While Cid repairs the airship, he asks you to meet with an aetheric scholar to find an aspected crystal to break through the wind barrier around Garuda's sanctuary.
This quest is available if you have completed the quest In Pursuit of the Past.
Starting the Quest
Talk to Cid at the airship landing in Gridania to begin the quest. (If you are outside of the airship landing, you can speak with Lionnellais in the airship landing area to reach Cid.) There will be a cutscene.
Speak with Lamberteint
Go to Camp Drybone in Eastern Thanalan. Go into the westernmost door on the lower level of the camp, then turn left and talk to Lamberteint to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Lamberteint to accept the next quest: Sealed with Science.