Nothing large gets built until somebody has decided, on the ground, exactly where it goes. A theodolite is the instrument that decides. It measures one thing supremely well: the angle between two directions — horizontally and vertically — from a point you have fixed over a mark.

That is enough to build a country. Measure one distance carefully — a baseline — then measure only angles from its two ends to a distant third point, and trigonometry gives you the other two sides without walking them. Use that new side as the next baseline, and the survey spreads across a landscape as a mesh of triangles. This is triangulation, and it is why one painstakingly measured line can position a whole nation.

The instrument that made it precise was built by Jesse Ramsden between 1784 and 1787 and delivered in July 1787 to William Roy, for the Anglo-French Survey — a project of the Royal Society to fix the relative positions of the Greenwich and Paris observatories. Its horizontal circle was three feet across and read to one second of arc. It weighed about 200 lb (91 kg), and its accessories and cases weighed as much again.

The name is older than the precision. It first appears as theodelitus in Pantometria, the surveying book Thomas Digges published in 1571 from his father Leonard's papers. Digges never wrote down where he got the word, and nobody has since worked it out.

Build a working one from a protractor, a tripod and a sighting tube, and survey something you cannot walk to.

Astrométrie

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The Theodolite