Why did Lockhart's spell stop at the arm?

Question

When Lockhart tried healing Harry's arm and ended up removing his bones, why did the spell only affect his arm? As bad as Lockhart is with magic, it's not impossible to imagine him turning Harry into a pool of skin soup with the wrong flick of the wrist, so what stopped the spell from dissolving Harry's entire skeleton?

“Stand back,” said Lockhart, who was rolling up his jade-green sleeves.
“No — don’t —” said Harry weakly, but Lockhart was twirling his wand and a second later had directed it straight at Harry’s arm.
A strange and unpleasant sensation started at Harry’s shoulder and spread all the way down to his fingertips. It felt as though his arm was being deflated. He didn’t dare look at what was happening. He had shut his eyes, his face turned away from his arm, but his worst fears were realized as the people above him gasped and Colin Creevey began clicking away madly. His arm didn’t hurt anymore — nor did it feel remotely like an arm.
“Ah,” said Lockhart. “Yes. Well, that can sometimes happen. But the point is, the bones are no longer broken. That’s the thing to bear in mind. So, Harry, just toddle up to the hospital wing — ah, Mr. Weasley, Miss Granger, would you escort him? — and Madam Pomfrey will be able to — er — tidy you up a bit.”
_{Harry Potter and the Chamber of Secrets, chapter 10}

Answer 1

Film Canon

"Brackium" means "arm" in (bad) Latin. "Emendo" means "to fix [a fault]" so Lockhart's spell was quite literally tasked with fixing Harry's arm, not his entire skeleton.

Obviously it didn't have quite the intended effect, but it was successful in dealing with the broken bone (e.g. by removing it entirely). Presumably had he broken his leg, Lockhart would have tried

"Crus emendo"

---

Book Canon

In the book, no specific spell is verbalised, but it's notable that Lockhart points his wand at Harry's arm.

‘No – don’t –’ said Harry weakly, but Lockhart was twirling his wand and a second later had directed it straight at Harry’s arm.
_{Harry Potter and the Chamber of Secrets, chapter 10}

One assumes that had the spell been directed elsewhere (such as at his head), it would have had a similar and potentially more dangerous effect.