  Dilaton contact terms in the bosonic and heterotic strings are examined
following the recent work of Distler and Nelson on the bosonic and semirigid
strings. In the bosonic case dilaton two-point functions on the sphere are
calculated as a stepping stone to constructing a `good' coordinate family for
dilaton calculations on higher genus surfaces. It is found that dilaton-dilaton
contact terms are improperly normalized, suggesting that the interpretation of
the dilaton as the first variation of string coupling breaks down when other
dilatons are present. It seems likely that this can be attributed to the
tachyon divergence found in \TCCT. For the heterotic case, it is found that
there is no tachyon divergence and that the dilaton contact terms are properly
normalized. Thus, a dilaton equation analogous to the one in topological
gravity is derived and the interpretation of the dilaton as the string coupling
constant goes through.
