By the start of July 1863, Pemberton (South) was out of road. His garrison was starving, half of it sick, the relief from Johnston (South) was not coming and he knew it, and the Union lines were practically on top of his works. On July 3 he sent out a flag of truce, carried by Major General John S. Bowen (South), his best division commander, and opened negotiations with Grant. Grant, true to the nickname he had earned at Fort Donelson, first demanded unconditional surrender. Then he reconsidered the arithmetic. Shipping nearly thirty thousand prisoners north up the river would tie up his boats and his men for weeks. So he offered terms instead: parole. The garrison would lay down its arms and sign an oath not to fight again until they were formally exchanged, traded back, prisoner for prisoner, in a swap between the two sides, and then go home.

On July 4, 1863, Independence Day, Vicksburg surrendered. About 29,495 Confederate soldiers marched out, stacked their arms, and signed their paroles, many of them gaunt from weeks of mule meat and pea bread. Grant’s army took the city, the garrison, around 172 cannon, and tens of thousands of small arms.

There is a long-told story that Pemberton, who was Northern-born, a Pennsylvanian who had cast his lot with the South, deliberately chose the Fourth of July, betting that Union pride in the date would win his men softer terms. The exact words put in his mouth aren’t reliable, but that he banked on the date is reasonably well attested through Grant’s memoirs.

Whatever the calculation, the date carved itself into local memory: by reputation, Vicksburg did not officially celebrate the Fourth of July again for something like 81 years, until the end of the Second World War.

The numbers around the surrender tell the story of how the siege ended without another grand battle, but only one of them really matters. The siege itself cost the Union roughly 4,800 men; the full campaign back to the spring landings cost something over 10,000 on each side in killed and wounded. But the figure that changed the war was the surrender: nearly 30,000 men taken out of it at a stroke, an entire field army gone in a single afternoon.

What it changed was the map of the war. Five days after Vicksburg fell, Port Hudson, Louisiana, the last Confederate post downstream, gave up too, there being no longer any point in holding it, and with that the Union controlled the entire Mississippi River, end to end. Texas, Arkansas, and most of Louisiana, the whole Trans-Mississippi, were now cut off from the rest of the Confederacy, severed from the beef and men they had been sending east. The river that had been closed was open, and Northwestern grain could float to the sea again. This was the moment Lincoln captured in the Conkling letter with the line that has outlived almost everything else about the campaign:

"The Father of Waters again goes unvexed to the sea."

Lincoln, letter to James C. Conkling, August 26, 1863

And it did not happen alone. Vicksburg surrendered on July 4, the day after the Confederate army was thrown back for the last time at Gettysburg, in Pennsylvania, hundreds of miles away. The two together, the great eastern invasion turned back and the great western fortress fallen in the same 48 hours, are conventionally counted as the military turning point of the entire Civil War, the week the Confederacy lost the initiative for good and never got it back. For Grant, the campaign made his name; the boldness of it, the river crossing, the army cut loose and living off the land, the wedge driven between two enemy armies, put him on the road to general-in-chief of all the Union armies within the year. The key was in the pocket at last.