Arniel's Endeavor

Quick Look

 

Part 1

1. Talk to Arniel Gane.
2. Obtain ten Dwemer Cogs.
3. Return to Arniel.

Part 2

1. Speak with Arniel once again.
2. Acquire the staff that Enthir sold.
3. Return to Arniel.

Part 3

1. Speak to Arniel
2. Place the Warped Soul Gem inside a Dwemer Convector three times
3. Use Arniel's Convection spell to heat the Dwemer Convector three times
4. Return to Arniel

Part 4

1. Talk to Arniel in the Hall of Countenance
2. Talk to Enthir
3. Retrieve item
4. Watch Arniel's experiment

In Depth

Part 1

 Talk to Arniel Gane and ask if there is any College business you can assist him with. He'll state that its nothing official, but he is working on a "project". He refuses to say anything about it, but he asks you to bring him 10 Dwemer Cogs. They can be found randomly throughout any and all Dwemer ruins. If you have not already found a Dwemer ruin, Alftand is near the College of Winterhold and the ruin under Markarth is easy to find and lower level friendly.
There are at least 10 Dwemer Cogs scattered around in display cases and on tables at the Dwemer Museum in Understone Keep. The main College quest line will take you to Mzulft, which also has more than 10 Dwemer Cogs. Depending on the ruins and your carry capacity you may end up needing two or three trips to get all the cogs.
Once you have obtained the ten Dwemer Cogs, return to Arniel and he will reward you with a level-specific amount of gold.

Part 2

Arniel needs a very specific item for his project and is having trouble getting Enthir to give it to him. He'd like you to speak to Enthir and return with the item to him. After speaking to Enthir he reveals that the item Arniel wants never belonged to him and is Enthir's property. He agrees to relinquish it though if you'll retrieve the Staff of Tandil he sold to an unscrupulous character.

The character is a boss level caster in a radiantly assigned dungeon. Depending on which one you get the quest may be increasingly more or less difficult. Some of the dungeons such as Boulderfall Cave and Cragwallow Slope are extremely small while others might be rather involved or of a difficult nature. The staff should be either on the boss level caster, somewhere nearby, or in the boss level chest.
Once you have the staff return to Enthir. He'll give you the Warped Soul Gem which can then be returned to Arniel for your reward

Part 3

Begin this quest by asking Arniel about the progress of his project. He will say that it is going terribly. He reveals that he is trying to simulate the disappearance of the Dwemer but he needs the Warped Soul Gem that you acquired for him charged. Unfortunately, the apparatus he was using to charge it was destroyed in the process and he has no time to build another. Thus, he is only too happy to accept your generous offer to charge it for him.
Arniel tells you that the Dwemer used to use convectors to charge their soul gems and that some of these devices probably still exist among Dwemer ruins. He needs two more charges after his own initial charge to power the gem. Due to the nature of the warped soul gem, it will destroy the convector it is charged in. What you need to do is find a few Dwemer Convectors and place the Warped Soul Gem inside. He will teach you a spell called Arniel's Convection that must be channeled onto the Dwemer Convector until the stone is charged. Keep channeling the convector until the quest updates. You will then have to find a new Convector and repeat this process up to two times. There seems to be some variance on whether it takes one to three times to fully charge the stone and use of dual casting can complicate the matter.
There are six Dwemer Convectors in all of Skyrim:

• Druadach Redoubt: Across the river from it in an unmarked ruin.
• Deep Folk Crossing: Across the bridge from it at an unmarked ruin.
• Dwarven Storeroom: Simple freestanding Dwarven structure near Mzulft. No enemies.
• Mzulft: Near the entrance in one of the first rooms after the hall. Must have started Revealing the Unseen.
• Ruins of Bthalft: Exterior only ruins, Bandits here.
• Shor's Stone: Southwest of the village at an unmarked ruin with a single Warlock.

Two northward of Karthwasten, one south of Ivarstead, one southwest of Shor's Stone, and two among the ruins of Mzulft. The two northwest of Karthwasten are probably the easiest to use since no enemies spawn at their locations (wild animals may be a nuisance however) and they are relatively close together. One is directly north of Karthwasten, northeast and across the river from Druadach Redoubt. It is at the base of the unmarked Dwemer pillar. If you cross the river and follow it upstream you will come to Deep Folk Crossing. Cross the bridge and the second Dwemer Convector will be in front of you. The one south of Ivarstead is at the Ruins of Bthalft and has bandits. The one southwest of Shor's Stone is between there and Autumnshade Clearing and has a rogue mage. At Mzulft, one is inside the storeroom (a separate building to the right of the ruin entrance when you arrive) and the other is within the ruins proper.

Part 4

Wait a couple of days and talk to Arniel again. He is often to be found on the upper floor of the Hall of Countenance. Once more he's used Enthir's services, and once more you have to pick up the pieces.
Talk to Enthir, who is almost always in his room in the Hall of Attainment. He's quite annoyed since he has no idea where the item is — or even what it is, for that matter. He was only tasked with providing transport for it from Morrowind and it simply hasn't arrived. Enthir tells you to go look for the courier somewhere in the east, and marks a location on your map.
The precise location of the courier varies. When you finally do locate him, it's immediately apparent why he didn't complete the delivery. Retrieve the blade "Keening" from his body and return it to Arniel. He is outraged that it wasn't wrapped properly, and amazed that you didn't die when you touched it. By way of explanation he relates something of the background of Keening and Sunder, the legendary tools of the Dwemer Tonal Architect Lord Kagrenac.
Arniel now conducts an experiment in an attempt to figure out how and why the Dwemer disappeared. Striking the warped soul gem twice with Keening, he achieves no apparent result. Having now lost his temper, he lashes out a third time — and disappears in a flash of light.
The quest is completed. Pick up Keening from the floor if you wish (although it seems to have come down in the world somewhat since the Third Era). Summon Arniel's Shade will be added to your spell list automatically.