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I've just dug out my copy of Fowler's Modern English Usage. The original rule was that if a word's origin had a Greek ending in -izo then it should be Z, if it was of a Latin or French origin then it is S. That said Fowler goes on to say that whilst the OED, OUP, Encyclopaedia Brit, The Times etc all prefer -ize. There are certain words that can only be spelled with -ise (advertise, devise, surprise etc) Fowler finishes off by saying "The difficulty in remembering which these -ise verbs are is in fact the only reason for making -ise universal, & the sacrifice of significance to ease does not seem just justified."
So pedants Z, and those of us who do not know their Greek can get away with S. By the way appetitus is Latin.