The whole story revolves around Tom's decision to climb out on the ledge to retrieve the document he had been working on. The author therefore takes great pains to make his action plausible. He devotes many paragraphs to explaining what is going on inside Tom's mind while he is still inside his apartment looking out the window, trying to decide whether to abandon the paper or climb out and get it. The fact that his wife had gone off to the movies and left him all alone is very important, because it is pretty obvious that she never would have let him climb out the window onto that ledge. Women have better sense than men.
The first paragraph in which he agonizes over what to do begins as follows:
It was hard for him to understand that he actually had to abandon it--it was ridiculous--and he began to curse.
The next paragraph begins as follows:
For many seconds he believed he was going to abandon the yellow sheet, that there was nothing else to do.
But in the next paragraph:
But just the same, and he couldn't escape the thought, this and other independent projects, some already done and others planned for the future, would gradually mark him out from the score of other young men in his company.
And in the next paragraph:
By a kind of instinct, he instantly began making his intention acceptable to himself by laughing at it. The mental picture of himself sliding along the ledge outside was absurd--it was actually comical--and he smiled.
And in the next paragraph he begins to talk himself into actually doing what he has imagined himself doing. The thought that convinces him to climb out the window eleven floors above the street is this:
It occurred to him that if this ledge and wall were only a yard above the ground--as he knelt at the window staring out, this thought was the final confirmation of his intention--he could move along the ledge indefinitely.
In other words, it was only the great height that presented a problem. Walking along the ledge would be easy as long as he didn't lose his nerve. And he believes he won't lose his nerve as long as he just doesn't look down. The author devotes five full paragraphs to having his character rationalize doing something that seems nearly suicidal once he is actually out on the ledge.
It isn't until he is outside hugging the wall with "his shoe soles shuffling and scraping along the rough stone" that he realizes that "the ledge was not quite as wide as he'd expected." The reader has identified with Tom and is out there on the ledge with him in imagination. The reader can feel the insecurity of Tom's position because the ledge is not even as wide as the length of his shoe. His heels are actually touching nothing but empty space. But after a few more steps both Tom and the reader have passed the point of no return. It would be just as dangerous to go back as to forward.
Then the situation gets even worse. He can't pick up the paper without looking down at it, and he can't look down at it without seeing a large part of Manhattan eleven floors below.
And a violent instantaneous explosion of absolute terror roared through him.
The author does an excellent job of making it plausible that his ambitious young character would climb out on the ledge of a high-rise building and risk his life for a piece of paper.