The Collaborative International Dictionary of English v.0.48:

somnolism \som"no*lism\, n.
   1. The somnolent state induced by animal magnetism
      (hypnotism); the hypnotic state. [archaic] --Thomas (Med.
      Dict.).
      [1913 Webster +PJC]

   2. the act or process of inducing the hypnotic state;
      hypnotism; hyonotizing. --Stedman.
      [PJC]