IIRC, It's been a while since I read it, but the USA had actually 3 nuclear bombs when we hit Nagasaki, (A history of the atomic bomb -- Richard Rhodes). So why didn't we nuke a forest like was planned, and then give the japanese the opprotunity to surrender? Just because we wanted to see the damage? (which is why hiroshima and nagasaki were targeted in the first place, (technically, hiroshima, Yokohama, Kyoto).
Why was the plan aborted? Foul weather?
Source:
https://www.answers.com/Q/What_was_the_primary_target_of_the_second_atomic_bomb
There seem to be some places of confusion in your understanding of the history.
The United States had one weapon ready for testing in July 1945. This was the Trinity test.
They had two more weapons ready by the end of the July which were shipped to Tinian. These were dropped on Hiroshima and Nagasaki.
The "third" bomb ready to use on Japan would not have been ready until August 17-18th or so. Truman halted the bombing before then.
Targeting a forest was never one of the "plans." There were some discussions as to whether to 'demonstrate' the bomb; those at the top of the Manhattan Project rejected it, on the assumption that a demonstration would never be as potent as "the real thing" and psychological potency was what was required with regards to Japan and even the entire world when it came to the atomic bomb.
The target list went through many changes in the spring and early summer of 1945. In mid-May 1945 the list of targets was Hiroshima, Yokohama, Kyoto, and Kokura. Yokohama was subject to a massive firebombing raid within days of that meeting, though; it was already slated for conventional destruction. Niigata was added in its place. Kyoto was removed at the behest of the Secretary of War, with Truman's assent, on the argument that it was not a valid military target (the military disagreed with this assessment). So that put Hiroshima as the #1 target, Kokura as the #2 target, Niigata as the #3 target, and — to fill Kyoto's place — Nagasaki as the #4 target.
However removing Kyoto also more or less removed Niigata for the short term, because Niigata was too far away from the other remaining targets for the mission to have a plausible "backup" target. So you have Hiroshima, Kokura, and Nagasaki as the likely targets, in that order of priority.
Weather conditions over Japan pushed the first use of the bomb from August 3rd to August 6th. This was the Hiroshima mission and it was executed flawless.
Weather conditions pushed the second use of the bomb up from August 10th to August 9th. This mission was not so flawless. The main target of Kokura was obscured by smoke, clouds, and/or steam (it is not really clear which, and could be all of the above), and visual targeting had been ordered. The plane went to the secondary target, Nagasaki. (Which was also obscured by clouds, and they most likely broke the visual targeting order to accomplish the bombing. The bomb was detonated significantly off-target.)
Atomic bombs were a very valuable weapon and at that time in short supply. The third bomb you mention could have been used rather quickly after the first two. After that it would be a quite long period before any new bomd could be produced because all available material for them had been used.
It would take several weeks before a 4th bomb could be produced. Thus it was considered a to valuable adset to "waiste" on a demonstration.
You have to place the bombs in their contect too. This was an all out war. Conventional bombing was already (even in single raids) killing more people than atomic bombs . The descicion makers simply had no time for the nicety of a "demonstration" .
On top it was feared that a demonstration would diminish the shock value of the weapon.