  Verlinde bundles are vector bundles $V_k$ arising as the direct image
$\pi_*(\mathcal L^{\otimes k})$ of polarizations of a proper family of schemes
$\pi\colon \mathfrak X \to S$. We study the splitting behavior of Verlinde
bundles in the case where $\pi$ is the universal family $\mathfrak X \to
|\mathcal O(d)|$ of hypersurfaces of degree $d$ in $\mathbb P^n$ and calculate
the cohomology class of the locus of jumping lines of the Verlinde bundles
$V_{d+1}$ in the cases $n=2,3$.
