  The universal order 1 invariant f^U of immersions of a closed orientable
surface into R^3, whose existence has been established in [N3], takes values in
the group G_U = K \oplus Z/2 \oplus Z/2 where K is a countably generated free
Abelian group. The projections of f^U to K and to the first and second Z/2
factors are denoted f^K, M, Q respectively. An explicit formula for the value
of Q on any embedding has been given in [N2].
  In the present work we give an explicit formula for the value of f^K on any
immersion, and for the value of M on any embedding.
