-- Nancy will say she ought to call Melina. Melina will give you the password for this program (which is CALLIOPE, but it won't work until Melina gives it to you) and ask you to test items in the museum to see if they're forgeries. The authentication database will tell you how.
Hint 6
Check the Messenger program first; Melina says to look specifically at the gold chain necklace in the broken case and the emerald earrings in the case to the left of that one.
Hint 7
The AD tells you to rub gold with unglazed pottery, use a blacklight on pottery, and use a spectroscope on gems. You don't have access to a blacklight yet, so concentrate on the necklace and the earrings. While you're here, flip through all the pages; you don't have to memorize this stuff, though.
Hint 8
You can find a piece of unglazed pottery in the Workshop. Look at the shelves where you were making pots and pick up one of the red shards on the bottom shelf.
Hint 9
There's a spectroscope just handily lying around (deus ex machina!) next to the lift in the Underworld, under the tree to the right of the ferryman.
Hint 10
Go back up to the museum to the coin display. Pick up the earrings from the left display (they're under the golden wreaths) and use the spectroscope on them. Then zoom in on the necklace behind the broken glass and use the pottery shard on it.