  We study double Hurwitz numbers in genus zero counting the number of covers
$\CP^1\to\CP^1$ with two branching points with a given branching behavior. By
the recent result due to Goulden, Jackson and Vakil, these numbers are
piecewise polynomials in the multiplicities of the preimages of the branching
points. We describe the partition of the parameter space into polynomiality
domains, called chambers, and provide an expression for the difference of two
such polynomials for two neighboring chambers. Besides, we provide an explicit
formula for the polynomial in a certain chamber called totally negative, which
enables us to calculate double Hurwitz numbers in any given chamber as the
polynomial for the totally negative chamber plus the sum of the differences
between the neighboring polynomials along a path connecting the totally
negative chamber with the given one.
