  In the following article we describe our measurement of the proton structure
function $F_2$ and of the gluon momentum density $xg$ in $ep$ collisions with
the ZEUS detector at HERA in 1993. The results for $F_2$ confirm our
measurement from the previous year but with much higher statistics and show a
strong rise towards small $x$. The gluon momentum density $xg$ is measured for
the first time in a range from $ 4 \cdot 10^{-4} < x < 10^{-2}$ at a value of
$Q^2 = 20$~GeV$^2$.
