  We use the method of images to present a worldsheet derivation of the sphere
partition function for the dilaton in half-space to leading order in $\apr$
with Neumann boundary conditions. We use Tseytlin's sphere prescription to
obtain the total (bulk and boundary) off-shell classical bosonic string action
for the dilaton in half-space and show that it satisfies the requirement for a
well-defined variational principle
