Latham graduated from the University of North Carolina at Chapel Hill in 1859 and later attended the Harvard Law School.
He entered the Confederate Army in 1861 where he was commissioned captain and afterward major of the First Regiment of North Carolina State troops, and served throughout the American Civil War. Following the war he resumed the study of law, was admitted to the bar in 1868 and commenced practice in Plymouth, North Carolina He was elected as a Democrat to the Forty-seventh Congress (March 4, 1881-March 3, 1883). Unsuccessful candidate for renomination in 1882.
Elected to the Fiftieth Congress (March 4, 1887-March 3, 1889).
Unsuccessful candidate for reelection in 1888 to the Fifty-first United States Congress. He resumed the practice of law in Greenville, North Carolina and died at Johns Hopkins University Hospital in Baltimore, Maryland on October 16, 1895.
He was interred in Greenville"s City Cemetery.
He was elected member of the North Carolina House of Commons in 1864 and to the North Carolina State Senate in 1870.