As a topic to this section of the forums I thought about what to make as a post, then I thought about the significance that Serpents have in Alchemy. Be it Snakes, or Dragons, they are united as serpents and hold many symbols and meanings in Alchemy. So, for this topic I would like to go over some symbols, facts and other interesting points of Dragons in Alchemy. A lot of this information will probably be a gather of info from other sites but I'll paste all the links down the bottom for reference, images kindly donated by Terran.
The first popular symbol of Alchemy would be the Caduceus. The Caduceus consists of a staff with two snakes intertwined around it, modern depictions of the Caduceus show wings surmounted to the top while in other depictions the top has the alchemical symbol for Mercury. Within its Greek origins, the Caduceus staff was carried by Hermes of Greek mythology as the 'herald's staff'.

In Roman origins it was carried in the left hand of Mercury the messenger of the gods, guide of the dead and protector of merchants, shepherds, gamblers, liars, and thieves. In later years the staff provided the basis for the astrological symbol representing the planet Mercury. Through its use in astrology and alchemy, it has come to denote the elemental metal of the same name.
The Caduceus staff has also been commonly confused as a symbol of Medicine and/or Medical practice (especially in North America) with the traditional medical symbol, the rod of Asclepius, which has only a single snake and no wings.

The Rod of Asclepius is the second symbol. Though not necessarily seen as a symbol of Alchemy, its symbolism still has similar origins as to the Caduceus. The rod of Asclepius is symbol of not only medicine and healing, but Astrology, and the Greek god Asclepius. The name of the symbol derives from its early and widespread association with Asclepius, the son of Apollo, who was a practitioner of medicine in ancient Greek mythology. His attributes, the snake and the staff, sometimes depicted separately in antiquity, are combined in this symbol. Hippocrates himself was a worshiper of Asclepius.
The Basilisk (Or Amphysian Cockatrice like below) is a symbolic alchemical creature said to have the head of a bird and the body of a dragon. The wingless serpentine animal was hatched from a hermaphroditic cock's egg and nursed by a serpent. Psychologically, the Basilisk represents the melding of our higher and lower natures in Conjunction, a process that must be continued in the next three operations of alchemy for this "Child of the Philosophers" to become the Living Stone of the fully integrated Self. Biologically, the Basilisk represents the mammalian embryology, the genetic replaying of the stages of evolution within the egg or womb. The Basilisk also has chemical connotations, which probably have to do with a metallurgical process involving cinnabar (Dragon's Blood).

The Ouroboros (or Uroborus) is an ancient symbol depicting a serpent or dragon eating its own tail. This is possibly one of the most common symbols seen that relates to alchemyThe name originates from within Greek language;(oura) meaning "tail" and (boros) meaning "eating", thus "he who eats the tail".
The Ouroboros represents the perpetual cyclic renewal of life,the eternal return, and represents the cycle of life, death and rebirth, leading to immortality, as in the phoenix. In alchemy, the Ouroboros is a sigil. Swiss psychologist Carl Jung saw the Ouroboros as an archetype and the basic mandala of alchemy.

The famous Ouroboros drawing from the early alchemical text The Chrysopoeia of Cleopatra (See below image) dating to 2nd century Alexandria encloses the words hen to pan, "one is the all". Its black and white halves represent the Gnostic duality of existence. As such, the Ouroboros could be interpreted as the Western equivalent of the Taoist Yin-Yang symbol.
Serpents themselves also hold a few meanings in Alchemy by themselves rather than with objects or other than the Ouroboros. These basic idealizations are related towards Alchemical work and substances. To name a few; two serpents represent the opposing masculine and feminine energies of the Work. Three serpents stand for the three higher principles of Sulfur, Mercury, and Salt. Winged serpents represent volatile substances; wingless serpents represent fixed substances. A crucified serpent represents the fixation of the volatile.

Feel free to add or talk about what I have gathered here. Any other symbols, facts or ideas of Dragons in Alchemy are welcome to be added to the collection here. But now, its 2 am, sleep is calling, its been fun and I hope this has been an interesting read

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Links ~
'Caduceus'
http://en.wikipedia.org/wiki/Caduceus#Mythology 'Rod of Asclepius'
http://en.wikipedia.org/wiki/Rod_of_Asclepius 'Alchemy Electronic Dictionary'
http://www.alchemylab.com/dictionary.htm 'Basilisk, or Amphysian Cockatrice'
http://www.sacred-texts.com/lcr/fsca/fsca26.htm 'Ouroboros'
http://en.wikipedia.org/wiki/Ouroboros#Alchemy'Ouroboros'
http://www.dragon.org/chris/ouroboros.html