Definition: This grusome looking symbol of a snake nailed to a cross is a common alchemical drawing representing the "fixing of the volatile," or, making the elixir of mercury, a legendary curative, by removing the volatile, or poisonous element. The crucified serpent is a symbol of overcoming one's base or materially inclined nature.
It is also a symbol of a biblical allegory linking the crucifixion of Christ with the the raising of the Brazen Serpent of the Old Testament:
"And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up: That whosoever believeth in him should not perish, but have eternal life."
Definition: Ouroboros is a greek word, and means "tail swallower." The ouroboros is usually depicted in the form of a snake swallowing its tail, and is usually circular, although it is sometimes depicted in a lemniscate shape. It originated in Egypt as a symbol of the sun, and represented the travels of the sun disk. In Gnosticism, it was related to the solar God Abraxas, and signified eternity and the soul of the world.
In alchemy, it represents the spirit of Mercury (the substance that permeates all matter), and symbolizes continuous renewal (a snake is often a symbol of resurrection, as it appears to be continually reborn as it sheds its skin.), the cycle of life and death, and harmony of opposites. A double ouroboros (two creatures swallowing one another) in alchemy signifies volatility.
The Ouroboros appears in many other cultures and settings as well...the Serpent Jormungandr of Norse legend, who encircled the world, and guarded Yggdrasil, the Tree of Life, is often depicted as an ouroboros. The Aztec serpent God Queztacoatl was depicted similarly, and Chinese alchemical dragons have both similar shapes and meaning.