 attenuation curve.

\begin{figure*}
\epsscale{1.15}
\plotone{f6.pdf}
\caption{Best-fitting models to the composite spectra ({\em black}) in
  the blue ({\em top}) and red ({\em bottom}) bins of $\ebmv$.  The
  intrinsic template was modified by the IGM opacity appropriate for
  the mean redshift of objects contributing to the composites.  The
  fits were then obtained in three steps.  In the first, we found the
  value of $\ebmv$ that minimizes the differences between the model
  and composite spectra in the ``Composite $\ebmv$'' wavelength
  windows specified in Table~\ref{tab:waves}, assuming the updated
  \citet{reddy15} attenuation curve and a unity covering fraction of
  dust $f_{\rm cov}^{\rm red}=1$ (in this first step, $\hi$ and
    $\molh$ absorption are ignored).  These fits are indicated by the
  {\em cyan} and {\em orange} lines in the top and bottom panels,
  respectively.  For comparison, the fits obtained assuming the
  original \citet{reddy15} attenuation curve are shown by the {\em
    dark blue} and {\em magenta} lines in the top and bottom panels,
  respectively; these fits underestimate the continuum at $\lambda <
  1050$\,\AA.  In the second step, we simultaneously varied the column
  density $\nhi$ and covering fraction $f_{\rm cov}(\hi)$ of neutral
  hydrogen until the differences between the model and composite were
  minimized in the ``$\nhi$'' wavelength windows specified in
  Table~\ref{tab:waves}.  In the third and final step, we
  simultaneously varied the column density $\nmolh$ and covering
  fraction $f_{\rm cov}(\molh)$ of molecular hydrogen until the
  differences between the model and composite were minimized in the
  ``$\nmolh$'' wavelength windows specified in Table~\ref{tab:waves}.
  The final fits for the $\ebmv$ and combined $\hi$ and $\molh$
  absorption are indicated by the solid ({\em blue} and {\em red})
  lines in the top and bottom panels, respectively.  For clarity, the
  far-UV region blueward of Ly$\alpha$ is shown in the right panels. }
\label{fig:hih2fit}
\end{figure*}

In the next iteration of the spectral fitting, we accounted for
absorption by neutral hydrogen within the galaxies as follows.  We
added $\hi$ Lyman series absorption to the intrinsic template assuming
a Voigt profile with a Doppler parameter $b=125$\,km\,s$^{-1}$ and
varying column densities $\nhi$.  The wings of the line profile are
insensitive to the particular choice of $b$.  We also blueshifted the
$\hi$ absorption lines relative to the model by $300$\,km\,s$^{-1}$ to
provide the best match to the observed wavelengths of the lines in the
composite.  This blueshift is generally attributed to galactic-scale
outflows of gas seen in absorption against the background stellar
continuum.  The composite spectra were compared to the model spectra,
where the latter were computed as:
\begin{eqnarray}
m_{\rm final} & = & 10^{-0.4\ebmv k} \times \nonumber \\
& & [f_{\rm cov}(\hi) m(\hi) + (1-f_{\rm cov}(\hi))m],
\label{eq:hifit}
\end{eqnarray}
where $f_{\rm cov}(\hi)$ is the covering fraction of neutral hydrogen;
$m(\hi)$ and $m$ are the intrinsic templates with and without $\hi$
absorption, respectively; and $\ebmv$ is the value found above (from
the $\ebmv$ Only fitting).  Note that the reddening was applied to the
entire spectrum; i.e., $f_{\rm cov}^{\rm red} = 1$.  These final
models were computed for a range of $\nhi$ and $f_{\rm cov}(\hi)$ and
modified by the IGM opacity appropriate for the average redshift of
each composite.

The final models were compared to the composite spectra in the
``$\nhi$'' wavelength windows specified in Table~\ref{tab:waves} to
find the best-fitting combination of $\nhi$ and $f_{\rm cov}(\hi)$.
The wavelength windows were chosen to avoid regions of strong metal
line absorption (e.g., \ion{C}{3}\,$\lambda$977 and
\ion{C}{2}\,$\lambda$1036) and strong Ly$\alpha$ emission, and include
the core and as much of the wings of Ly$\beta$ and Ly$\gamma$, and the
wings of Ly$\alpha$, particularly the region between Ly$\alpha$ and
\ion{N}{5}\,$\lambda$1238.  The higher Lyman series lines (Ly$\delta$
and greater) were not used due to the larger random errors at these
wavelengths and because these lines begin to overlap.  The covering
fraction is constrained primarily by the depths of the lines, whereas
the column density is most sensitive to the wings.  The fitting
suggests column densities of $\lognhi\approx 20.8-21.3$ and covering
fractions of $f_{\rm cov}(\hi)\approx 0.70-0.78$ for the two bins of
$\ebmv$ (Figure~\ref{fig:hih2fit}).  By perturbing the composite
spectra and re-fitting the data many times, we estimated the
(measurement) errors in $\lognhi$ and $f_{\rm cov}(\hi)$ to be
$\sigma(\lognhi)\approx 0.20$\,dex and $\sigma(f_{\rm cov}(\hi))
\approx 0.01$.  The systematic error in $\lognhi$ from changing the
Doppler parameter by a factor of two from our assumed value is
$\sigma(\lognhi)\approx 0.10$\,dex.

Note that the values of $f_{\rm cov}(\hi)$ derived here are physically
meaningful only if the $\hi$ lines are optically thick {\em and} the
residual flux observed at the $\hi$ line cores is not an artifact of
limited spectral resolution, redshift imprecision, or foreground
contamination.  In the first case, a high $\nhi$ is required to
reproduce the damping wings of Ly$\alpha$, Ly$\beta$, and Ly$\gamma$,
implying optically thick gas.  In the second case, as shown in detail
in Reddy et~al. (2016b), redshift and spectral resolution
uncertainties are not sufficient to account for the residual flux seen
at the $\hi$ line centers.  Briefly, we executed simulations where we
added $\hi$ of varying column densities to the intrinsic spectrum,
replicated many versions of this $\hi$-absorbed spectrum with slightly
different redshifts based on the typical redshift uncertainty for
galaxies in our sample, smoothed these versions with various values of
the spectral resolution, and then produced a composite of all these
versions.  This exercise revealed that we would have had to
systematically underestimate the rest-frame spectral resolution by
more than $50\%$ in order to reproduce the amount of residual flux at
the $\hi$ line centers.  This $50\%$ is much larger than the rms
uncertainties in determining the spectral resolution from the widths
of night sky lines.  Lastly, we ruled out foreground contamination as
a source of the residual flux based on the exclusion of spectroscopic
blends from our sample and the fact that this flux inversely
correlates with reddening, a result that would not be expected if the
flux was dominated by foreground contaminants (see Reddy et~al. 2016b
for more discussion).  Thus, we conclude that the spectra can be
modeled with a partial covering fraction of optically thick $\hi$.

In the final iteration of the fitting, we included $\molh$
Lyman-Werner absorption in the models as follows:
\begin{eqnarray}
m_{\rm final} & = & 10^{-0.4\ebmv k} \times \nonumber \\
& & [(f_{\rm cov}(\hi)-f_{\rm cov}(\molh)) m(\hi) + \nonumber \\
& & f_{\rm cov}(\molh) m(\hi+\molh) + (1-f_{\rm cov}(\hi))m],
\end{eqnarray}
where $f_{\rm cov}(\molh)$ is the covering fraction of molecular
hydrogen, $m(\hi+\molh)$ is the model including both $\hi$ and $\molh$
absorption, and the remaining variables have the same definitions as
in