When a royal commission declared his cure a product of imagination, Franz Anton Mesmer offered to prove them wrong by mesmerizing a horse.
Mesmer was born in Swabia, in southern Germany, in 1734. He studied theology before turning to medicine in 1759, and his dissertation dealt with the influence of the planets on the human body. In 1774 he began treating a young woman with magnets. Controversy over his treatments followed, and he moved his practice from Vienna to Paris, where he quickly gained fame and fortune.
Etymonline dates his Paris launch of the theory to 1778. Its claim was that an invisible fluid, which he called animal magnetism, ran through living bodies, and that illness came from its blockage. His signature device was the baquet, a shallow wooden tub of magnetized water and iron bars. Up to thirty patients sat around it at once, linking hands so the fluid could circulate.
In 1784 Louis XVI appointed a commission to investigate. Its members included Benjamin Franklin and Antoine Lavoisier, and its tests have been called probably the first blind trial. The report, printed in more than 20,000 copies, credited the effects to the patients' imaginations. Mesmer's popularity faded and he left Paris, though followers kept his methods alive.
The words outlived the man. Mesmerism, from French mesmérisme, is recorded in English from 1798. The verb mesmerize came next, meaning to put someone into a mesmeric state. Merriam-Webster dates it to 1829, while Etymonline gives 1819.
By the 1840s a rival vocabulary had arrived. Dr. James Braid of Manchester coined hypnotism in 1843, short for his earlier neuro-hypnotism, from Greek roots meaning sleep. Mesmerism became practically a synonym for it.
The figurative sense, to enthrall or hold spellbound, is attested by 1862. That is the sense most people use today, with no tub or iron rods in sight. A discredited medical theory survives as an everyday compliment for a performer or a view.