A measurement is presented, using data taken with the H1 detector at HERA, of the contribution of diffractive interactions to deep-inelastic electron-proton (ep) scattering in the kinematic range 8.5 < Q2 < 50GeV2, 2.4 × 10-4 < Bjorken-x < 0.0133, and 3.7 × 10-4 < χp < 0.043. The diffractive contribution to the proton structure function F2(x,Q2) is evaluated as a function of the appropriate deep-inelastic scattering variables χp, Q2, β (= χ χp) using a class of deep-inelastic ep scattering events with no hadronic energy flow in an interval of pseudo-rapidity adjacent to the proton beam direction. the dependence of this contribution on χp is measured to be χp-n with n = 1.19 ± 0.06 (stat.) ± 0.07 (syst.) independent of β and Q2, which is consistent with both a diffractive interpretation and a factorisable ep diffractive cross section. A first measurement of the deep-inelastic structure of the pomeron in the form of the Q2 and β dependences of a factorised structure function is presented. For all measured β, this structure function is observed to be consistent with scale invariance. © 1995.