In response to both Dave Bell and John Carmichael, I took the small mirror as fixed, and required it only to be flat and, of course, stable.  These are necessary conditions for any ceiling sundial.
 
My proposal does not require any knowledge of the actual alignment of the mirror.  John Carmichael is certainly correct in noting that very slight errors in placing transparencies and lasers would cause large errors on the ceiling.  That's life!
 
But uncertainty in the actual alignment of the mirror would not be a source of error.  Nor would an uneven, sloping or vaulted ceiling.
 
John Carmichael's final paragraph is dead right, but it would take months and still needs a reasonably flat ceiling.
 
John Lynes

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