N.M. Stat. § 4-7-2
The dividing line between the counties of Dona Ana and Socorro, in this territory, is hereby established as follows, to wit: commencing at a point on the Rio Grande one mile south of the dwelling house of Tomas Gonzales, and thence a little southwest to a point one-quarter of a mile to the south of the Ojito del Cuervo, a ranch of the said Tomas Gonzales; thence in a westerly direction to a point one mile west of the Ojo de Berrendo, and running in a northwesterly direction to the ranches respectively known by the name of the Ojo del Berrendo, the Cienega de los Pasenos, Jaraloso, Eucisio, Cienega de los Apaches, Las Perchas and Ojo Caliente, to an equal line with that of the northern line of the county of Grant, so that all the ranches and ojos and ojitos above-mentioned be included in the county of Socorro, and the town and settlement of Hillsboro and Santa Barbara shall be included in the county of Dona Ana; and returning to the Rio Grande at the point of commencement, running thence in a straight line to the corner of the county of Lincoln, a few miles north and west of the town of Tularosa, in the county of Dona Ana.
NMS § 4-7-2