  A projective variety whose Gauss map has positive dimensional fibres
corresponds to a special kind of scroll called \emph{Gaussian}. A Gaussian
scroll is a member of a canonical derived \emph{ Gaussian flag}. We introduce a
duality in the class of Gaussian scrolls and flags and study its consequences.
In particular, a Gaussian scroll is dual to the derived or tangent developable
scroll of a Gaussian scroll in the dual projective space, and is the 'leading
edge' or antiderived scroll of its derived stationary scroll.
