  The Lyman-$\beta$ forest refers to a region in the spectra of distant quasars
that lies between the rest-frame Lyman-$\beta$ and Lyman-$\gamma$ emissions.
The forest in this region is dominated by a combination of absorption due to
resonant Ly$\alpha$ and Ly$\beta$ scattering. When considering the 1D Ly$\beta$
forest in addition to the 1D Ly$\alpha$ forest, the full statistical
description of the data requires four 1D power spectra: Ly$\alpha$ and
Ly$\beta$ auto-power spectra and the Ly$\alpha$-Ly$\beta$ real and imaginary
cross-power spectra. We describe how these can be measured using an optimal
quadratic estimator that naturally disentangles Ly$\alpha$ and Ly$\beta$
contributions. Using a sample of approximately 60,000 quasar sight-lines from
the BOSS Data Release 9, we make the measurement of the one-dimensional power
spectrum of fluctuations due to the Ly$\beta$ resonant scattering. While we
have not corrected our measurements for resolution damping of the power and
other systematic effects carefully enough to use them for cosmological
constraints, we can robustly conclude the following: i) Ly$\beta$ power
spectrum and Ly$\alpha$-Ly$\beta$ cross spectra are detected with high
statistical significance; ii) the cross-correlation coefficient is $\approx 1$
on large scales; iii) the Ly$\beta$ measurements are contaminated by the
associated OVI absorption, which is analogous to the SiIII contamination of the
Ly$\alpha$ forest. Measurements of the Ly$\beta$ forest will allow extension of
the usable path-length for the Ly$\alpha$ measurements while allowing a better
understanding of the physics of intergalactic medium and thus more robust
cosmological constraints.
