Hypnosis is associated in the public's mind with two things: a swinging watch, and a rotating spiral. The hypnotic spiral is actually called an Archimedes spiral. Whether it actually has any connection to Archimedes is unknown.
It is also known as Plateau's spiral, after the Belgian physicist Joseph Plateau (1801–1883.) Plateau published a description of its use in 1878. The spiral is generally mounted on a card about 15 cm in diameter, with a little motor behind it that causes it to rotate slowly. The original spiral, in the mid-19th century, was driven by a sort of windmill affair, by the hot air given off by a spirit lamp.
Archimedes spiral induction
The Archimedes spiral induction is quite effective. It is caused by a physical effect called a "spiral motion after-effect". After staring at the spiral for a while, if you look at something stationary, it appears that the stationary object is actually turning. If you look at the hypnotist's face, it appears to expand or contract, depending on the direction the spiral was turning.
The Archimedes spiral induction uses this optical illusion to put people into trance. The hypnotist tells the person that what they are seeing is their mind taking them into trance. The hypnotist suggests that every time the face expands and contracts the person will go deeper into trance. The effect is quite strong, so the suggestions are easily believed. The listener cannot deny what they are seeing. Therefore the suggestion that "this means that you are going into trance" is accepted by the unconscious mind. Most people will sink into trance immediately.
The Archimedes spiral was an immensely popular scientific toy in the mid-19th century. This is probably why it was picked up by hypnotists. The spiral, and other mechanical aids, has fallen out of use. Those objects were associated with the "direct command" style of authoritarian hypnosis. That style has largely been replaced by more permissive styles of hypnosis.