  The fraction of ionizing photons that escape high-redshift galaxies
sensitively determines whether galaxies reionized the early universe. However,
this escape fraction cannot be measured from high-redshift galaxies because the
opacity of the intergalactic medium is large at high redshifts. Without methods
to indirectly measure the escape fraction of high-redshift galaxies, it is
unlikely that we will know what reionized the universe. Here, we analyze the
far-ultraviolet (UV) H I (Lyman series) and low-ionization metal absorption
lines of nine low-redshift, confirmed Lyman continuum emitting galaxies. We use
the H I covering fractions, column densities, and dust attenuations measured in
a companion paper to predict the escape fraction of ionizing photons. We find
good agreement between the predicted and observed Lyman continuum escape
fractions (within $1.4\sigma$) using both the H I and ISM absorption lines. The
ionizing photons escape through holes in the H I, but we show that dust
attenuation reduces the fraction of photons that escape galaxies. This means
that the average high-redshift galaxy likely emits more ionizing photons than
low-redshift galaxies. Two other indirect methods accurately predict the escape
fractions: the Ly$\alpha$ escape fraction and the optical [O III]/[O II] flux
ratio. We use these indirect methods to predict the escape fraction of a sample
of 21 galaxies with rest-frame UV spectra but without Lyman continuum
observations. Many of these galaxies have low escape fractions ($f_{\rm esc}
\le 1$\%), but 11 have escape fractions $>1$\%. The methods presented here will
measure the escape fractions of high-redshift galaxies, enabling future
telescopes to determine whether star-forming galaxies reionized the early
universe.
