the line at greenwich and the satellites' zero are 5.3 arcseconds apart, which at that latitude is 102 metres

There is a metal strip — brass originally, stainless steel now — set into the courtyard at the Royal Observatory in Greenwich, and there is nearly always somebody standing astride it with one foot in each hemisphere. It marks the line of sight of the Airy Transit Circle, the telescope through whose centre the 1884 International Meridian Conference recommended, 22 votes to one and binding on no government, that the prime meridian of the world should pass. It is the most photographed zero in geography.

Stand on it holding a phone and the phone will tell you that you are not at zero. You are about a hundred metres west of it. The satellites put longitude zero a little way east, out past the courtyard wall, running through the park where nobody is queuing.

The explanation you usually get for this is administrative: GPS uses a different reference frame, the modern system had to pick its own zero, the old line is a historical curiosity now. That story is tidy, and it lets the discrepancy be nobody’s mistake — just two committees using two conventions.

It is not what happened. The 2015 paper that worked through it — Malys, Seago, Pavlis, Seidelmann and Kaplan, in the Journal of Geodesy, under the excellent title Why the Greenwich meridian moved — found that the offset is not a change of convention at all. It is the plumb line — and gravity accounts for the whole of it, to within a model error of about half an arcsecond.

Airy’s telescope was levelled against local gravity. That is the only vertical a nineteenth-century transit instrument can have: Airy pointed the telescope straight down into a trough of mercury and compared the crosswires against their own reflection, because a liquid surface sits perpendicular to local gravity by definition. That is how the instrument learned where down was. A meridian swept by an instrument levelled that way is a plane containing the local vertical — and the local vertical is not the direction of the centre of the Earth. Mass nearby pulls on the weight. Hills, the density of the rock underneath, the shape of the land for miles around all lean it fractionally off. The angle between the direction a plumb bob actually hangs and the normal to the reference ellipsoid is called the deflection of the vertical, and at Greenwich it is a few seconds of arc.

Five point three seconds of arc, taken from the ground up through the atmosphere and out to where a satellite decides what it is orbiting, is about a hundred metres on the courtyard floor — at this latitude. The angle is the fixed quantity; the gap between the two lines closes towards the poles.

So the modern meridian is not a replacement for Airy’s. It is Airy’s, with the local lean in his down taken out. Not the correction of a mistake: a surveyor with a spirit level and a star catalogue, standing on the strip today, would still measure zero longitude, and would still be right. The line in the metal is where the prime meridian is if you build it out of a hanging weight in south-east London. The line the satellites use is where it is if you build it out of the whole Earth’s mass at once. The instrument was not misaligned. It was aligned, very precisely, to a local truth.

I like this because the failure is invisible from inside the method. There is no step in Airy’s procedure you could improve with more care. Level the instrument better, check it more often, re-measure every star — and you converge, beautifully, on a line 102 metres from the one the satellites use, because the thing you are using to define correctness is itself leaning. You cannot find it by being more rigorous with your plumb line. You find it by getting far enough away from London to see that London is pulling.

Two essays ago I wrote about a woman who carried a watch out of that same observatory every week for forty-eight years, because the time in the building was better than the time anywhere else. It did not occur to me then that the building’s other famous number had the same shape: correct, carefully kept, and quietly local. The strip of metal is not a mistake anyone made. It is a record of what the best possible measurement looked like when the only available vertical was a piece of string.

Nobody has moved it, and nobody should. But the queue is standing on the answer to a slightly different question than the one on the sign.