This is to be my last major comment on this battle, which is the most complex battle in in the Inheritance trilogy so far. I will continue in the future with the other major battle in the series, that taking place under Farthen Dur, a general commentary on the Varden as a military force, the rise of Galbatorix, the dwarves and the Elves and other comments. I will try to set my writings in the form of a web-page so that they can become more accessible. Do not expect me to update as often as I did for my firs article series.
Casualties
Basically anybody's guess is good. Before the invention of gunpowder battles would produce 3 dead for every wounded. In the age of gunpowder this ratio was reversed. In this battle, with Eragon's advanced magical knowledge, many magical healers, defections to and from and unknown troop numbers everything is open. We are told that the bulk of Galbatorix's army escaped beyond the river. The bulk can mean anything upwards of 2/3. Eragon and Saphira are shown to kill by the dozens, while of his bodyguard 2 of the 4 Kull and 3 of the 7 dwarves get killed, something not surprising since they were the front line crack troops. In most historical battles before gunpowder it was harder to have more than one casualty per enemy soldiers, unless we are talking about true tactical blunders by enemy commanders and defections like Plataea or Cannae.
In one of the largest military disasters that befell Athens, the battle of Delium, the Athenians lost 22% of their forces and the winning Thebans 8%. In Cannae the losing Romans lost 55% of their force and the winning Carthaginians less than 10%. Something over 10% casualties for the joint anti-Galbatorix force would be a surprise since the dwarves probably suffered little due to their late arrival. If I would have to place a max on Galbatorix's dead it would be 20 to 25%. At the end of the battle most of Galbatorix's force has escape beyond the river, no longer forms an army but is still alive. We are not told if they can be rallied into a new army (but are led to believe they cannot) but Galbatorix probably needs in any case to snd new officers to lead them. He might as well raise a knew army to replace them, this might even be simpler.
Respone to unfair criticism
This is to respond to the unfair criticism written at the bottom of the battle's page in Wikipedia:
1.It is humanly impossible to run 800 meters in full gear: In Marathon the Athenians run 1500 meters in heavier gear. In any case it depends on the meaning of run: We cannot expect them to do the distance in under 1 minutes like Olympic runners but have them walk at three times the normal pace could be called running and would have taken under 15 minutes
2.The Varden leave prepared defences to fight a numerically superior army Nassuada decided to take the initiative. Probably she wanted to catch her enemy unprepared (which she mostly did), perhaps she wished to keep the morale boost given by Eragon before it dropped, perhaps she knew from the Durgrinst snt earlier that the dwarves were near.
3The Kings cavalry is forgotten. Not quite. Eragon, not Orrin is the focus of the book. We are told that they throw themselves at the flank like the cavalry before them, implying the cavalry is still ther fighting at the side.
4The Battle is physically impossible to have lasted the whole day. This is what happened in Cunaxa, the 10,000 Greek mercenaries attack and fought all day without even having eaten breakfast. Many battles have lasted an entire day before gunpowder.
5 Eragon leaves at the height of the battle over a ship. Eragon could have smote down the ship on his own before it became a threat to anybody. Nobody else is simply capable of doing so
6 The Deus ex machina dwarves. Nasuada has some idea when they are expected to arrive. Perhaps she chose to battle on that day for this reason, knowing that the Empire could have neutralised her forces first and the dwarves in succession before they could unify, and hope that by wearing down the imperial forces they cannot threaten the dwarves who are expected soon and could catch the imperials weary. In any case Deus ex machina is common in fantasy battles, see Helm's Deep of the Pellanor Fields in the Lord of the Rings.
Characterisation
In a nutshell Nassuada is good (but not great) and lucky, her counterpart horrible and Hrothgar unlucky. The Burning Plains are far greater a victory than Farthen Dur which was fought in an obscure (for those living in the Empire) place by two non-human races. That the Urgals are fighting for Galbatorix is unknown to most living in the Empire, on the other hand here is a major victory against a known enemy by known foes. Whatever the result of Murtagh's appearance if Galbatorix is as unpopular in the South as in the North he should be facing major upheavals on his path and have trouble from now own concentrating his forces, even more since he should be facing an Elvish invasion.
Perhaps this will be Nassuada's Granicus: After that battle (and combined with brilliant tactical moves) Alexander the Great found himself in control of the biggest part of Asia Minor, more than any Greek general before him had even hoped to dream. We need to wait and see when in the next book what will the influnce be to nearby cities: will they surrender, will they resist. We will find out together with the publication of book III, whenever that is to happen.
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