On Dangling Participles

They are grammatically ambiguous phrases that occur as the result of a writer modifying the wrong part (i.e. object, subject) of a sentence. 

Incorrect:

• After performing in the dance hall for years, the policeman finally asked the ballerina out.
• Having arrived late to school, a note was required.
• The audition was a failure, not having practiced their lines enough.

Revised:

• After performing in the dance hall for years, the ballerina was finally asked out by the policeman.
• Having arrived late to school, the student required a note.
• They failed the audition, not having practiced their lines enough.

(After changing colours in the fall, the leaves looked beautiful)