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Look at a cliff with stripes of rock, or at a quartz crystal that has grown lopsided, and you are looking at the two puzzles Nicolaus Steno solved in a short book of 1669. He was trained as a doctor, yet his rules for reading rocks and crystals are still in geology courses. This post covers who he was, what he saw, and how to apply his ideas with simple worked examples.
Who was Nicolaus Steno?
Niels Stensen, Latinised as Nicolaus Steno, was born in Copenhagen on 11 January 1638, the son of a goldsmith, according to a 2025 profile in the *Journal of Medical Biography*. As a medical student in Amsterdam he found the duct of the parotid salivary gland, still called Stensen's duct, and then studied at Leiden from July 1660. In 1666 he moved to Florence and joined the circle of Galileo's followers in the Accademia del Cimento.
In 1667 he dissected the head of a large shark and argued that the "tongue stones" found in rocks were fossil shark teeth. The same year he became a Catholic. He was ordained a priest in 1675, became a bishop in northern Germany, and died in poverty in Schwerin on 5 December 1686. His remains were taken to Florence and buried in the Basilica of San Lorenzo.
What did Steno say about rock layers?
His 1669 book, *De solido intra solidum naturaliter contento dissertationis prodromus*, asked how a solid object such as a fossil or a crystal could end up inside another solid. An English translation by John Garrett Winter (1916) is free online. Steno wrote that "at the time when any given stratum was being formed, all the matter resting upon it was fluid, and, therefore, at the time the lowest stratum was being formed, none of the upper strata existed." He also argued that layers were first laid down parallel to the horizon, so tilted layers must have been disturbed later.
Geologists now call these the principles of superposition, original horizontality and lateral continuity. An introduction to a 2021 collection of papers on Steno in the journal *Substantia* calls them founding principles of modern stratigraphy.
What did Steno notice about crystals?
Steno studied quartz, which grows as a six-sided prism capped by six-sided pyramids. Real crystals are rarely perfect: some faces are wide, others narrow. Winter's translation gives his conclusion that in the plane of the axis "both the number and the length of the sides are changed in various ways without changing the angles."
He also argued that crystals grow by adding matter to their faces from a surrounding fluid, not from inside like a plant. The *Substantia* introduction is careful about credit. It reports the view that Steno was the first to state constancy of interfacial angles for quartz, but did not generalise it to all crystals; that came from Romé de l'Isle in the 1780s.
Your Class 9 science book, *Exploration*, Chapter 5 "Exploring Mixtures and their Separation", defines a crystal as "a solid that is made up of particles arranged in a regular geometric pattern." That regular inner pattern is why the angles stay fixed even when the faces grow unevenly.
Worked example 1: the angle between prism faces
A quartz prism has six side faces. Seen end-on, they form a hexagon.
Interior angle of a regular hexagon: (6 − 2) × 180° ÷ 6 = 720° ÷ 6 = 120°.
Distorted crystal: if two opposite faces grow twice as wide as the others, the hexagon is no longer regular, but its sides keep the same directions, so each interior angle is still 120°.
Check: the six angles still add up to 6 × 120° = 720°, as they must for any hexagon.
Worked example 2: reading a rock face
This is a hypothetical cliff, with sample layers. From bottom to top: sandstone, shale, limestone containing fossil shark teeth, and a layer of gravel lying flat across the tilted edges of the others. The first three layers dip at 30°.
Order of deposition: sandstone, then shale, then limestone (superposition).
Tilting: the three lower layers were laid flat and tilted later (original horizontality).
Gravel: it lies flat across the tilted edges, so it formed after the tilting.
Environment: shark teeth in the limestone mean that layer formed under the sea.
Common mistakes when applying Steno's ideas
Assuming lower is always older. Folding can turn layers upside down; superposition holds only for undisturbed sequences.
Measuring the wrong angle. Crystallographers compare angles between matching faces, not face lengths.
Treating "constant angles" as "identical crystals." Two quartz crystals can look very different and still share the same angles.
Our posts on Mary Anning and her fossils and Dorothy Hodgkin's crystallography carry both stories forward.
If you want to explore how particles arranged in a pattern produce a crystal's shape, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing.
What can a student take from Steno?
Steno moved between anatomy, geology and crystals by asking the same question each time: what sequence of events could have produced what I see? He trusted careful observation of ordinary objects, a shark's head or a quartz crystal, over the authorities of his day.
Practice routine for this week:
Grow salt or copper sulfate crystals as in your Class 9 activity and sketch three of them.
Measure the angles between neighbouring faces with a protractor and compare them across crystals.
Photograph any layered wall, road cutting or cliff and write the order in which its layers formed.
Start with step 1 this weekend; the crystals need a few days to grow.
