What was solving it border disputes between Texas and New Mexico part of?

Answer 1

Compromise of 1850

Answer 2

The Compromise of 1850 set the border between Texas and the Territory of New Mexico based on the intersection of the Rio Grande and the 32nd parallel. Texas gave up its claim on New Mexico but retained control over El Paso.

The Congressional Act of 1854 gave all the Gadsden Purchase lands to the Territory of New Mexico, creating a 12-mile-long Rio Grande boundary between the State of Texas and New Mexico Territory.

Over time, the course of the Rio Grande changed and an error was made in an 1859 border survey. By the time New Mexico gained statehood in 1912, the Country Club Area was the object of a border dispute between Texas and New Mexico, known as the Country Club Dispute. The United States Supreme Court settled this dispute in the 1927 case of New Mexico vs. Texas. A master was appointed by the Supreme Court in 1924 to make determinations of fact, and the master made extensive findings. "The master concluded on all the evidence that the allegations in New Mexico's bill as to the location and course of the Rio Grande 'as it existed in the year 1850' were not sustained, and that the river did not then flow on the eastern side of the valley as claimed by New Mexico; that its location and course in 1850 was, in general, as alleged in the cross- bill of Texas."

The Court sided with Texas with respect to most facts in the case and in its final verdict. They also implied that New Mexico had no standing to dispute any changes to its borders made before it gained statehood in 1912; those boundaries were an issue between Texas and the U.S. Federal Government.