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Frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) was utilized to make quantitative laboratory-based measurements of electric quadrupole transitions within the $\mathrm{<mrow\; data-mjx-texclass="ORD">16</mrow>}$O$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ $A$-band. We report the first observations of eight extremely weak (line intensities ranging from 3x$10-30$ to 2x$10-29$ cm molec.$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$) transitions within the $NO$, $PO$, and $RS$ branches. New theoretical calculations of line intensities and positions are also presented and compared to these measurements. \begin{wrapfigure}[9]{i}{10.5cm} \vspace{-0cm} \hspace*{-0cm} \epsfig{file=OSU_Quad_Abstract222.eps} \end{wrapfigure} $$ $\mathrm{Left}$: Measured spectrum (symbols) and Voigt fit (line) of electric quadrupole line in the wings of the $PQ$(11) hot band, magnetic dipole line. Peak signal-to-noise ratio on electric quadrupole line is 16:1. $\mathrm{Right}$: Fit-derived peak areas vs. number density for the $NO$ branch electric quadrupole lines.