Her shape. A bird is worked out from what museums have measured of her. AVONET is a ledger of the bodies of every living species of bird, eleven thousand of them, from some ninety thousand birds measured, most of them skins in museum drawers: bill, wing, tail, leg and weight. Everything AVONET leaves out is set once and inherited: a default, then some fifteen body types, then forty-seven families, then the genus, then her. The shape follows from rules. Her body is twenty times the cube root of her weight. A heavy bird on short wings is a plump bird. The tips of her primaries show by exactly as much as the measurements say they do. Every bird was first sorted as a grey shape, because a bird that reads right as a silhouette will draw right. The raptors’ leg measurements fold into a perched form, and the waders hunker down against the weather.

Her brid. Her Latin name and the name of the kilometre square she stands in are stirred together into one number, a seed. A seed unrolls into a long list of numbers, always the same list, and read in order each settles one thing: whose bill, whose tail, what crown, what song, and at which notch it arrives. Call them dice, already thrown, the throws written down before anyone looked. The dial only lets them land. Turn it back and forth and the same things happen at the same notches, on any phone, every time. The feathers are grown the same way, which is why a place is always the same feather.

Her hand. The brids elsewhere in this book are cut with a burin, light carved out of darkness, after Thomas Bewick, who was born at Cherryburn on the Tyne and cut his History of British Birds into the end grain of boxwood. Up the South Tyne, on the moor where everything tilts a little imaginary, the plate keeps the bench’s pencil, the hand the brids were worked out in, because colour shows where a borrowed part has gone.

Her number. 176 birds, one brid each in every kilometre square on Earth: roughly ninety billion brids, about eleven for every person alive. Not one of them is stored anywhere. Each is a place and some arithmetic, waiting for someone to stand there.

The ground. A feather is the same thing as a place; a place is a name. So a map of the grids is a map of every feather there could be.

The home grid. The British National Grid — a transverse Mercator of the Airy 1830 ellipsoid, a figure of the earth fitted to Britain alone, in the decade of its measuring. Two letters for a hundred kilometres — NY, SD, TQ — halved, and halved again, down to a ten-metre box. The moor is named this way.

The Bureau. But the world is made of feathers too, and it seemed unfair for a walker in Köln or Ushuaia to be held at the edge of a British map sheet. So a Bureau was founded, with all the solemnity such an institution deserves: where a nation has a grid it is recognised; where there is none, the Bureau issues MGRS of its own, drawn violet on the plate.

The passage. Your phone speaks WGS84; the moor is named in Airy 1830. Every fix crosses between the two before it can be told where it is — three shifts, three small rotations, one change of scale. Which is also why the violet grid leans a fraction of a degree against the black.

The red line. The edge of the published OS index — easting 700 km, northing 0. Beyond it the National Grid strides the Channel and plants its numbers on France, past Agincourt; so a walker in Calais is handed the feathers of the Ordnance Survey, whether France consented or no.