When the members of an audience sit mesmerized by a speaker, their reactions do not take the form of dancing, sleeping, or falling into convulsions; however, if Franz Anton Mesmer were addressing the audience, such behavior could be expected.
Mesmer was a visionary 18th-century physician who believed cures could be effected by having patients do things such as sit with their feet in a fountain of magnetized water while holding cables attached to magnetized trees. Mesmer then came to believe that magnetic powers resided in himself, and during highly fashionable curative sessions in Paris he caused his patients to have reactions ranging from sleeping or dancing to convulsions.
These reactions were actually brought about by hypnotic powers that Mesmer was unaware of possessing. One of his pupils, named Puységur, then used the term mesmerism (first recorded in English in 1802) for Mesmer's practices. The related word mesmerize (first recorded in English in 1829), having shed its reference to the hypnotic doctor, lives on in the sense “to enthrall”.