Abstract
In part I we have studied a map of ”osculating elements” of an affine Cayley-Klein (CK-) plane into the Lie algebra A4(ɛ2) of the aequiform transformations A4(ɛ2) of the given plane A2(ℜ, ɛ2). If we use the real projective space P3(ℜ) over A4(ɛ2) each osculating element defines a straight line in P3(ℜ). We now give a one parameter motion in A4(ɛ2) and study second order properties and their analogon in the Lie algebra and P3(ℜ), respectively. We show that the wellknown relationship between the points of the moving frame and the osculating circles of the point paths in the fixed frame may be interpreted as part of a quadratic map Γ of certain straight Lines of P3(ℜ). An analogous result holds for the curvature of pairs of envelopes; the mapV induced in P3(ℜ) than is contained in a cubic relationship of straight lines.
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