Which of these possessive forms is correct? Why is one not correct? Moses's book or Moses' book  

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Surprisingly, this rule is fairly clear:  When a noun ends in an “s” the possessive is formed by placing the apostrophe outside the word: Moses’.  The confusion here probably comes from the pronunciation of the final syllable in Moses, “-es”, which is pronounced the same as many possessives:  hous: house’s, face: face’s, etc.   Under no condition is “Moses’s” a correct possessive form.  Often the confusion can be avoided by a slight change of wording: (“the words of Moses”).  Remembering that the possessive apostrophe is a written distinction, not a voiced one, may help.  The apostrophe as a signal of a contraction (didn’t, couldn’t, etc.) should not be confused with the apostrophe for signaling possession.

You will find that some nouns, especially proper nouns, especially when there are other -s and -z sounds involved, turn into clumsy beasts when you add another s ... you're better off with "Mrs. Chambers' estate."  (Guide to Grammar and Writing, Capital Community College)