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Deep inelastic scattering and its diffractive component, $ep \toe^{\prime}\gamma^* p \to e^{\prime}XN$, have been studied at HERA with the ZEUSdetector using an integrated luminosity of 52.4 pb$^{-1}$. The $M_X$ method hasbeen used to extract the diffractive contribution. A wide range in thecentre-of-mass energy $W$ (37 -- 245 GeV), photon virtuality $Q^2$ (20 -- 450GeV$^2$) and mass $M_X$ (0.28 -- 35 GeV) is covered. The diffractive crosssection for $2 < M_X < 15$ GeV rises strongly with $W$, the rise becomingsteeper as $Q^2$ increases. The data are also presented in terms of thediffractive structure function, $F^{\rm D(3)}_2$, of the proton. For fixed$Q^2$ and fixed $M_X$, $\xpom F^{\rm D(3)}_2$ shows a strong rise as $\xpom \to0$, where $\xpom$ is the fraction of the proton momentum carried by thePomeron. For Bjorken-$x < 1 \cdot 10^{-3}$, $\xpom F^{\rm D(3)}_2$ showspositive $\log Q^2$ scaling violations, while for $x \ge 5 \cdot 10^{-3}$negative scaling violations are observed. The diffractive structure function iscompatible with being leading twist. The data show that Regge factorisation isbroken.

Deep inelastic inclusive and diffractive scattering at $Q^2$ values from 25 to 320 GeV$^2$ with the ZEUS forward plug calorimeter