As pointed out above the possessive apostrophe doe's not signify any missing letter's, and is merely a spelling convention to make things a bit more understandable. The greengrocer's apostrophe (bean's, pea's orange's) also seem's to be gaining wider usage, as in thi's post

The abbreviating apostrophe doe's indicate any number of missing letter's, and could formerly appear more than once in a word - Lewi's Carroll use's forms like sha'n't, where the first apostrophe represent's LL, and the second O. But that would nowaday's only be used by pedant's.