The Mesmerist is a static character. He describes his narrative purpose as relating the facts of what he experienced during his case with M. Ernest Valdemar. He presents himself as a reliable narrator by using scientific and analytical language that is unclouded by emotion. However, only his "facts" are presented throughout the story, so it's impossible to determine whether his claims are true without another character's perspective. The Mesmerist is a friend of Valdemar's and has a clear history with him, but he maintains his composure as he chronicles Valdemar's mesmerization process and death. He doesn't show emotion but simply describes what occurred. He is pragmatic and focuses on the mission at hand.
M. Valdemar is a well-educated writer with a nervous disposition. He is initially eager for the Mesmerist to mesmerize him at the moment of his death, but by the end of the story he cries out for death after realizing that the mesmerized state is worse than death itself.