"Rythor needs time to examine the Horn of Zyyr. In the meantime perhaps I can be of assistance to Aster Cei."
When you approach Aster Cei and mention that he's been looking for you, he says he hasn't, but now that you're here he could use your help. He's been plotting the existing Spire locations on the map, trying to find a pattern. Neither you nor Aster Cei can see one, and you suggest the locations could just be random.
Aster Cei suggests you go to the new Spire and explore it, whilst he tries to find out from Rythor where he found the Pendant. When asked about a reward, he gives you another key, this one to Display Case E, at the top of the right hand stairs next to Case F, which contains a Dwemer Dragon Schematic.
In one room in the Spire ruin there is a lower level that has a dais with a Warlock Chest on it, two Speckled Clannfear and a Speckled Xivali. In front of the dais is what appears to be a body. The Xivali and Clannfear can't climb up to your level, so if you can finish them off from a distance. The only way og getting to the lower level is by jumping down; the entrance into it is blocked by a rockfall. You can climb back up again using a fallen beam on the north side.
"The corpse of Wymere Solan! What is it doing here? Teav told me Solan was killed in a cave-in at Lindai. I should investigate."
Search Solan's corpse and you will find Solan's Diary. Read it, and your log updates again.
"In his diary, Solan tells of murderous betrayal at the hands of his apprentice, Rythor. Rythor is planning to use ancient Warlock artifacts to dpawn a demon of unimaginable powers. I should report this to Aster Cei immediately."
Your suspicions may have been aroused by Rythor's recent actions. His reaction to you clearing out the last Spire seemed to be a bit extreme simply to be about your safety, and certain parts seemed more like a threat than concern for you. He was a bit too eager to get his hands on the Horn of Zyyr, then lied about Aster Cei needing to speak to you to get rid of you, and his possession of what was seemed like a Warlock artifact without telling anyone was somewhat odd. Seems that, if you had any, your suspicions were right.
Return to the Guild and speak to Aster Cei. When you talk to him, he asks you if you've seen ythor, as he is missing. You explain about the discovery of Solan's corpse and the recovery of his diary. Cei reads the diary, and asks if you've read it - if you say no, he gives you a summary. Aster Cei gives you the key to Rythor's office, and asks you to investigate whilst he tells the others.
If asked about a reward, he gives you the key to Display Case H, at the far end near the entrance to the collapsed passage, which contains a Magical Feather.
"I am the only one who can stop Rythor now. I must break into his office and search it for clues to his whereabouts."
Go up the right hand stairs and go along the balcony to Rythor's office. Open it with the key Aster Cei gave you. In the office is a wooden door, that also needs a key. Search Rythor's desk; your quest log will update.
"In Rythor's desk I found a note, the Runes of Cyrodiil, and a key to his Lair."
The note is a note to the bandit Dwyff who you killed in A Vengeance Unfulfilled. In it, Rythor is hiring Dwyff to attack the archeologists and kill them all, stealing the Brilliant Shard and returning it to Rythor - the bandits can keep everything else. It appears Rythor was behind the death of Teav, and that of the scribe Miro given that he has the Runes of Cyrodiil.
The key from the desk will open the wooden door, which leads into a storage area. At the end, behind crates and barrels, is a door that leads to Hidden Passage. Go through that. Hidden Passage is a dungeon filled with a variety of undead, including a dangerous lich called The Soothsayer, who has a unique item, Haunted Lamp. When activated, you will get a new Conjuration spell that allows you to summon Ethereal Imps. The exact effect of the spell depends on the Conjuration level you have - full use will not be gotten from it until your level is 100, and below 50 is too low to have any effect.
In the north east corner of Haunted Passage is a door to Rythor's Lair. Before entering, it would probably be an idea to bring some potions; of healing and of fatigure restoration especially.
Rythor's Lair is mostly empty. As you enter the second chamber, Kal Rythor will appear behind you. When Rythor appears, kill him, and your quest log will update.
"Rythor is dead, but the Avatar has already been spawned. My only chance of defeating the Avatar is by enslaving it with the Horn of Zyyr."
Search Rythor's body. Amongst other loot, he has the Sacred Warlock Scroll, three Brilliant Shards, the key to Display Cabinet L in his quarters which contains a Dwemer Screw Schematic and the Horn of Zyyr. When the Horn is equipped, you are bombarded with several healing balls of light, then the following message appears: "Holding the Horn in your hands, you free Luminai's divine soul - she whirs loose from ages of enslavement. The Horn is now vacant. It alone can enslave the Avatar." Take any loot you want now, you won't have time later.
Equipping the Horn also removes the central grating, allowing access to the Avatar.
This is not a time for subtlety. Wield the Horn, enable as many protections as you can, and charge straight at the Avatar. Ignore the Wisps; although they are dangerous, only when the Avatar is defeated will they permanently die. Until then, the Avatar can keep summoning more. Attack the Avatar and keep attacking it without let up - with luck, you may be able to defeat it in a few seconds, but only with the Horn and even then it is not guaranteed, and you can still always be crushed by the falling roof.
Once you defeat the Avatar, your log updates again.
"The Avatar has been enslaved. I must escape this crumbling Lair."
Although you've defeated the Avatar, you are still in a lot of danger. It may take several attempts to escape as escaping can be at least as dangerous as the fight with the Avatar so, unless you want to have to defeat the Avatar every time, saving the game here is a good idea.
Now the Avatar is enslaved, the Lair is falling to pieces and going up in flames. You need to get out. Drinking some health and fatigue restoration potions will help here, if low on health and fatigue.
Run up the stairs and past Rythor. If you didn't loot him before the fight, don't try now, you don't have time. The ceiling at the top of the stairs will collapse; jump over this, then jump into the right hand aisle and run up there, cutting back into the centre aisle at the end to run back up the entrance stairs. Watch out for falling rocks and flames on the way. Leave the Lair through the door to Hidden Passage.
Still not out of danger; the following message appears on entering Hidden Passage - "I remember seeing a small pool of water here. Perhaps it can save me from the relentless flame." Another save would not go amiss here.
You need to get to the pool of water, and the ceiling is collapsing here too, including at the base of the stairs you are on. The closes water pool is straight on from the bottom of the stairs, right when you come to the wall, then first left. Rocks will still fall on the way. Get underwater, and wait for the flame to pass - you should be able to hold your breath long enough.
Make your way to the exit. Bits of ceiling are still falling down, but these are pressaged by the screen shaking. When that happens, back off a bit and wait for the rocks to finish falling. These are dangerous, and will kill you, but there is none of the urgency there was before you hid from the flames.
Go back to Rythor's Quarters, and your log will update.
"I've escaped! Just barely intact. I am now responsible for safeguarding the Horn of Zyyr, making sure that it never falls into the wrong hands again."
When you enter the Lobby of the Guild, you will see Cei, Sova, Verus and Norlene standing waiting for you. Go speak to one of them, and tell them what happened. They have come to the decision to offer you the position of Headmaster of the Archeology Guild if you want - you can refuse, but there's no real point. Whether you accept or refuse, the quest is now completed, as is the quest series.
The final glass case from a pedastal stand has been removed, by the pillar near the library entrance, which contains a Glowing Zodiac. Aster Cei will now sell you a Dragon Study.
So, that's it. You've completed the quest series, and may now be Headmaster of the Archaelogy Guild if you chose to accept it. You will have picked up a lot of unique and valuable items on the way, and now you are entitled to pretty much everything in the Guild itself. Many items are fairly commonplace, but others are unique and some may have special powers. You can also use Rythor's room to store items and sleep in - after all, it's not like he needs it any longer.