Archelaus (Arch) M. Cochran, physician and politician, was born to William M. and Nancy Jane (Hughes) Cochran at Columbia, Tennessee, on December 25, 1839. In the fall of 1843 the family moved to Dallas County, where his father was the first county clerk and his brother John represented the district in the state legislature. Arch was educated in the county's common schools and attended McKenzie College and the University of Louisiana in New Orleans, where he studied medicine. He completed his education about 1861 and returned to Texas to establish a medical practice in Dallas. His professional career was interrupted by the onset of the Civil War, and in June 1861 he enlisted in the Confederate Army as a third lieutenant in the Eighth Texas Cavalry (Terry's Texas Rangers). He was eventually promoted to captain and served in Texas, Louisiana, and Tennessee. He was captured at Arkansas Post and held at Camp Chase, Ohio, until the end of the war.
After release, Cochran returned to Dallas and reestablished his medical practice. In 1866 he married Laura Knight, who bore one child before her death in 1870. Cochran married Mary A. Collins the following year, and this couple had two children. Cochran was a Republican, a fact that contributed to his appointment to various federal positions in the years after 1870. He served in the state legislature in 1866 and in 1867 was elected to the Dallas City Council. He was elected again in 1872 but resigned his seat in April of the following year. President Rutherford B. Hayes appointed him postmaster of Dallas in 1879; Cochran held this position until 1883, when he was selected internal revenue collector for the Dallas district. He won the Republican gubernatorial nomination in 1886 and campaigned statewide against prohibition in 1887. He also served as Texas commissioner to the 1890 Columbian Exposition. He died in Columbia, Tennessee, on August 4, 1910, while visiting his son there.