01Executive summary
Seven milestones in roughly a century, after which an engineer could calculate in advance what had previously only been learned by building.
Between about 1585 and 1687, forces acquired a way of being added, materials acquired a measurable strength, air acquired weight, gases and solids acquired laws, time acquired an accurate instrument, calculation acquired logarithms and a slide rule, and motion acquired three general statements. None of these people was an engineer. Together they gave engineering the ability to predict.
02Adding forces, and measuring materials
Simon Stevin, working in the Netherlands, published in 1586 the parallelogram or triangle of forces — the demonstration that three forces in equilibrium at a point can be represented in both magnitude and direction by the sides of a triangle. He described it as "a wonder, yet no wonder". With it he established principles of statics that an engineer must apply to know in advance that a structure is economically designed and will stand.
The same year he published on decimal fractions, which sounds minor and is not. Methods of computation had barely changed since Egyptian practice apart from the adoption of zero and Arabic numerals. Decimals gave speed as well as accuracy, and laid groundwork for the metric system two centuries later.
Falling bodies, before Galileo
Stevin dropped two lead balls, one ten times the weight of the other, about 9 metres onto a board. They struck as one, contrary to Aristotle. The often-repeated story of Galileo dropping weights from the tower at Pisa in 1590 is now regarded as without foundation.
The first testing machines
Galileo hung weights on copper rods and on a cantilever beam jutting from a wall, establishing the strength of materials as a subject. His cantilever analysis was wrong: he missed that the fibres on the underside are in tension and those above in compression, which Mariotte corrected in 1680.
Galileo's error is instructive rather than embarrassing. He measured carefully and reasoned from a wrong internal picture, and it took forty-two years for someone to see it. Careful measurement does not protect against a wrong model of what is happening inside the material, and that remains true.
03Air has weight, and fluids transmit pressure
Stevin had found that water pressure is proportional to depth. Torricelli, Galileo's secretary, linked hydrostatics to dynamics by showing that fluid escaping through an orifice under a head moves practically as fast as if it had fallen from that height. Pascal reduced the propositions to the law that carries his name: pressure applied to an enclosed fluid transmits equally in all directions and acts with equal intensity on equal areas. Every hydraulic press, jack and brake follows from that sentence.
The barometer came out of the same work. Torricelli's tube of 1643 left a space at the top into which the weight of the atmosphere could not force the mercury, and in 1648 Pascal showed that the mercury stands lower on a mountain than at sea level, because the column of air above is lighter. Between them they disposed of the doctrine that nature abhors a vacuum: nature abhors only such empty space as it has the power to fill.
If the atmosphere has finite weight, then a suction pump cannot raise water beyond the height of a water column weighing the same as the air above it — roughly 10.3 metres at sea level. This was a practical scandal for mine drainage and it has an exact explanation. It also implies the converse: if you can remove the air from a vessel, the atmosphere will push on it with a large, calculable force. Otto von Guericke demonstrated exactly that in 1650, evacuating his Magdeburg spheres so that atmospheric pressure held the halves together against sixteen horses. The engines of the following part of this series are all applications of that observation, and they arrive within two generations of it.
It is worth noting the honest detail about the Magdeburg demonstration: the eight horses on each side could have been replaced by an anchor and eight horses on one side, since the second team only provided the reaction. It was a public demonstration as much as an experiment, and it worked as both.
04Elasticity, gases, time and motion
Hooke's law repays a second look because of the qualification attached to it. The proportional relation holds only up to an elastic limit, that limit differs between materials, and for some materials it is not well defined at all. A law that arrives with the boundary of its own validity attached is unusually good science, and engineers who quote the relation without the limit are misusing a result that was correctly stated the first time.
05Instruments and calculation
Surveying instruments in the seventeenth century were still substantially Roman. The dioptra continued with little change beyond the addition of a graduated arc with a movable sight by 1616. Distances were measured with wooden poles, or by a wheel of known circumference — which is inaccurate on anything but flat ground, since a map is a projection onto a surface. The surveyor's chain of nine links appearing in England around 1600 gave way after 1620 to Gunter's chain of a hundred links.
| Development | Date | Effect |
|---|---|---|
| Triangulation over long distances | 1615 | Snell laid out a chain of triangles over roughly 130 kilometres — the first geodetic as distinct from plane surveying |
| The vernier | 1630 | Two scales sliding against each other allow subdivisions to be read precisely, without finer graduations |
| Logarithms | 1614 | Multiplication and division reduced to addition and subtraction; Briggs put them on base ten |
| The slide rule | c.1622 | Oughtred made logarithms mechanical — the engineer's calculating instrument for the next 350 years |
| Analytic geometry | 1630s | Descartes and Fermat joined algebra to geometry, allowing relationships between variables to be represented and analysed |
| Calculus | 1670s–80s | Newton and Leibniz independently; rates of change become computable, which is most of engineering analysis |
| The telescopic sight in survey | after 1800 | Invented 1608 and used by Picard in 1669, but not ordinary surveying equipment for well over a century |
The last row deserves attention. The telescope existed from 1608 and was used for serious geodetic work by 1669, and it did not become standard surveying equipment until after 1800 — a gap of nearly two centuries between demonstrated capability and routine adoption. This series and the three that follow return to that gap constantly: PERC solar cells waited thirty years, additive manufacturing thirty, carbon fibre airframes forty-eight. The interval between a thing working and a thing being used is a permanent feature of engineering, not a modern failing.
These people knew each other. They corresponded, argued, and formed societies — the Academy of the Lynx in 1603, the Royal Society chartered in 1662, the French Academy in 1666, the Berlin Academy in 1700. And printing meant the results propagated: Vitruvius in print by 1486, Biringuccio on metallurgy in 1540, Agricola on mining and metallurgy in 1556, Stevin in 1585, Gilbert on magnetism in 1600, then Napier, Descartes, Galileo, Boyle, Pascal, Huygens, Leibniz and Newton in succession. Only Leonardo's notes failed to reach print anywhere near his own time, scattered across private collections for centuries — which is precisely why his remarkable range of mechanical ideas influenced almost nothing.
06Takeaways for current practice
- Careful measurement does not protect against a wrong internal model. Galileo measured well and analysed the cantilever incorrectly for forty-two years.
- Quote a law with its validity boundary. Hooke stated the elastic limit as part of the result; dropping it is a misuse.
- An unexplained practical limit usually points at a principle. The 10.3 metre suction limit was a mine drainage nuisance and a measurement of the atmosphere.
- Publication is what makes work count. Leonardo's notebooks were extraordinary and influenced essentially nothing because they were not read.
- Expect decades between capability and routine use. The telescope took nearly two centuries to reach the ordinary surveyor.