Online grammar's answer: There are numerous different rules around this; one based on sound, another on the number of syllables and the most amusing on the importance of the person — biblical and classical people don't need an extra 's' (Jesus' words, Achilles' words), but mere mortals such as Frances do (Frances's words).

The Australian Government style manual, Style Manual: For Authors, Editors and Printers (2002), comes down in favour of adding an extra 's' for all names — Jesus's words, Achilles' words and Frances's words.

I use the extra 's', but when I ask people in training courses if they do, I think the majority of people drop it off. I am not sure that it matters as long as you are consistent.

Grammar e-book and e-newsletter

If you found this tip useful, you might like to read more grammar tips, sign up for the e-newsletter and buy the grammar e-book.

Other punctuation grammar tips include:
apostrophes
colons
ellipses
em and en rules
hyphens