Douglas Harper's Etymology Dictionary
anaesthesiology
1908, from anaesthesia + -ology.\n\nAnesthesiology. This is the new term adopted by the University of Illinois defining "the science that treats of the means and methods of producing in man or animal various degrees of insensibility with or without hypnosis."
["Medical Herald," January, 1912]
Wiktionary
anaesthesiology
alt. (context British spelling medicine English) science of administering anaesthetics. n. (context British spelling medicine English) science of administering anaesthetics.