  We report measurements of the absorption strength of the cesium $6s \:
^2S_{1/2} \rightarrow 7p \: ^2P_{3/2} $ and the $6s \: ^2S_{1/2} \rightarrow 7p
\: ^2P_{1/2} $ transitions at $\lambda = 456$ nm and 459 nm, respectively, in
an atomic vapor cell. By simultaneously measuring the absorption strength on
the Cs D$_1$ line ($6s \: ^2S_{1/2} \rightarrow 6p \: ^2P_{1/2} $), for which
the electric dipole transition moment is precisely known, we are able to
determine the reduced dipole matrix elements for these two lines. We report
$\langle 7P_{3/2} || r || 6S_{1/2} \rangle = 0.5780 \: (7) \: a_0$ and $\langle
7P_{1/2} || r || 6S_{1/2} \rangle = 0.2789 \: (16) \: a_0$, with fractional
uncertainties of 0.12% and 0.6%, respectively. Through these measurements, we
can reduce the discrepancy between values of the tensor polarizability for the
Cs $6s \: ^2S_{1/2} \rightarrow 7s \: ^2S_{1/2} $ transition that have been
determined through two different methods.
