The US Army Medical Corps insignia is a caduceus, a staff with wings and two entwined
snakes. I have read that this amuses the Brits, who knew that caduceus belonged to
Mercury. The Brits' knowledge of mythology led the to use caduceus of Aesculapius,
with only one snake.
The two snake caduceus belonged to Mercury. My dictionary says medical can be two
snakes, but British medical insignia has only one, in all illustrations I have ever seen.

Edit: I goofed and put an "e" after the "d" where it does not belong. Shame on me.