After speaking with Urag we'll have to go meet Tolfdir. Follow the marker and speak to him. Follow him as he observes the orb and soon you'll be interrupted by Ancano. Follow him into the Arch-Mage Quarters and up here, speak to the monk from the Psijic Order named Quaranir. Talk with him and you'll be given another objective: "Find Augur of Dunlain" .
From the Arch-Mage's room leave and go to the Hall of Attainment. Speak to Tolfdir and he'll tell you where to find Augur. Return outside and go to the northwest side of the garden to find a trapdoor with the entrance to the Midden. Once down here, when you reach the large room, go downstairs and you'll find two ways to go. Both lead to the same place, but the tunnel to the right gets you there much faster. The tunnel ahead of you has an interesting "forge" that you can check out.
Loot any treasure you find and when you get to the room with the pool of water, go through the doors to get to the Midden Dark. In here, at the ice bridge, drop down to your left, open the chest and you'll have to ways to go. Follow the tunnel path (the one with the torch), kill the spiders that appear and move to the northeast side of the room. Burn or cut down the webs that block your path and you'll find yourself enough in a freaky room with a hand in the center of it.
You can't do anything with it right now so carry on and kill some Skeletons in the next room, and in the next hall, you'll find an Alchemy Station with an Alchemy Skillbook **** named "De Rerum Dirennis" . Proceed onwards and you'll now find yourself in the room that's just after the room with the ice bridge. Go west from here and approach the door. It'll say it's locked, but then you can hear a voice. Try entering (keep trying) and the voice will unlock the door.
The well activates and now you have to activate Augur of Dunlain. Speak to him and after the chat, you need to return to the Arch-Mage. Head back and find the Arch-Mage. After chatting with him for a bit the quest will end, but not before the Arch-Mage gives you the Mage's Circlet, which increases your Magika by 30 points if you equip it. Not bad.