When someone is “blowing smoke up your arse” today, it is a figure of speech that means that one person is complimenting another, insincerely most of the time, in order to inflate the ego of the individual being flattered.
Back in the late 1700s, however, doctors literally blew smoke up people’s rectums. Believe it or not, it was a general mainstream medical procedure used to, among many other things, resuscitate people who were otherwise presumed dead. In fact, it was such a commonly used resuscitation method for drowning victims particularly, that the equipment used in this procedure was hung alongside certain major waterways, such as along the River Thames (equipment courtesy of the Royal Humane Society). People frequenting waterways were expected to know the location of this equipment similar to modern times concerning the location of defibrillators. [link]