Complex sentence: On that day he resigned, having been elected by the Kansas Legislature to the U.S. Senate seat left vacant by the resignation of Joseph R. Burton, to serve the remainder of the current term, ending on 3 March.
Split into simpler sentences: On that day he resigned, having been elected by the Kansas Legislature to the U.S. Senate seat left vacant by the resignation of Joseph R. Burton. Curtis served the remainder of the current term, ending on 3 March.