Born in Canton, Connecticut, Barbour was graduated from Amherst College in 1837. He moved to Indiana the same year and settled in Madison, Jefferson County. He studied law. He was admitted to the bar and commenced practice in Indianapolis, Indiana, in 1839. Acted a number of times as arbitrator between the State of Indiana and private corporations. He was appointed United States district attorney for the district of Indiana by President Polk. He served as member of the commission to codify the laws of Indiana in 1852.
Barbour was elected as an Opposition Party candidate to the Thirty-fourth Congress (March 4, 1855-March 3, 1857). He was not a candidate for renomination in 1856. He was affiliated with the Republican Party in 1860. Practiced law in Indianapolis, Indiana, until his death in that city on July 19, 1880. He was interred in Crown Hill Cemetery.
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