Well said Loamer.
There is a Law in most if not all States where a person can be charged with "Stealing by finding"
Offence under: Section 74, Crimes Act 1958
Overview: A person can be charged with theft if he or she finds or accidentally comes across something belonging to another and then keeps it or deals with it as if he or she is the owner.
Of course, finding coins it would be difficult to prove, however, the ring such as you note was stolen and therefore any possession is attached to the original crime.
Had the same ring have been lost, say at the beach, because of its value, you could be charged if caught selling it. Who is to say it wasn't stolen and lost or discarded by a thief.
The best course of action if you find something of value and wish to keep or sell it, is to hand it into the police along with details of where and when found and your own details. You need to nominate to the Police, that if not claimed you wish to have it returned (usually 3 months later). It is then legally yours.
Moral - If claimed, you've done your good deed, if unclaimed, it's legally yours and you can do as you wish with it.