It is common knowledge that Yours sincerely is the phrase used to end a formal letter that is sent to a particular person. And Yours faithfully is used at the end of a formal letter beginning with "Dear Sir" or "Dear Madam".
What's the origin of the phrases and why are they used this way? Why isn't it the other way round, i.e. Yours sincerely for an unknown recipient and Yours faithfully for a particular person?