Because they've already planned the number of guns, and can make simple calculations.
Please give me evidence that can back up that quote. You stated that at the time of the Maryland Campaign there were approximately 120 guns in all the Washington forts combined, according to the AORs. Can you please supply the message you got those figures from?
It says there are 443 emplacements, and that not all are mounted yet (in fact he implies about half, which is perhaps optimistic).
In no place does it read or imply replacement. The quote, as written in the report I supplied, reads: "the entire defensive line, 35 miles in length, consisting of about fifty different works, and mounting four hundred and forty-three guns, was, though not completed, essentially brought to the condition in which it was left when the Army of the Potomac commenced its campaign in Virginia."
Throughout the report, the word "guns" is used, not "emplacements." That does not imply to me that they are simply counting empty emplacements. That implies actual guns, not sites for them.
The "half" figure to which you refer, does talk about emplacements, however. Barnard mentions that "approximately 200 platforms should be made, embrasures cut, &c, for field or siege guns". This is due, Barnard says, to the fact that many of the guns already emplaced are more vulnerable than he'd like to counter-battery fire. It's not referring to the number of guns, but the number of sheltered emplacements for them.
No, artillery manufacture is quite slow. The defenses of Washington primarily mounted 32pdr naval pieces and some 24pdrs.
Slow compared to what? It's slow compared to the rate of manufacture of small arms, but when compared to the months needed to build a fort, it's quite quick. In addition, guns can be manufactured at factories at different places. A fort is built and used in only one place, but even big guns can be mobile -- they can be forged in one place and moved to another. I know I'm stating the obvious with that observation, but we shouldn't think of gun manufacture as being a slow process.
The 24- and 32-pounder guns were interim armament, as shown in the link I posted previously. In the first months of the war, there weren't enough siege and field guns to go around, so the Eastern Branch forts were armed with these naval guns. A few were mounted in other forts north of the Potomac, but the vast majority were only used in the Eastern Branch fortifications -- the remainder of the forts received normal siege and field guns for defense.
The Eastern Branch fortifications were never intended to defend against a frontal Confederate attack -- they were only intended to deny the Confederates the ability to bombard the Naval Yard and Arsenal. Therefore, they were the last to receive their armament, and were the forts that got the naval guns. But as the report reveals, after the Maryland invasion, Barnard placed a high priority on removing or protecting those guns, which were of limited use at close range.
The 24-pounders used at Fort Stevens in 1864, though the same weight as those naval guns, could be reloaded more quickly and were more effective at close range than their naval counterparts. These were the guns that were typical in Washington's forts, not the awkward naval versions.
3,000 in 30 minutes (the charge itself, approx 1 casualty per minute per regiment that charged, actually a lower rate than a conventional firefight) and another 4,000 in the 9 hours the 40,000 attackers laid in the killing area before withdrawing after nightfall. Poor attack, it would have taken less casualties had the attackers kept going (and even less had the attacks been properly coordinated and not allowed 30,000 Confederates to concentrate their rifle fire on them).
I disagree on the exact figures, but the principle is the same. Whether you're at Fredericksburg, Cold Harbor, Gettysburg, or Fort Stevens, attacking into the artillery of your opponent is stupidity paramount. Even if you reach your opponent's infantry (as happened in Pickett's Charge), you'll be so mauled that you'll never be able to fight through the defending infantry and hold against the inevitable counterattack.
You've got to have the numbers and the willingness to take the necessary casualties in order to take such a position. At Fort Stevens, Early has neither.
What 10 inch guns? The armament of Ft Stevens was 10x 24pdrs (4 on Barbettes, 6 on Siege mounts), 2x 8" Mortars, 1x Coehorn Mortar, 1x 10" Mortar and 5x 30pdr Parrotts.
The primary armament was the 24pdrs which should put out 7-800 canister balls per minute between them. Canister is far less effective than musketry, especially at extreme range (300 yds), the effect of the Forts battery is probably about the same as a regiment of 2-300 riflemen.
Sorry about the 10-inch gun reference. A bit of hyperbole on my part, and I apologize.
And you're absolutely right about the effectiveness of canister. It's not effective at long range. But that's not what's going to be happening in this alternate battle. Early has to attack the fort in order to take it. He can't simply dance around the guns and walk into Washington, otherwise he'd have done it. His troops will have to mass and charge the guns of Fort Stevens, braving the canister fire the whole way.
At Marye's Heights, Pickett's Charge, and Cold Harbor, we saw what the end result of that strategy is. The attackers will be bloodied and disorganized if they make the fort's walls, facing defenders, who, though inexperienced, are defending their nation's capital and are organized and can concentrate their effort against the Confederates. If, by some miracle the Confederates manage to carry the fort, it will be a hollow victory. They will not have enough soldiers to hold against the inevitable counter-attack, let alone advance into Washington.
.