The "wand of Hermes", also referred to as a caduceus, was carried in the left hand by the ancient Greek God signifying Peace. Hermes, along with being the messenger of the gods, was the guide of the dead (psychopomp) and protector of merchants, shepherds, gamblers, liars and thieves.
The caduceus is sometimes mistakely used as a symbol for medicine even though the symbol has no connection with Hippocrates. The error might have come from a printer's vignette that separated the chapters of a medical book by using a caduceus.
If one observes the logos of modern medical associations they will notice the correct usage of the Rod of Asclepius instead.