This paper presents the first direct measurement of the $B$ meson differential cross section, $d\sigma/dp_T$, in $p\overline{p}$ collisions at $\sqrt{s}=1.8$ TeV using a sample of $19.3 \pm 0.7$ pb$~{-1}$ accumulated by the Collider Detector at Fermilab (CDF). The cross section is measured in the central rapidity region $|y| < 1$ for $p_T(B) > 6.0$ GeV/$c$ by fully reconstructing the $B$ meson decays $B~{+}\rightarrow J/\psi K~{+}$ and $B~{0}\rightarrow J/\psi K~{*0}(892)$, where $J/\psi \rightarrow \mu~+\mu~-$ and $K~{*0} \rightarrow K~+ \pi~-$. A comparison is made to the theoretical QCD prediction calculated at next-to-leading order.
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