  The Riemann curvature correction to the type II supergravity at
eight-derivative level is given schematically as
$(t_8t_8+{1}{8}\eps_{10}\eps_{10})R^4$ at tree-level. The replacement of the
generalized Riemann curvature in $t_8t_8R^4$, proposed by Gross and Sloan,
produces various NS-NS couplings which are invariant under T-duality. Recently,
using the combination of S-duality and T-duality transformations on these
couplings, we have found groups of couplings which are invariant under the
S-duality transformation. In this paper, we have examined the couplings
involving the dilaton with direct scattering amplitude calculations of four
NS-NS vertex operators in the superstring theory and found exact agreement.
  The coupling $\eps_{10}\eps_{10}R^4$ is a total derivative term at four-field
level. The $\sigma$-model beta function approach implies the presence of this
term at the tree-level. By examining the sphere-level scattering amplitude of
five gravitons, we have also confirmed the presence of this term in the
tree-level effective action.
