A White Stone was a symbol that an Atlantean was free from the role of tribute and would not have to enter the Labyrinth as sacrifice to the Minotaur.
The stones were drawn in front of King Minos and Queen Pasiphae from the mouth of a hollow bull statue. A white stone meant you were safe, a black stone meant you were to be a tribute to the Minotaur. Jason and Hercules picked one. (The Earth Bull)