Cartographic Projection
every map is wrong, and by exactly how much
Concept

Arcsecond — where it appears

A three thousand six hundredth of a degree, which on the ground is 30.9 metres of latitude. It is the unit an astronomical position was quoted in, so it is the scale a nineteenth-century boundary commission could argue about and the threshold a geometric ambiguity has to reach to matter.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The line a commission can actually run. A boundary described as a parallel of latitude and marked by monuments 220 kilometres apart, with the offset exaggerated 700 times so that it can be seen at all. A commission cannot run a parallel: it can set a monument, sight a straight line to the next and clear the trees between, and a straight line between two points of equal latitude is a geodesic, which passes POLEWARD of the parallel everywhere between them. So the marked line lies north of the described one, by 1176.5 metres at the middle of each of its 9 chords, and encloses 1611.2 square kilometres that the words put on the other side. At the 20-kilometre spacing this ladder measures at, the same offset is 9.03 metres.

The line a commission can actually run

A boundary commission cannot run a parallel of latitude. It can sight a straight line between monuments, and a straight line between two points of equal latitude passes poleward of the parallel — by s² tan φ / 8R, which at a mile of spacing is fifty-eight millimetres and at a hundred kilometres is two hundred and twenty-six metres. The described line and the marked line are different curves, and the marked one governs.

practice · Boundary One meridian, two datums, and the ground between them. "the meridian line of the 141st degree of west longitude" — Anglo-Russian Convention, 1825. The line whose longitude is exactly 141° west, drawn twice: once on nad27 and once on WGS84, with the east–west separation exaggerated 3,000 times. The two are 129.0 metres apart, and remarkably constant — the shift changes by five centimetres over nine degrees of latitude — so the strip between them is a ribbon 129 metres wide and 1039 kilometres long, which is 134.0 square kilometres. The sentence has not changed. The surface the number refers to has.

A meridian boundary moves when its datum does

The 141st meridian is the one boundary description in this collection with no geometric ambiguity in it: every reading of it is the same curve, exactly. It has a different one. A longitude refers to a datum, the 1825 convention named none, and the line of longitude exactly 141° west sits 129.0 metres apart on NAD27 and WGS84 — a ribbon 1,039 kilometres long and 134 square kilometres in area.

practice · Boundary

Named alongside it

The objects these essays reach for when they reach for this one.

AreaBoundaryConventionToleranceVerificationCentral meridianClosed formDatumEllipsoidGeodesicGeodetic datumGreat circle

All concepts