At the Hatchie? I see this is after Van Dorn retreated from Corinth. I am still not there yet in the book. I might have to come back to this comment later.
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I noticed before that you thought the fallout between Grant and Rosecrans started afterwards. I think for Grant that's obviously true. Immediately after, he was concerned about the next move, very characteristic for him. His first report was favorable to Rosecrans.
For Rosecrans however, I think it was different. Although comments made 20 years later can be tainted by the history of animosity that developed afterwards — I think this is maybe what you are saying. However, Rosecrans wrote to his wife that he couldn't shake the feeling that had the attack from the west been made, his trap would have succeeded. He just wouldn't let that go, and was completely blind to the reasons the attack from the west was postponed. This kind of "blindness" or lack of acknowledgment of his role in the postponement can help explain his confusing statements about the communication with Dickey and Lagow. He had a very formidable blind spot, where he was in denial that his delay caused a corresponding change. Like the saying goes: "There's none so blind as he who will not see." Cozzens added that Rosecrans never accepted the explanation of the acoustic shadow either.
I am citing this paragraph from Castel for the reference to the Rosecrans letter. You must have seen it before.
View attachment 519164
When isolated from Castel's opinions there ^ the letter and corresponding disappointment seem normal and not raging. However, Rosecrans was bitter about "the tardy justice" of getting his promotion to major general in September. That comment had nothing to do with Grant or Iuka and I think lies closer to the truth of all their problems… the quest for more rank, an independent command, etc.
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I also think that had this kind of unsatisfying battle result happened with someone else, it wouldn't have been a source of everlasting bitterness or angry feelings. Consider the disappointments Sherman and Grant had gone through. Shiloh, shocking battle, even in victory it was a source of much press criticism. Sherman and Grant could have blamed each other for the surprise but didn't. Grant almost quit and went home when Halleck placed him in a "time out" and Sherman convinced him to stay and wait things out, instead of ridding himself of Grant.
Then, it must have been a big disappointment for General Sherman to attack Chickasaw Bluffs in December and find it well defended, contrary to his plan with Grant. His attack was reported as a repulse, when it was one prong of a coordinated plan that failed on Grant's end. Again Sherman and Grant could have been at odds with each other, in some rivalry power play. Lucky for the U.S. they didn't play that game.
Meantime, this Iuka battle didn't accomplish all it intended, but it was not a repulse, a humiliation, or some shock, surely Rosecrans could still spin it to his advantage. Corinth was a battle with a favorable result for the Union, a victory. Rosecrans got the independent command he desired out of it. Yet it all ended poorly between Grant and Rosecrans?
The only explanation must be that the source of their problems was somewhere else. I am still trying to understand that. My impressions are still incomplete but my disposition is to think that the battles themselves aren't it.