We had left with the announcement of Hring on the first day of the Althing, which was made all the more momentous by interruption by an eclipse. Everyone at the Althing are buzzing with the meaning and import of the event, but few know what to do about it. Vigfus the Proud invites many important people to his camp, where it is implicitly agreed that they will discuss what to do about Hring's offer. Brygjafael, Raudarbank, and Syfjaourholur are there. As Vigfus' son-in-law, Skallagrim is invited -- but it only arrives at the last minute, showing Vigfus' disfavor.
Once all are gathered at the feast proper, Vigfus makes a speech where he denounces Hring's offer as a ploy to undermine the Commonwealth by causing disunity. He notes, however, that to refuse the offer would show weakness and simply leave him with his considerable forces. He goes on, eventually suggesting that he could lead these troops in his own expedition southwards this summer.
This is discussed roundly by many. Eventually, though, Melnir calls for attention. He says that he has seen that Skallagrim is a skilled war leader, and yet is neutral among the important families here. Moreover, he adds, Skallagrim is the killer of Hring's son Agnar. Thus, he concludes, to make Skallagrim lead the army would place Hring in a bind. If his men refused to follow, then he would have broken his promise. If they do, then he has given power over to his son's killer.
This is widely discussed, while meanwhile Silksif considers what she has seen of her new husband. From their wedding night, she felt sure that he did seem to have real passion for her. Later, she asked him quietly in private about his feelings. He replied, "You are so different from other women. They are either afraid of my power or greedy for my wealth. But you remain above that, distant almost as though unaware of your austere beauty." She was taken aback, and for a moment considered whether there is some sort of spell on him. However, at a glance she reassured herself that there is no magical influence on him. He also thought little of her enchanted necklace, showing that he has little greed in his heart. He did not, of course, believe in the enchantment when told -- but he was reassuring to her.
Back at the party, Skallagrim gives a short speech claiming little ambition for the post that Melnir suggested -- but that he would accept it if selected. It is perhaps the best speech that Skallagrim has ever given, who is reknowned for roaring speeches which no one can understand. Meanwhile, Silksif questions Melnir about how he came to suggest Skallagrim. He explains his logic, which was fairly spontaneous but reasonable, with no apparent influence from Aud -- even though this is exactly what she had planned. Amongst the table, there is much discussion of the ramifications. Kjartan speaks up that this should be a public, legally-defined post where the leader is chosen in open debate -- though of course they could favor Skallagrim as a candidate.
Near the end of the party, Kjartan approaches Thjohild to talk. She is shy of him at first, and has little to say about the politics. However, she does open up about her family some. Eventually she goes with him for a romantic walk in the starlight, to return holding hands.
The next morning, Hallgerd goes to visit Hring's wife Gullrond to welcome her, bringing token gifts for her and exchanging pleasantries. She soon sees right through Gullrond, finding her a bitter and bossy woman, sad over the loss of her son and frustrated in marriage. She speaks longingly of the niceties of Hvalrik. Hallgerd takes this in, and maneuvers to bump into Hring as she leaves. There just outside the tent, she brazenly flirts with him, to which he eagerly responds.  He mentions that he is going to horse-fights later, and could use some advice. Horse-fights are sporting matches held outside the Althing grounds, since they are technically illegal. Hallgerd smiles at this and says, "Oh, I have a talent for picking out winning stallions." Hring eagerly accepts, but soon his wife hears of this and thinks black thoughts of Hallgerd. 
Also that day, Skallagrim visits Melnir's camp to question him about his suggestion. He explains that he wants to speak with both him and his wife Silksif over different issues. Speaking first to Melnir, he asks why Melnir suggested him. Melnir is somewhat apologetic, and offers to try to reduce the chance of him being elected if that is what he wants. Skallagrim thanks him but refuses. Melnir explains his reasons for choosing Skallagrim, summing up "I say as a compliment that your axe is more dangerous than your tongue. With others their tongue is more dangerous than their sword." Skallagrim briefly mutters, "Yes, my wife.", then thanks Melnir for his compliment.
Skallagrim then asks to consult Silksif in her capacity as prophetess. Melnir gives him a somewhat dark look, being now possessive of his wife, but professes no objection. Outside, Skallagrim explains to Silksif that he has a family curse from many generations ago, from when .
Later that day, the time comes for proposal of new laws. Though ultimately the godi decide, this is open to any man to suggest. Ambitiously, Kjartan calls out a proposal for the new position of Commander. His speech is well-delivered, but legally it has unintended consequences which make the position less answerable to the godi. Despite or perhaps because of this, there are many who speak out favorably.  It soon becomes a contentious issue.  There is considerable debate, and eventually it is decided to weaken the position from Kjartan's proposal -- but there are still many who support him.
The following day, Skallagrim is quickly chosen as the person to fill this new position of Commander. While he is much more wealthy, Vigfus is envious of Skallagrim's popularity in this regard, especially since his own bid was turned down.  By the last day of the Althing, Skallagrim finds himself preparing to lead a force of some 60 men: 30 from Hring, and 30 volunteered from various clans of the Commonwealth.
Shortly before this, however, Skallagrim had a long put-off meeting with his step-daughter Vagnhild. It is a long and painful conversation, full of hedging from him and sniping from her. In short, he suggests that she come on the westward expedition, to show her bravery and see the world. He notes that both Silksif and Thorgerd came to know their husbands from the expedition two summers ago. And he also suggests that it would be a welcome change from being at home with her mother. Vagnhild, however, is mortally insulted at being pimped out to an army of smelly men, and walks off in a huff.