  We calculate the cycle class of the Hurwitz divisor $D_2$ on the moduli space
of stable curves of genus $g=2k$ given by the degree $k+1$ covers of the
projective line with simple ramification points, two of which lie in the same
fibre. We also study some aspects of the geometry of the natural map of the
Hurwitz space of admissible covers of degree $k+1$ and genus $2k$ to the moduli
space of stable curves of genus $2k$.
