As the father of three girls, I get to referee a lot of arguments. I also get to see a lot of misunderstandings and console a lot of hurt feelings.
Naturally, when one of my daughters hurts another, she's supposed to apologize. And naturally, around age 5 they start tossing off those useless apologies. You know, the quick "Sorry!" thrown over the shoulder as the apologizer goes off to do something more interesting; or the apology followed immediately by the same behavior that caused the problem in the first place; or the "I'm sorry you're so sensitive" non-apology.
In desperation, I did some thinking. (Funny, how it takes desperation before I start thinking. :-D) After much smoke from my ears, I finally came up with guidelines for what constitutes a proper apology. I taught them to my girls, although they don't always use them.
I recently got a bad apology at work. It was one of those "Sorry I'm calling you over to the lab for something this trivial" apologies, when the person doing the apologizing knew how to do the job, had the time to do the job, but didn't want to do the job. And we both knew darn well it would happen again the next time, too. That apology was a worthless as a plugged nickel. We'll see what happens if I get asked for input on that person's review.
So, some of us need a lesson in how to apologize. In the interest of enlightenment for all of civilization, I present the anatomy of an apology. If you really want to apologize, make it look like this.
Part 1: Explain what you're sorry for. This is more than just "I'm sorry", it's "I'm sorry I hurt you", or "I'm sorry to inconvenience you like this", or "I'm sorry I was loud while you were trying to sleep". Be specific, so I know which of your many transgressions I'm about to forgive.
Part 2: Briefly mention the circumstances. For instance, "It was an accident", or "I'm not trained in this area", or "I didn't realize you were asleep". I don't want an excuse: I'm not trying to judge your actions. I just need to know why it happened, so the next step makes sense.
Part 3: Explain what you're going to do so it won't happen again. That's right. You're apologizing, so you did something wrong, even if it was unintentional. Take this opportunity for self improvement, and make an effort to avoid having to apologize again.
If you can do those three things, you're guaranteed forgiveness. If you can't, then don't even bother apologizing to me: I know you don't care, I don't need you to pretend that you're interested.