Drop down to the gore-strewn floor and scramble up onto the ledge on the right.
Use your axe to turn the wheel there, opening the grate in the floor above a deep pit.
Drop back down and move across the room and into the alcove to the left of the painted scrambling wall. Here you'll find another relic (2/3), a Ban Chiang Vase. Grab it. Then climb onto the ledge above.
Head to the right end of the ledge to find another document (2/3). In case you had any doubts about Whitman, this note, which is part of the Endurance Officers set, makes his intentions clear.
Use your rage-fueled strength to crank the second wheel, raising a large, metal cage out of the pit.
When you've cranked it all the way up, the cage locks into place.
Turn around, run up the wooden ramp and jump to grab the ladder made of planks. Climb onto the ledge above. Follow it around to the left.
Jump across the gap near the dangling corpses. Pry open the salvage trunk and take the Chasm Shrine Treasure Map from the table.
Then jump back across the gap and move to the middle of the walkway, above the entrance.