The stairs at the ends of the bookcases lead to a balcony, in the centre of which is a wooden door. You find an inscription carved into the wall beneath the statue on the left of the door. Unless you're fluent in Sanskrit, you need to translate the inscription. You happen to know an archaeologist, so all you have to do is find a way to copy the inscription and show it to her. I hope that you also checked the communications room while on board the Hindenburg, otherwise you won't have the lead pencil and fine paper. Combine the pencil and paper (in your inventory) then use them on the inscription to trace a scrumble of it.
Take the scumble to Kate Sullivan and show it to her. Note that you have to stand at the front of the gazebo cage to interact with her. She translates it as follows:
 He who seeks after Truth must take the path of Enlightenment
 whose place of departure is Balance.

 When he opens the Seventh Book of Knowledge, the ignorant
 one will be blessed with Wisdom.

 This understanding will give him the strength he needs to attain
 Purity. Only then will the truth be revealed to him
Note: After Kate Sullivan translates the inscription you can view it on the scumble in your inventory.
From Kate's comments and the book on precious stones you know that the reflection of the rays of the sun play an important part. Look carefully and you see a ray of sunlight shining directly onto the statue near the first bookcase on the left.

This is the 'place of departure' referred to in the inscription. Use the zeppelin knife to remove the ivy around the statue and note the block in the centre of the two bulls. Captain Blackwood told you that the emerald represents the forces of balance, which ties in with the inscription. Put the emerald on the statue and it reflects a green ray of light towards the statue near the last bookcase.
According to the second part of the inscription you need to find the Seventh Book of Knowledge. Go to the statue near the last bookcase and similarly remove the ivy with the zeppelin knife. Try placing each of the three remaining gemstones on the statue. Of these, only the moonstone will deflect the ray of light towards a bookcase. You need to check all four bookcases and find the Seventh Book of Knowledge in the seventh position on the top shelf of the second bookcase on the left. Remove the book to get the sapphire gemstone. Show the sapphire to Nathaniel Blackwood, who tells you that its name means 'beautiful thing' and it brings wisdom.
As the sapphire fits in with reference to 'Wisdom' in the second inscription, remove the moonstone from the statue and replace it with the sapphire. A blue ray of light is now reflected towards the third statue. Note that it doesn't end at the statue, but passes over it.
Again remove the ivy with the zeppelin knife to reveal a statue of two sphinx heads. The third part of the inscription refers to 'the strength he needs', so you need to place the ruby (it symbolizes power) on the statue. This causes a red ray of light to reflect towards the door on the balcony.
The third part of the inscription also refers to 'purity'. Both the pearl and moonstone are associated with purity, so test each one in the slot in the door. The moonstone will reflect a light blue ray of light back downstairs, directly onto a pillar near the left stairs. Note the panel on the pillar.

Open the panel on the pillar to find the other half of the bas-relief.