Thomas Henry Ball (January 14, 1859 – May 7, 1944) was a Texas politician and a Democratic member of the United States House of Representatives. He was mayor of Huntsville, Texas from 1877 to 1892, and moved to Houston in 1902.Thomas Henry Ball and Frank Andrews formed a law firm in Houston in 1902. Melvin Kurth joined in 1913. Andrews Kurth was important to Texas railroad firms early in the twentieth century.