  Two fields are Witt equivalent if, roughly speaking, they have the same
quadratic form theory. Formally, that is to say that their Witt rings of
symmetric bilinear forms are isomorphic. This equivalence is well understood
only in a few rather specific classes of fields. Two such classes, namely
function fields over global fields and function fields of curves over local
fields, were investigated by the authors in their earlier works. In the present
work, which can be viewed as a sequel to the earlier papers, we discuss the
previously obtained results in the specific case of function fields of conic
sections, and apply them to provide a few theorems of a somewhat quantitive
flavour shedding some light on the question of numbers of Witt non-equivalent
classes of such fields.
