.
Crystal system
The pattern in which the atoms are stacked, which decides whether a stone shows one colour or several, whether it splits light, and whether it cleaves. See how crystals grow: the crystal systems.
And the streak
One test the card does not show: rubbed on unglazed porcelain, a mineral leaves a powder streak whose colour can differ from the stone's. Hematite is grey-black but streaks red; most gems leave a white or colourless streak. It is a mineralogist's test rather than a jeweller's, because it damages a cut stone.
What this means for you
You do not need any of these instruments. What you need is to know that they exist, so that a laboratory report or a goldsmith's identification is a measurement and not an opinion, and so that it looks like is never the reason you pay for a stone. See grading reports.