Q. In the sentence “The times, they are a changin’,” does the period come before or after the apostrophe? Logic would dictate after, but it does not look right aesthetically.
A. Logic wins in this case: The apostrophe is part of the word, not punctuation for the sentence, and therefore it must cleave to the word, ugly or not: changin’. (And note that we’ve added a comma to your original question—after the apostrophe.)