  Deep inelastic scattering and its diffractive component, $ep \to
e^{\prime}\gamma^* p \to e^{\prime}XN$, have been studied at HERA with the ZEUS
detector using an integrated luminosity of 52.4 pb$^{-1}$. The $M_X$ method has
been used to extract the diffractive contribution. A wide range in the
centre-of-mass energy $W$ (37 -- 245 GeV), photon virtuality $Q^2$ (20 -- 450
GeV$^2$) and mass $M_X$ (0.28 -- 35 GeV) is covered. The diffractive cross
section for $2 < M_X < 15$ GeV rises strongly with $W$, the rise becoming
steeper as $Q^2$ increases. The data are also presented in terms of the
diffractive 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 $\xpom \to
0$, where $\xpom$ is the fraction of the proton momentum carried by the
Pomeron. For Bjorken-$x < 1 \cdot 10^{-3}$, $\xpom F^{\rm D(3)}_2$ shows
positive $\log Q^2$ scaling violations, while for $x \ge 5 \cdot 10^{-3}$
negative scaling violations are observed. The diffractive structure function is
compatible with being leading twist. The data show that Regge factorisation is
broken.
