I have invested in Ralis' expedition 3 times now, and just got called back for the 3rd time to clear the draugr. Every time returning, there has been new pieces of Ahzidal's artifacts on top of pillars throughout the barrow. The 3rd time around, I found where the item should be (I believe) but there is no item there. It's behind a gate that requires you to walk on the platforms in order to open it, followed by a deep pool of water you must cross to get to the pillar. Is it possible that this was a ring and I shouted it into the water or something? because i can't find it on top of the pillar, or in the large pool of water either.