Mesmerism
2 of the 7 encyclopedias on this shelf carry an entry for Mesmerism. Both are reproduced below, so you can see where they agree and where they differ.
Aiton's Encyclopedia (1910)
mez'mer-ism, the theory that one person by means of animal magnetism can act upon the nervous system and will of another so as to control his sensibilities and to some extent his actions. The process was brought first to public attention by a German physician named Mesmer. He was a native of Constance, and was educated for medicine. He experimented with magnets in the curing of disease, and came to believe that he and others possessed an occult power or force which he called animal magnetism. In 1778 he went to Paris and created quite a stir. The French academy appointed a committee of which our Franklin was a member, to investigate the claims of Mesmer. This committee reported that Mesmer undoubtedly possessed a peculiar power of getting people under his influence, and of causing them to sink into apparent slumber, in which condition they followed his suggestions and did many acts of which they were more or less unconscious. Franklin considered the cause, however, to be entirely physiological. The word hypnotism has, at present, almost entirely superseded that of mesmerism. While the two are theoretically different, the practical results of hypotism and mesmerism are the same. See Hypnotism
Collier's New Encyclopedia (1921)
the system popularized by Mesmer, and by him called animal magnetism. Mesmer delighted in mysterious surroundings, and affected a strange weird style of dress; but one of his disciples, the Marquis de Puysegur, showed that sleep might be induced by gentle manipulation alone, thus removing mesmerism from the sphere of mystery. The chief phenomena are a hypnotic state induced by the patient gazing fixedly at some bright object, or by passes made by the operator; muscular rigidity, sometimes to such an extent as to admit of the body resting supported only by the head and heels on two chairs, insensibility to pain, and perverted sensation, as exhibited in a slightly hypnotized patient drinking water and imagining it to be delicious wine or nauseous medicine at the will of the operator. See HYPNOTISM.