Barnabus Hurma is one of the archaeologists inside the Varrock Museum in Varrock. Although free-to-play players can talk to him, the activities that he offers can only be accessed in the members' world. He is on the same level as the main entrance to the museum in the southwest corner.
If it is your first time exchanging strange rock for experience then you will need to speak with him before adding the rock to the plinth. He will then examine the rock and will allow you to add it to the plinth if you have a pair of identical rocks.