Looking back at the Burning Plains there is little to add. I did not discuss cavalry tactics (but then again we are not told anything about them) I did not question thouroughly whether the fortifications were manned, but these are theoretical rather than practical question, worthy perhaps of a later mention or better yet of more commentary after I set up my projected webpage.
On to Farthen Dur. Basically it is a much simpler battle and we know fewer things. The entire battle, including Durza's end takes only one chapter in Eragon while the aftermath takes another at Eldest without adding much new knowledge. If at Farthen Dur we had one bad general, right here we have several bad generals, which I will explain later.
Composition and size of enemy armies
About the general composition of the Varden and the dwarves I have discussed earlier. Basically the Varden are rather lightly armed: it is implied that they fight unarmoured while the dwarves have mail armor. Of the Urgals a good description is not given at the chapter, but earlier we are told that they protected themselves with a shield at Yazuac (if I remember correctrly) while we are told Garzhvog is only wearing a loincloth (rather than armor). Their offensive weapon is in most cases the sword though a few spearmen do encircle Saphira at some point.
For the Urgals we are not told number and they do not really matter anyway. They were simply massively more than the Varden and the dwarves. For the Varden we know they number about 4,000 at Farthen Dur, according to Orik. This number definitely includes non-combatants. How many of the Varden are non-combattants we are not told but we can guess. Jormundur has a wife and child with him, while the council of elders has 2 female and 3 male members. While women were generally evacuated this is not absolute: magic users took part in combat as we are told in Eldest. In any case we do not know if the 4,000 number includes children. In any case if the ratio of the council is an indication 3/5 of the 4,000 are men thus 2,400. I would round this to 3,000 since at desperate times even women took arms, like Nasuada and the magic users.
The Varden/dwarves are arrayed in three lines, one led by Hrothgar that inludes only dwarves (or at least that was Eragon's impression when he came to aid them) and two led by Ajihad and Jormundur. In Jormundur's formation fight Eragon, Arya and Orik (probably for dramatic effect). We are told that it includes both humans and dwarves. Since Ajihad leads the third line it must also include humans. It seems possible that these two lines have more humans than dwarves since humans are leading them but this is not necessary: the dwarves definitely lack experienced fighters. Eragon comments earlier lead us to believe that the villagers of Carvahall
think that dwarves are fictional, implying that they do not leave their cities often to attack the Empire like the Varden. Orik is ordered by Nassuada at the Burning Plains to take control of the dwarves, implying that they lack leaders with war experience, even at such a late hour!
If the three lines are equal in numbers and the Varden are evenly split between the two and in these two there are equal number of humans and dwarves then the Urgals are facing 9,000 fighters. However Arya's (and Eragon's but to a lesser extent since he is more mobile) presence makes Jormundur's line stronger than the rest. There is no reason to do so ans in any case it seems more likely to me than there are more dwarves at Jormundur's line than humans for the simple reason that the dwarves at Tronjheim far outnumber the humans, as we saw during Saphira's and Eragon's procession towards Ajihad. Hence I am inclined to believe that there are 3 dwarves for every human in the battle (to reflect the demographic difference) and the Urgals are facing about 3,000 humans and 9,000 dwarves overall. More to come next week
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