  In this paper we continue the investigation of coherent systems of type
$(n,d,k)$ on the projective line which are stable with respect to some value of
a parameter $\alpha$. We consider the case $k=1$ and study the variation of the
moduli spaces with $\alpha$. We determine inductively the first and last moduli
spaces and the flip loci, and give an explicit description for ranks 2 and 3.
We also determine the Hodge polynomials explicitly for ranks 2 and 3 and in
certain cases for arbitrary rank.
