DURHAM, N.C. — IN 1970, the United States gave away 413 acres of American territory on the southern bank of the Rio Grande called the Horcón Tract. The handover was something of a formality, since for more than half a century everyone had thought that this remote patch of bottomland was actually part of Mexico. It wasn’t — it had just been forgotten after a Texas company illegally diverted the Rio Grande in 1906.

At a time when Americans seem obsessed by the sanctity and immutability of their borders, you have to wonder how the government could essentially lose track of a chunk of American soil. You also have to wonder why we are cutting off new patches of American land again today through another construction project along the Rio Grande: the 18-foot-high border fence with Mexico.

Since Congress is considering doubling the length of that fence, this is a good time to tell the Horcón Tract’s cautionary tale.

The story begins in 1906, when an American irrigation company grew worried that a loop of the Rio Grande near Mercedes, Tex., might suddenly switch its course and leave the company’s new pumping station high and dry. The river, which marks the international boundary with Mexico, meanders in large horseshoe-shaped loops through this part of Texas. The loop that troubled the company ballooned south into Mexico.