  We show how the real lines on a real del Pezzo surface of degree 1 can be
split into two species, elliptic and hyperbolic, via a certain distinguished,
intrinsically defined, Pin-structure on the real locus of the surface. We prove
that this splitting is invariant under real automorphisms and real deformations
of the surface, and that the difference between the total numbers of hyperbolic
and elliptic lines is always equal to 16.
