  The reaction e+p --> e+X is studied with the H1 detector at Hera. The data
cover momentum transfers Q^2 between 200 GeV^2 and 30,000 GeV^2 and correspond
to an integrated luminosity of 35.6 pb^(-1). The differential cross section
dsigma/dQ^2 is compared to the Standard Model expectation for neutral current
scattering and analysed to search for bar(e)e bar(q)q contact interactions. No
evidence for new phenomena is observed. The results are used to set limits on
scales within models of electron--quark compositeness, quark form factors and
the exchange of virtual heavy leptoquarks. A search for gravitational effects
mediated through the exchange of virtual gravitons which propagate into large
extra dimensions is presented.
