Complex sentence: During that time Tinkham was nicknamed "the conscience of the House" for his efforts to protect voting rights for African Americans, in part by highlighting of the South's disproportionate representation in the House related to that region's voting population.
Split into simpler sentences: During that time Tinkham was nicknamed "the conscience of the House" for his efforts to protect voting rights for African Americans. He noted the South's disproportionate representation in the House related to the region's voting population.